adapters: route pointer events by cell rect

A grid was the axes rect in device pixels, so dragging a window wide made the
image wider with it -- and the per-frame pass over it is O(cells): the fade
multiplies every cell, a host's ink()/peak() read every cell, and a frame the
fade moved converts and uploads every cell as one byte. At 2x device scale a
1520x850 window's axes rect is 2877 device pixels wide, so four rows of one
trace are 4.5 M cells and 4.9 MB uploaded a frame; measured headless on
llvmpipe with a 2 s window, 12.9 ms of tick and 12.8 ms of draw a frame, every
frame under a time fade -- a cost that follows the window and has no ceiling.

The grid is now the axes rect up to kDensityCellCap (2^18 cells, a mebibyte of
counts), scaled down uniformly past it so cells stay square and the picture
keeps the axes' aspect, and magnified back over the rect with a linear filter:
a cell is a count, so a fragment between two of them is between their two ink
levels, which a point sample cannot give once a cell is several pixels wide.
The same four rows at the cap are 1.05 M cells, 3.9 ms of tick and 5.6 ms of
draw and 1.0 MB uploaded, while a grid under the cap is untouched -- a 640x360
viewport's 573x313 axes is still 179 349 cells, one a device pixel.

The image's footprint is the axes rect rounded up to whole device pixels on
both sides of the pipe, so a grid under the cap keeps the exact
one-texel-a-pixel mapping it has always had (sx/sy come out exactly 1) and only
a capped grid reads its cell index through a scale. Moving the decay itself to
the GPU was considered and left out: the CPU grid is what ink()/peak() read,
what the deposit adds to and what the per-sweep dedupe keys on, so a GPU image
would have to be reconciled with it per frame -- a larger change than this
bound, and not one to half-do.

Tests: a_density_grid_is_capped_whatever_the_window reads the bound off a
3840x2160 viewport (261 504 cells of a 3784x2138 axes, aspect kept),
a_capped_density_is_magnified_over_the_axes_rect reads the screen side of it
(569x460 cells covering all 832 of the rect's columns), and the density cases
now assert their capped figures. 399 cases, 0 failed.

.gitignore

@@ -3,3 +3,15 @@ build/
 # Not this project's and not generated by it: a Solarus game-engine message that
 # happens to sit in the repo root.
 error.txt
+
+# An *in-tree* configure writes these beside the sources. `build/` above only covers the
+# directory the presets use, and `cmake -S . -B .` leaves the whole of CMake's output in the
+# repository root -- which then reads as an untracked submodule to whoever has it checked out.
+CMakeFiles/
+CMakeCache.txt
+cmake_install.cmake
+Makefile
+CTestTestfile.cmake
+CPackConfig.cmake
+# Configured from `include/plot/version.hpp.in`, so it is output and not a source file.
+include/plot/version.hpp

README.md

@@ -14,6 +14,12 @@ built on top of it.
 | Qt6 | `plot::qt6` | `adapters/qt6/` |
 | GTK4 | `plot::gtk4` | `adapters/gtk4/` |
 
+The GTK4 adapter exists for, and is exercised by, a real consumer: **udpscope**, an oscilloscope-style viewer
+for a UDPStreamer source, at <https://git.ferrarinas.it/martino/udpscope>. It embeds the core through
+`plot::gtk4`, and the library's interaction layer — cursors, measurement marks, the shading of a span a host
+has declared invalid — has been shaped by what that host needed. The notes in `src/`, `docs/` and `tests/`
+that say "in udpscope's case" are those places.
+
 The visible x range is mapped onto sample indices through the series' own x
 (`Series::neighbours()`, a binary search over the real stamps), never through the
 `(x - x0()) / dx()` grid: `dx()` is a *nominal* spacing, and a series whose x is a streamed
@@ -37,6 +43,35 @@ run touched a GPU, so read it as an upper bound and a record of the software pat
   window's worth, the scroll offset is bounded by `retained - span`, so a pan or a zoom-in near an
   edge cannot leave the window's own span over data the scope never had (a window *wider* than the
   data keeps the older placement -- right edge on the newest sample);
+- a trace whose gathered window is denser than the axis is reduced **onto the pixel grid** --
+  one snapped vertical segment per integer column, lit from that column's own extremes --
+  because an LOD envelope staged as a polyline puts three or four near-vertical hairlines per
+  column at as many sub-pixel phases, and the beat between the bucket pitch and the pixel pitch
+  is a crawling moiré; one segment per column leaves one phase, so there is nothing to beat
+  (`FrameStats::column_traces`, and `docs/data-and-performance.md` for the four rules it keeps);
+- and such a column can be drawn **graded by dwell** instead of as one flat band
+  (`Style::intensity_grading`, off by default, `FrameStats::graded_traces`): bright where the
+  signal sits, faint where it only passes through, the way a digital-phosphor scope reads. It is
+  what puts back the information the reduction throws away — a column's min and max are the same
+  whether its samples fill the span or pile at its two ends — so the gather is asked at a level
+  finer than the pixel grid and the distribution read from those sub-buckets. Below the density at
+  which columns are reduced the same switch grades the **polyline** by each segment's slope
+  (`FrameStats::slope_traces`), so the look does not change as a window narrows past the
+  threshold;
+- a **phosphor density** a host can turn on for a plot (`Plot::set_density()`, an image rather
+  than a set of retained traces): **one grid per trace**, in that trace's own colour, the axes
+  rect in device pixels, drawn *in place of* the traces -- a host may not also draw them over it --
+  into which each acquisition is deposited, 1.0 per cell a trace crosses, so brightness is how
+  often it passed. It fades either by a **time constant** in stream seconds or by a
+  **per-acquisition factor**, and the newest acquisition is deposited like every other, so it
+  fades too. The resolution is bounded (`kDensityCellCap`, 262 144 cells -- a mebibyte of counts --
+  a grid, past which the rect is scaled down uniformly and the image magnified back over it with a
+  linear filter), because the per-frame pass is `O(cells)` and the window is not bounded at all:
+  memory is the cap times the traces on screen times 4 bytes, whatever the window (a 640x360
+  viewport's axes is 179 349 cells per trace, 717 kB, under it, while four rows of one trace in a
+  3040x1700 one used to be 4.5 M cells and 18 MB between them). The deposit walks the axes'
+  columns rather than the samples, and a frame whose grids did not move costs one draw call per
+  trace (`FrameStats::density_cells`/`density_upload_bytes`); see `docs/data-and-performance.md`;
 - sample **markers** when a window is sparse enough that its samples are the shape
   (`Style::marker_below_samples`, 50 by default, `marker_px` across, in the trace's own colour);
 - grid with independent major/minor line classes (`Style::grid_major_visible`,
@@ -66,7 +101,10 @@ run touched a GPU, so read it as an upper bound and a record of the software pat
 - input parity across hosts: pinch-zoom and pan gestures on Qt6 and GTK4 drive the same
   controller paths as mouse and wheel (touch parity), with keyboard panning
   (arrow keys), Escape cancelling a drag or box-zoom, double-click re-fitting the axes,
-  and modifier-masked box zoom (Shift = both axes, Ctrl = x only, Alt = y only);
+  and modifier-masked box zoom (Shift = both axes, Ctrl = x only, Alt = y only), the area being
+  chosen framed as the drag runs -- a low-alpha fill under a light border, widened along the axis
+  the release will *not* zoom, so Ctrl's frame is the band it is about to apply rather than the
+  sliver a straight horizontal drag sweeps;
 - DPI-consistent sizing: metrics are logical units converted once through
   `Style::ui_scale`;
 - an anti-aliased embedded monospaced font, plus an optional runtime TrueType backend
@@ -172,12 +210,12 @@ documentation.
 ```sh
 cmake --preset linux-debug
 cmake --build build/debug
-ctest --test-dir build/debug --output-on-failure   # 350 cases, 0 failed
+ctest --test-dir build/debug --output-on-failure   # 396 cases, 0 failed
 
 tools/coverage.sh                                  # configure+build+run+capture+floor check
 ```
 
-The `linux-debug` suite runs **350 cases**; the `linux-coverage` preset builds **333** of
+The `linux-debug` suite runs **396 cases**; the `linux-coverage` preset builds **379** of
 them, because its adapters are off and 17 cases need an adapter target (11 in
 `test_imgui_widget.cpp`, 6 in `test_glfw_host.cpp`). Coverage is enforced by
 `tools/coverage.sh` against `tools/coverage_floor.py`: **80%** per file under `src/` and

adapters/glfw/glfw_host.cpp

@@ -455,9 +455,11 @@ void Host::set_figure(Figure* figure) noexcept {
     row_rects_.clear();  // no figure, no rows: the handlers fall back to `controller_`
     return;
   }
-  const u32 rows = figure_->row_count();
+  // One controller per **plot** (a row of several cells has one for each), indexed by the
-  row_controllers_.reserve(rows);
+  // flattened plot index the figure uses.
-  for (u32 i = 0; i < rows; ++i) {
+  const u32 plots = figure_->plot_count();
+  row_controllers_.reserve(plots);
+  for (u32 i = 0; i < plots; ++i) {
     row_controllers_.push_back(std::make_unique<input::Controller>(figure_->plot(i)));
   }
   // The new figure's rects go into the cache now, not at the next frame: an event
@@ -469,8 +471,10 @@ void Host::set_figure(Figure* figure) noexcept {
 
 void Host::refresh_row_rects() noexcept {
   // The one `Figure::layout()` per call: every event handler reads `row_rects_`
-  // instead of paying this again, which is the whole point of the cache (R7).
+  // instead of paying this again, which is the whole point of the cache (R7). The rects
-  row_rects_ = figure_ != nullptr ? figure_->layout().rows : std::vector<Rect>{};
+  // are the figure's **cells** (one per plot, flattened), which for a figure with one
+  // cell per row are exactly its row rects.
+  row_rects_ = figure_ != nullptr ? figure_->layout().cells : std::vector<Rect>{};
 }
 
 input::Controller* Host::row_controller(u32 row) noexcept {
@@ -486,8 +490,7 @@ input::Controller& Host::controller_at(f32 x, f32 y) noexcept {
   // frame stale, which is the documented worst case.
   const std::vector<Rect>& rows = row_rects_;
   if (rows.empty() || rows.size() != row_controllers_.size()) return controller_;
-  (void)x;  // the rows tile the figure vertically, so y alone picks one -- see row_in()
+  const u32 row = row_in(rows, x, y);
-  const u32 row = row_in(rows, y);
   last_row_ = row;
   input::Controller& controller = *row_controllers_[row];
   // The row's own viewport, so the geometry this controller hit-tests is the geometry
@@ -506,7 +509,6 @@ void Host::feed_pointer_event(const input::PointerEvent& e) noexcept {
 
 input::Controller& Host::pointer_target(f32 x, f32 y, input::Button button, bool pressed,
                                         bool released) noexcept {
-  (void)x;  // the rows tile the figure vertically, so y alone picks one -- see row_in()
   if (figure_ == nullptr || row_controllers_.empty()) return controller_;
   const std::vector<Rect>& rows = row_rects_;
   if (rows.empty() || rows.size() != row_controllers_.size()) return controller_;
@@ -523,7 +525,7 @@ input::Controller& Host::pointer_target(f32 x, f32 y, input::Button button, bool
     // drag, and its press must not steal the capture to the row it landed in.
     if (released && button == captured_button_) captured_ = false;
   } else {
-    row = row_in(rows, y);
+    row = row_in(rows, x, y);
     if (pressed) {
       captured_ = true;
       captured_row_ = row;
@@ -541,27 +543,29 @@ input::Controller& Host::pointer_target(f32 x, f32 y, input::Button button, bool
 
 u32 Host::pointer_row(const std::vector<Rect>& rows) noexcept {
   if (captured_ && captured_row_ < rows.size()) return captured_row_;
-  return row_in(rows, last_pointer_y_);
+  return row_in(rows, last_pointer_x_, last_pointer_y_);
 }
 
-u32 Host::row_in(const std::vector<Rect>& rows, f32 y) noexcept {
+u32 Host::row_in(const std::vector<Rect>& rows, f32 x, f32 y) noexcept {
   if (rows.empty()) return 0u;
-  // The row the pixel is in, or -- when it is in none of them, which is the row gap a
+  // The cell the pixel is in, or -- when it is in none of them, which is the row gap or
-  // host has asked for with `Figure::set_row_gap()` or the figure's own margins -- the
+  // column gap a host has asked for with `Figure::set_row_gap()`/`set_col_gap()` or the
-  // row whose rect is nearest. Selection by distance rather than by "the first that
+  // figure's own margins -- the cell whose rect is nearest (squared distance from the
-  // matches" is what makes a pixel in a gap belong to the row it is *near*: the rows
+  // pixel to the rect). Selection by distance rather than by "the first that matches" is
-  // tile the figure at the default gap of 0, so this is unreachable until a host asks
+  // what makes a pixel in a gap belong to the cell it is *near*, and a gesture in a
-  // for one, and a gesture in a visible gap must not be routed to row 0 by default.
+  // visible gap must not be routed to plot 0 by default. For a figure with one cell per
+  // row every cell spans the figure's width, so this reduces to the nearest row by y.
   u32 row = 0u;
   f32 best = std::numeric_limits<f32>::infinity();
   for (u32 i = 0; i < rows.size(); ++i) {
-    const f32 top = rows[i].y;
+    const Rect& r = rows[i];
-    const f32 bottom = rows[i].y + rows[i].h;
+    const f32 dx = x < r.x ? r.x - x : (x >= r.right() ? x - r.right() : 0.0f);
-    const f32 distance = y < top ? top - y : (y >= bottom ? y - bottom : 0.0f);
+    const f32 dy = y < r.y ? r.y - y : (y >= r.bottom() ? y - r.bottom() : 0.0f);
+    const f32 distance = dx * dx + dy * dy;
     if (distance < best) {
       best = distance;
       row = i;
-      if (distance == 0.0f) break;  // inside this row: nothing can be nearer
+      if (distance == 0.0f) break;  // inside this cell: nothing can be nearer
     }
   }
   return row;

adapters/glfw/glfw_host.hpp

@@ -121,18 +121,21 @@ class Host {
   /// `plot_` is then untouched by any of this.
   void set_figure(Figure* figure) noexcept;
   Figure* figure() noexcept { return figure_; }
-  /// One figure row's controller -- the one a gesture on that row reaches -- or
+  /// One figure plot's controller -- the one a gesture on that plot reaches -- or null
-  /// null while no figure is set or the row does not exist. A host reads a drag
+  /// while no figure is set or it does not exist. `row` is the **flattened plot index**
+  /// (`Figure::plot_count()` of them: the row count when no row holds several cells). A host reads a drag
   /// mode or a hover out of it (`controller()` is the single-plot loop's, and is
   /// not the one figure gestures go to).
   input::Controller* row_controller(u32 row) noexcept;
   /// The controller an event at framebuffer pixel (x, y) belongs to: `controller_` --
   /// the single-plot loop -- while no figure is set, and the controller of the figure
-  /// row that pixel lands in otherwise. The row rects come from the cache
+  /// plot (cell) that pixel lands in otherwise -- x and y both pick it, as a row may hold
+  /// several cells side by side. The cell rects come from the cache
   /// `refresh_row_rects()` fills -- the same ones the renderer draws -- so a gesture
   /// lands on the row it was aimed at and no event lays the figure out; a pixel
-  /// inside no row -- the row gap a host asked for with `Figure::set_row_gap()`,
+  /// inside no cell -- the row or column gap a host asked for with
-  /// or a margin -- is the *nearest* row rather than dropped or defaulted, so a drag
+  /// `Figure::set_row_gap()`/`set_col_gap()`, or a margin -- is the *nearest* cell rather than
+  /// dropped or defaulted, so a drag
   /// that leaves the data area still ends where it should.
   ///
   /// It also hands that row its own viewport, which is what keeps the controller's
@@ -217,11 +220,12 @@ class Host {
   void on_scroll(f64 dx, f64 dy) noexcept;
   void on_key(int key, int action, int mods) noexcept;
 
-  /// The index of the row of `rows` a framebuffer y belongs to: the row it is in, or the nearest
+  /// The index of the cell of `rows` (the figure's flattened cell rects) a framebuffer pixel
-  /// row when it is in none (a row gap, a margin outside the figure). One rule, shared by the event
+  /// belongs to: the cell it is in, or the nearest cell when it is in none (a row or column gap,
-  /// routing and the crosshair sync -- and taking the rects rather than reading them, so a caller
+  /// a margin outside the figure). One rule, shared by the event routing and the crosshair sync
-  /// that has just laid the figure out does not make it lay out again for this.
+  /// -- and taking the rects rather than reading them, so a caller that has just laid the figure
-  static u32 row_in(const std::vector<Rect>& rows, f32 y) noexcept;
+  /// out does not make it lay out again for this.
+  static u32 row_in(const std::vector<Rect>& rows, f32 x, f32 y) noexcept;
 
   /// The controller a pointer event at (x, y) belongs to, applying the button capture:
   /// a press claims the row it landed in (`captured_row_` + `captured_button_`) and
@@ -231,10 +235,10 @@ class Host {
   input::Controller& pointer_target(f32 x, f32 y, input::Button button, bool pressed,
                                     bool released) noexcept;
 
-  /// The row the pointer's events currently go to: the captured row while a drag owns
+  /// The plot (flattened index) the pointer's events currently go to: the captured one
-  /// the button, the row under the pointer otherwise. The run loop uses it to clear
+  /// while a drag owns the button, the one under the pointer otherwise. The run loop uses
-  /// every *other* row's hot handles, so a row the pointer left cannot keep drawing a
+  /// it to clear every *other* plot's hot handles, so one the pointer left cannot keep
-  /// hover or a grab it last published.
+  /// drawing a hover or a grab it last published.
   u32 pointer_row(const std::vector<Rect>& rows) noexcept;
 
   /// Spreads the hover over a whole `Figure` (spec §15).
@@ -292,7 +296,7 @@ class Host {
   u32 captured_row_ = 0u;
   input::Button captured_button_ = input::Button::Left;
 
-  /// The figure's row rects as of the last `refresh_row_rects()` -- the cache the
+  /// The figure's cell rects (one per plot, flattened; the row rects when no row is split) as of the last `refresh_row_rects()` -- the cache the
   /// event routing reads instead of laying the figure out per event (R7). Filled by
   /// `set_figure()` and once per frame by the run loop; empty while no figure is
   /// set, which is the state `controller_at()`/`pointer_target()` fall back to the

adapters/gtk4/gtk_plot_area.cpp

@@ -245,9 +245,11 @@ void PlotArea::set_figure(Figure* figure) noexcept {
     row_rects_.clear();  // no figure, no rows: the routing falls back to `controller_`
     return;
   }
-  const u32 rows = figure_->row_count();
+  // One controller per **plot** (a row of several cells has one for each), indexed by the
-  row_controllers_.reserve(rows);
+  // flattened plot index the figure uses.
-  for (u32 i = 0; i < rows; ++i) {
+  const u32 plots = figure_->plot_count();
+  row_controllers_.reserve(plots);
+  for (u32 i = 0; i < plots; ++i) {
     row_controllers_.push_back(std::make_unique<input::Controller>(figure_->plot(i)));
   }
   // The new figure's geometry goes into the cache now, not at the next frame: an event
@@ -269,8 +271,10 @@ void PlotArea::lay_figure_out(Rect px) noexcept {
 
 void PlotArea::refresh_row_rects() noexcept {
   // The one `Figure::layout()` per call: every event handler reads `row_rects_`
-  // instead of paying this again, which is the whole point of the cache.
+  // instead of paying this again, which is the whole point of the cache. The rects are
-  row_rects_ = figure_ != nullptr ? figure_->layout().rows : std::vector<Rect>{};
+  // the figure's **cells** (one per plot, flattened), which for a figure with one cell
+  // per row are exactly its row rects.
+  row_rects_ = figure_ != nullptr ? figure_->layout().cells : std::vector<Rect>{};
 }
 
 input::Controller* PlotArea::row_controller(u32 row) noexcept {
@@ -283,8 +287,7 @@ input::Controller& PlotArea::controller_at(f32 x, f32 y) noexcept {
   // -- and not a fresh `Figure::layout()`: an event pays no layout, or a burst of
   // pointer motion over a multi-row figure would re-lay every row out per move.
   if (row_rects_.empty() || row_rects_.size() != row_controllers_.size()) return controller_;
-  (void)x;  // the rows tile the figure vertically, so y alone picks one -- see row_in()
+  const u32 row = row_in(row_rects_, x, y);
-  const u32 row = row_in(row_rects_, y);
   input::Controller& controller = *row_controllers_[row];
   controller.set_viewport(row_rects_[row]);
   return controller;
@@ -292,11 +295,11 @@ input::Controller& PlotArea::controller_at(f32 x, f32 y) noexcept {
 
 u32 PlotArea::row_at(double x, double y) const noexcept {
   if (figure_ == nullptr || row_rects_.empty()) return 0;
-  (void)x;
+  const Vec2 p = to_device(x, y);
-  return row_in(row_rects_, to_device(x, y).y);
+  return row_in(row_rects_, p.x, p.y);
 }
 
-input::Controller& PlotArea::target_controller(f32 y) noexcept {
+input::Controller& PlotArea::target_controller(f32 x, f32 y) noexcept {
   if (figure_ == nullptr || row_controllers_.empty()) return controller_;
   if (row_rects_.empty() || row_rects_.size() != row_controllers_.size()) return controller_;
   // The capture: while a press is open the gesture belongs to the row that press
@@ -304,7 +307,7 @@ input::Controller& PlotArea::target_controller(f32 y) noexcept {
   // the release to the row the pointer is over *now* would leave the first row's drag
   // open for ever -- its controller never sees the release that ends it -- and let a
   // later gesture resume it from the stale anchor.
-  u32 row = press_open_ ? press_row_ : row_in(row_rects_, y);
+  u32 row = press_open_ ? press_row_ : row_in(row_rects_, x, y);
   // Re-read against this frame's rects: the widget can be resized mid-drag, and the
   // guard keeps a stale index from reaching past the controller list.
   if (row >= row_controllers_.size()) row = 0;
@@ -314,23 +317,25 @@ input::Controller& PlotArea::target_controller(f32 y) noexcept {
   return controller;
 }
 
-u32 PlotArea::row_in(const std::vector<Rect>& rows, f32 y) noexcept {
+u32 PlotArea::row_in(const std::vector<Rect>& rows, f32 x, f32 y) noexcept {
   if (rows.empty()) return 0;
-  // The row the pixel is in, or -- when it is in none of them, which is the row gap a
+  // The cell the pixel is in, or -- when it is in none of them, which is the row or
-  // host asked for with `Figure::set_row_gap()` or the figure's own margins -- the row
+  // column gap a host asked for with `Figure::set_row_gap()`/`set_col_gap()` or the
-  // whose rect is nearest. By distance rather than by "the first that matches": the
+  // figure's own margins -- the cell whose rect is nearest (squared distance from the
-  // rows tile the figure at the default gap of 0, so this is unreachable until a host
+  // pixel to the rect). By distance rather than by "the first that matches": a gesture
-  // asks for a gap, and a gesture in a visible gap must not default to row 0.
+  // in a visible gap must not default to plot 0. For a figure with one cell per row
+  // every cell spans the figure's width, so this reduces to the nearest row by y.
   u32 row = 0;
   f32 best = std::numeric_limits<f32>::infinity();
   for (u32 i = 0; i < rows.size(); ++i) {
-    const f32 top = rows[i].y;
+    const Rect& r = rows[i];
-    const f32 bottom = rows[i].y + rows[i].h;
+    const f32 dx = x < r.x ? r.x - x : (x >= r.right() ? x - r.right() : 0.0f);
-    const f32 distance = y < top ? top - y : (y >= bottom ? y - bottom : 0.0f);
+    const f32 dy = y < r.y ? r.y - y : (y >= r.bottom() ? y - r.bottom() : 0.0f);
+    const f32 distance = dx * dx + dy * dy;
     if (distance < best) {
       best = distance;
       row = i;
-      if (distance == 0.0f) break;  // inside this row: nothing can be nearer
+      if (distance == 0.0f) break;  // inside this cell: nothing can be nearer
     }
   }
   return row;
@@ -341,7 +346,22 @@ u32 PlotArea::pointer_row() const noexcept {
   // The captured row while a press owns the gesture, so an in-flight drag keeps its
   // highlight even after the pointer has left the row it began in.
   if (press_open_ && press_row_ < row_rects_.size()) return press_row_;
-  return row_in(row_rects_, pointer_.y);
+  return row_in(row_rects_, pointer_.x, pointer_.y);
+}
+
+void PlotArea::sync_selection_frames() noexcept {
+  const auto frame_for = [](input::Controller& c) -> Rect {
+    return c.drag_mode() == input::DragMode::BoxZoom ? c.selection_preview() : Rect{};
+  };
+  if (figure_ != nullptr) {
+    for (u32 i = 0; i < row_controllers_.size(); ++i) {
+      // An empty rect on the rows that are not choosing: `Rect` has no equality to compare
+      // with, and a store of the same value is what keeps this path free of anything else.
+      figure_->plot(i).set_selection_rect(frame_for(*row_controllers_[i]));
+    }
+    return;
+  }
+  plot_->set_selection_rect(frame_for(controller_));
 }
 
 void PlotArea::sync_figure_crosshair() noexcept {
@@ -534,6 +554,9 @@ void PlotArea::render() noexcept {
   // `::resize` ratio, not `gtk_widget_get_scale_factor()` -- the latter is the
   // ceiling under fractional scaling and would over-scale the chrome by up to 60%.
   renderer_->style().ui_scale = mapping_.factor;
+  // After the scale and before the draw: the preview reads the row's layout, and a layout measured
+  // with the previous frame's scale is not the one being drawn.
+  sync_selection_frames();
   renderer_->begin_frame(static_cast<u32>(viewport.w), static_cast<u32>(viewport.h), viewport);
   if (figure_ != nullptr) {
     renderer_->draw(*figure_);
@@ -598,7 +621,7 @@ void PlotArea::pointer_press(input::Button button, u32 mods, double x, double y,
   // The figure row this gesture belongs to for its whole life, claimed from the press's
   // own position *before* the event is dispatched (see `target_controller()`). Harmless
   // and unread while no figure is set.
-  press_row_ = figure_ != nullptr ? row_in(row_rects_, p.y) : 0;
+  press_row_ = figure_ != nullptr ? row_in(row_rects_, p.x, p.y) : 0;
   press_open_ = true;
   press_button_ = button;
   press_mods_ = mods;
@@ -616,7 +639,7 @@ void PlotArea::pointer_press(input::Button button, u32 mods, double x, double y,
   e.down = true;
   e.pressed = true;
   e.time_s = pointer_time_s(time_ms);  // the double-click detector differences these
-  target_controller(p.y).on_pointer(e);
+  target_controller(p.x, p.y).on_pointer(e);
   gtk_gl_area_queue_render(GTK_GL_AREA(widget_));
 }
 
@@ -625,7 +648,7 @@ void PlotArea::pointer_release(Vec2 position, u32 time_ms) noexcept {
   // Resolved while the press is still open, so the release reaches the row the press
   // claimed rather than the row the pointer ended over -- the controller that owns the
   // drag is the only one that can close it.
-  input::Controller& target = target_controller(position.y);
+  input::Controller& target = target_controller(position.x, position.y);
   press_open_ = false;
 
   input::PointerEvent e;
@@ -730,7 +753,7 @@ void PlotArea::on_drag_update(GtkGestureDrag* gesture, double offset_x, double o
       gtk_event_controller_get_current_event_time(GTK_EVENT_CONTROLLER(gesture)));
   // The press's row, not the row the pointer has reached: `press_open_` is true here,
   // so a drag that crosses a row boundary stays with the controller that began it.
-  area->target_controller(sample.position.y).on_pointer(e);
+  area->target_controller(sample.position.x, sample.position.y).on_pointer(e);
   gtk_gl_area_queue_render(GTK_GL_AREA(area->widget_));
 }
 
@@ -777,7 +800,7 @@ void PlotArea::on_zoom_scale_changed(GtkGestureZoom* gesture, double scale,
       static_cast<f32>(scale), Vec2{static_cast<f32>(cx), static_cast<f32>(cy)}, area->mapping_);
   // The folded event carries the focal point, which is the position this pinch belongs
   // to; while a press is open the capture overrides it, as it does for a drag.
-  area->target_controller(g.y).on_gesture(g);
+  area->target_controller(g.x, g.y).on_gesture(g);
   gtk_gl_area_queue_render(GTK_GL_AREA(area->widget_));
 }
 
@@ -816,7 +839,7 @@ int PlotArea::on_scroll(GtkEventControllerScroll* scroll, double dx, double dy,
   e.dx = static_cast<f32>(scroll_notches(dx, unit));
   e.dy = static_cast<f32>(notches);
   e.mods = gesture_mods(GTK_EVENT_CONTROLLER(scroll));
-  area->target_controller(at.y).on_wheel(e);
+  area->target_controller(at.x, at.y).on_wheel(e);
   gtk_gl_area_queue_render(GTK_GL_AREA(area->widget_));
   return TRUE;  // consumed: the plot zoomed
 }
@@ -840,7 +863,7 @@ void PlotArea::on_motion(GtkEventControllerMotion* motion, double x, double y, v
   e.down = false;
   e.time_s = PlotArea::pointer_time_s(
       gtk_event_controller_get_current_event_time(GTK_EVENT_CONTROLLER(motion)));
-  area->target_controller(p.y).on_pointer(e);
+  area->target_controller(p.x, p.y).on_pointer(e);
 }
 
 // --- keyboard -------------------------------------------------------------

adapters/gtk4/gtk_plot_area.hpp

@@ -260,15 +260,17 @@ class PlotArea {
   Figure* figure() noexcept { return figure_; }
   const Figure* figure() const noexcept { return figure_; }
 
-  /// One figure row's controller -- the one a gesture on that row reaches -- or null
+  /// One figure plot's controller -- the one a gesture on that plot reaches -- or null
-  /// while no figure is set or the row does not exist. A host reads a drag mode or a
+  /// while no figure is set or it does not exist. `row` is the **flattened plot index**
+  /// (`Figure::plot_count()` of them: the row count when no row holds several cells). A host reads a drag mode or a
   /// hover out of it.
   input::Controller* row_controller(u32 row) noexcept;
 
   /// The controller an event at device pixel `(x, y)` belongs to: `controller()`
-  /// while no figure is set, and otherwise the controller of the figure row that
+  /// while no figure is set, and otherwise the controller of the figure plot (cell)
-  /// pixel lands in -- a pixel inside no row (a `Figure::set_row_gap()` gap, a
+  /// that pixel lands in -- x and y both pick it, as a row may hold several cells side
-  /// margin) is the *nearest* row rather than dropped, so a drag that leaves the data
+  /// by side. A pixel inside no cell (a `Figure::set_row_gap()`/`set_col_gap()` gap, a
+  /// margin) is the *nearest* cell rather than dropped, so a drag that leaves the data
   /// area still ends where it should. It also hands that row its own viewport, which
   /// is what keeps the controller's hit-test geometry in step with the layout between
   /// two frames.
@@ -277,10 +279,10 @@ class PlotArea {
   /// press capture, so a host may call it freely.
   input::Controller& controller_at(f32 x, f32 y) noexcept;
 
-  /// The figure row a point in the widget's **logical** coordinates lands in -- the
+  /// The flattened plot index a point in the widget's **logical** coordinates lands in -- the
   /// coordinates every GTK event controller reports, so a host's own drop target or
-  /// context menu can name the row a pointer is over without converting anything. The
+  /// context menu can name the plot a pointer is over without converting anything. The
-  /// same nearest-row rule as `controller_at()`, and 0 while no figure is set.
+  /// same nearest-cell rule (x and y) as `controller_at()`, and 0 while no figure is set.
   u32 row_at(double x, double y) const noexcept;
 
   /// Re-reads the figure's row rects into the cache the event routing answers from --
@@ -376,20 +378,21 @@ class PlotArea {
   /// into device pixels. The one place that mapping exists.
   Vec2 to_device(double x, double y) const noexcept;
 
-  /// The controller one event of this area's goes to, given the event's device y.
+  /// The controller one event of this area's goes to, given the event's device (x, y).
   /// `controller_` while no figure is set; otherwise the row the gesture *belongs*
   /// to: the row the open press claimed while a press is open, and the row under `y`
-  /// between gestures. That is the capture `controller_at()` deliberately omits, and
+  /// between gestures (x and y pick the cell). That is the capture `controller_at()` deliberately omits, and
   /// it is why this -- not `controller_at()` -- is what every handler below calls.
   ///
   /// Hands the chosen row its own viewport, so the geometry it hit-tests is the
   /// geometry the last frame drew.
-  input::Controller& target_controller(f32 y) noexcept;
+  input::Controller& target_controller(f32 x, f32 y) noexcept;
-  /// The row of `row_rects_` a device y belongs to: the row it is in, or the nearest
+  /// The cell of `row_rects_` (the figure's flattened cell rects) a device pixel belongs
-  /// one when it is in none (a row gap, a margin outside the figure). Selection by
+  /// to: the cell it is in, or the nearest one when it is in none (a row or column gap,
-  /// distance rather than "the first that matches" is what makes a pixel in a visible
+  /// a margin outside the figure). Selection by distance rather than "the first that
-  /// gap belong to the row it is *near* instead of to row 0.
+  /// matches" is what makes a pixel in a visible gap belong to the cell it is *near*
-  static u32 row_in(const std::vector<Rect>& rows, f32 y) noexcept;
+  /// instead of to plot 0.
+  static u32 row_in(const std::vector<Rect>& rows, f32 x, f32 y) noexcept;
   /// The row this area's events currently go to: the press's row while one is open,
   /// so an in-flight gesture keeps its highlight, and the row under the last pointer
   /// position otherwise. 0 with no rows.
@@ -397,6 +400,17 @@ class PlotArea {
   /// Spreads one row's crosshair over the whole figure (see "Figure mode"). Run once
   /// per frame, from the render callback, after this frame's row rects are cached.
   void sync_figure_crosshair() noexcept;
+  /// Hands each row's plot the box-zoom frame its controller is showing, or takes it off
+  /// the ones whose gesture is over. Run once per frame from the render callback, like
+  /// the crosshair's spread and for a related reason: a frame has to go away when a drag
+  /// ends by *any* route -- the release, Escape, a row rebuilt mid-gesture -- and a
+  /// per-event hook would have to be repeated at every one of them, which is how a frame
+  /// ends up stuck on screen after a cancelled zoom.
+  ///
+  /// Reads `selection_preview()`, which needs the row's layout, only for a controller
+  /// actually in `BoxZoom`: the cost is paid while a range is being chosen and never
+  /// otherwise.
+  void sync_selection_frames() noexcept;
   /// `figure_->set_viewport(px)`, one `layout()` into the rect cache, and each row's
   /// own rect to its controller. The figure-mode half of `refresh_viewport()` and of
   /// `render()`, which must not drift apart.
@@ -446,7 +460,8 @@ class PlotArea {
   /// `set_figure()` is called, and the single-plot path reads neither.
   Figure* figure_ = nullptr;
   std::vector<std::unique_ptr<input::Controller>> row_controllers_;
-  /// The figure's row rects as of the last `refresh_row_rects()`: the cache the event
+  /// The figure's cell rects (one per plot, flattened; the row rects when no row is split)
+  /// as of the last `refresh_row_rects()`: the cache the event
   /// routing reads instead of laying the figure out per event. Empty while no figure
   /// is set, which is the state the routing falls back to `controller_` on.
   std::vector<Rect> row_rects_;

docs/building-and-testing.md

@@ -41,11 +41,18 @@ ctest --test-dir build/debug --output-on-failure
 
 ctest registers four tests: `plot_tests` (the test binary), the two header/umbrella build
 checks (`plot_headers_self_contained`, `plot_umbrella_covers_public_headers`) and
-`plot_umbrella_check`. The `plot_tests` binary itself runs **350 cases** in the `linux-debug`
+`plot_umbrella_check`. The `plot_tests` binary itself runs **396 cases** in the `linux-debug`
-preset; its harness prints one line per case and a final `350 cases, 0 failed` summary line.
+preset; its harness prints one line per case and a final `396 cases, 0 failed` summary line.
 The case counts per file are the `PLOT_TEST(...)` declarations under `tests/` — recount them
 (`grep -c '^PLOT_TEST(' tests/test_*.cpp`) after adding or removing cases.
 
+`PLOT_TEST_FILTER=<substring>` runs only the cases whose name contains that substring, and
+is for working *on* a case rather than for checking the library: most of the render cases
+create their own EGL context and read pixels back, so the whole binary is far slower than
+the one case being edited and its one line of measured output scrolls past 376 others. The
+summary line still counts the whole suite, so a filtered run says `396 cases, 0 failed`
+having run one — it is never evidence that the suite passes. Unset, every case runs.
+
 ## Install layout
 
 `cmake --install` follows `GNUInstallDirs`, so every path honours the standard cache
@@ -119,7 +126,7 @@ per-file table and the floor verdict live in [docs/coverage.md](coverage.md), wh
 `tools/coverage.sh` rewrites from the very run that measured them. Re-run the command for the
 live numbers.
 
-**One thing to know about the coverage preset:** it builds **333 of the 350 cases**. The 17
+**One thing to know about the coverage preset:** it builds **379 of the 396 cases**. The 17
 that are missing are the adapter cases that need an adapter target to exist — 11 in
 `test_imgui_widget.cpp` and 6 in `test_glfw_host.cpp` — and the coverage preset turns the
 adapters off. The toolkit-free adapter seams still run there: `test_qt_pointer.cpp` (5 cases)

docs/data-and-performance.md

@@ -166,6 +166,277 @@ series therefore stages O(visible pixels) vertices, not O(samples), and `FrameSt
 which path each trace took. Below the threshold the raw samples are drawn instead; both
 sides go through the same instanced anti-aliased quad pipeline.
 
+## Dense traces are reduced onto the pixel grid
+
+A gathered window denser than the axis is **not** staged as a polyline. For each integer
+column of `layout.axes`, `Renderer::draw_traces` emits one exactly vertical segment from the
+lowest to the highest screen y any gathered point put in that column, flushed in framebuffer
+pixels with `u_snap` on. `FrameStats::column_traces` counts the traces that took this path.
+
+It exists because a polyline over such a window **moirés**, and three things compound to make
+it. `MinMaxPyramid::level_for()` picks the level whose buckets hold about
+`samples_per_pixel` samples, so a bucket spans **one to two pixel columns**;
+`GatherMode::Envelope` emits two points per bucket, so each bucket contributes a near-vertical
+min→max hairline *and* a near-vertical connector to the next — about 3.6 near-vertical
+hairlines per column; and each of those lands at a **fractional** x, so with ordinary
+src-alpha compositing a column's brightness is a non-linear function of the sub-pixel phases
+overlapping it. The phase pattern repeats at the beat between the bucket pitch and the pixel
+pitch, which is a visible banding, and panning sweeps the beat so it crawls. Reducing to one
+segment per column leaves the trace **one** sub-pixel phase, so there is nothing left to beat,
+and the snap then puts that one phase on the grid.
+
+Four properties of the reduction are load-bearing:
+
+- **It is gated on the gathered *density*, not on the level.** It runs when the window is
+  `GatherMode::Envelope` and carries at least two gathered points per column of the axes —
+  the raw path at 1.5–64 samples per pixel has the same beat and the same cure. The density
+  term is also what keeps it away from a *sparse* window, whose trace is drawn by the two
+  segments that enter and leave the frame (`a_sparse_window_between_samples_still_inks_both_margins`);
+  `Nearest` and `Mean` are excluded because they are one-point-per-bucket modes a band defeats.
+- **A hole stays a hole.** A column no gathered point landed in emits nothing. Bridging it
+  would draw a vertical line over x the series says nothing about.
+- **Disjoint columns are joined.** Two neighbouring columns' extremes need not overlap — a
+  fast edge rises through a whole column — and two disjoint vertical segments read as a broken
+  trace, which is what the polyline's connector prevented. The later column is extended to
+  meet the earlier one's nearest bound, so the join is made inside the column that moved.
+- **A span shorter than the stroke is drawn *as* the stroke.** The line fragment shader ramps
+  on the distance to the segment's axis and does not cap its ends, so a vertical segment
+  shorter than its own width rasterises a sliver of itself, and a flat trace's column, where
+  the two bounds are equal, nothing at all.
+
+This is the **one carve-out** in `u_snap`'s rule that chrome may be snapped and data may not
+(see `LineProgram::set_snap()`): a column *is* a pixel column and its x is already a screen
+coordinate, so there is no data position to move it off, and the y bounds the segment reports
+are untouched by the snap.
+
+`a_dense_trace_is_drawn_as_whole_pixel_columns` is the guard, and what it measures is the
+**number of distinct coverage levels** in the ink: 4 with the reduction against 126 with the
+polyline, over one sine period across 60 000 samples. A count of *partially covered pixels* is
+**not** the reading and was tried first — a 1.5 px stroke with a 1 px anti-aliasing fringe
+always spills into its neighbour column, so the two renderings measure 577 and 652, which
+separates nothing. The frame's whole geometry collapses with it: 627 segments against 60 054.
+
+## A reduced column can be graded by dwell
+
+`Style::intensity_grading` draws each of those columns **graded** rather than as one flat band:
+bright where the signal sits, faint where it only passes through, the way a digital-phosphor
+scope reads. It is off by default — a change of look, not a correction of one — and
+`FrameStats::graded_traces` counts the traces that took it, a subset of `column_traces`, since
+grading is a way of drawing the reduction and not a third path.
+
+What it puts back is the information the reduction throws away: a column's min and max are the
+**same** whether its samples fill the span evenly or pile at its two ends, so a ramp and a pulse
+are one band. The distribution cannot be recovered from the band, which is why the gather is
+asked at a level **finer than the pixel grid** (`intensity_sub_columns` sub-buckets per column)
+and the dwell read from those sub-buckets.
+
+Five things carry it, and each was arrived at by being wrong first:
+
+- **The measure is dwell per row, each segment depositing one unit spread over the rows it
+  spans** (`1 / height`). Counting +1 per row instead grades a sine's fast middle as brightly as
+  its rails, which is the pattern inverted — the middle is where the signal spends the *least*
+  time.
+- **The accumulator is one column wide.** Gathered x is monotonic, so points arrive column by
+  column: accumulate, read, clear. A full `axes.w × axes.h` density image is 33 MB at 4K; one
+  column of `axes.h` floats is L1-resident. A span is written as a `+1/height` delta at its first
+  row and the negation one past its last, so it costs two writes whatever its height, and the
+  running sum over the column is the per-row dwell.
+- **Normalisation is per column, against the column's own peak.** A frame-wide scale needs the
+  whole image to exist before anything can be drawn, *and* reads worse: a column the signal flew
+  through uniformly comes out faint at every row, so the trace fades out exactly where it moves
+  fastest. The cost of the local scale is one extra non-clearing walk of the accumulator to find
+  the peak.
+- **Alpha is quantised into `intensity_steps` tiers, one `LineBatch` and one draw call each.**
+  The line pipeline's colour is a **uniform**, not per-instance (`LineInstance` is four floats of
+  geometry; only `TextInstance` carries `a_colour`), so a per-segment alpha is inexpressible and
+  the tiers are what make the gradient drawable at all. `intensity_floor` keeps the faintest tier
+  visible — a fast riser is one sub-bucket deep everywhere and must not be dimmed out of
+  existence — and `intensity_gamma` lifts the faint end. The floor only holds if the riser's rows
+  **reach** a tier: the "lit at all" cutoff that discards a column's empty rows is
+  `min(0.01 × peak, 0.5 × w_min)` over the smallest deposit any of that column's own segments
+  made, and not the first term alone. A column holding a flat level *and* a riser has its peak set
+  by the level — one unit in one row — while the riser spreads a unit over 300, which is three
+  orders of magnitude under `0.01 × peak`, so the riser was discarded before the floor could apply
+  to it. Measured on a 2098-sample square wave at 105 samples a column: **2 916 of the ungraded
+  path's 35 884 riser rows**, 106 of 116 riser columns gutted entirely, with a 311-row dark run in
+  a 312-row axis; the ten survivors were the phase that put a riser in a column of its own, which
+  is why it read as a riser *flickering* under a pan rather than as a missing edge. With the second
+  term it is 35 572 rows and 115 of 116 columns, for 48 extra segments
+  (`a_graded_column_keeps_a_riser_it_shares_with_a_flat_level`). A connector between two disjoint columns
+  is emitted at the **faintest** tier: it is inferred geometry, not a place the signal was
+  measured to dwell.
+- **Grading may not undo the reduction.** `level_for()` answers 0 — raw samples — as soon as the
+  asked-for fraction of a column falls under one bucket (`kBucket` is 64), so the finer ask is
+  **floored at level 1** whenever the flat path would have used the pyramid. Without the floor
+  every moderately dense frame became an O(visible) gather: measured in udpscope at 1.3 MS/s over
+  a 2 s window, 172 samples a pixel, the flat path sat on the pyramid and grading dropped the
+  whole figure to raw (`raw=1154 lod=0` against `raw=710 lod=453`) and cost 2.3 → 6.4 ms of draw
+  mean. The floor degrades the *look* instead — fewer sub-columns than asked for, down to what the
+  coarsest buckets give, which at 64 samples a bucket is still two or three per column. That is
+  also why raising `intensity_sub_columns` past about 8 buys nothing: the bucket size is the
+  limit, not the number.
+
+`a_dense_trace_can_be_graded_by_dwell` is the guard, and it draws the same frame both ways. It
+profiles the mean peak coverage over the band's two outer fifths against its middle fifth: the
+flat band is flat (**191 and 191**, one ink) and the graded one is **191 against 131**, a middle
+at 0.69 of the edge. That ratio is a *tier* ratio and not the dwell ratio — the default gamma
+0.45 and floor 0.3 compress it on purpose. The geometry stays bounded by the axis and not by its
+area: **8303 segments over a 572 px axis**, 14.5 runs a column, against the flat path's 627 at
+one end and `572 × 156` rows at the other. A fourth frame over a window wide enough that the
+flat path is on the pyramid is what exercises the floor (`raw=0 lod=1 … seg=634
+visible=200001`); the test's first window sits at 105 samples a pixel, where both paths are raw
+and the floor is never reached.
+
+## A sparse polyline is graded by slope
+
+The column reduction stops at `dense_threshold_spp` (1.5 samples a device pixel), below which the
+trace is a polyline. Grading used to stop there with it, because it was staged *inside* the
+reduction — and that coupling was a defect, not a design. The reduction's gate is a density, and
+its only purpose is removing the moiré beat between the bucket pitch and the pixel pitch. Dwell
+has nothing to do with that beat, so zooming past the threshold turned the phosphor model off in
+one step: the same square-wave edge measured **71 of 191** at 3.4 samples a pixel and **191 of
+191** at 1.0, a 2.7× jump across one pixel of zoom, which reads as a discontinuity *lighting up*
+the moment you look at it closely. The thing a reader most needs told apart from a real signal
+excursion is a transition, and it was being drawn at full ink exactly when it filled the screen.
+
+`Renderer::stage_trace_slopes()` grades the polyline on the same principle, differing only where
+it must:
+
+- **The measure is the segment's own slope**, `1 / (1 + |Δy_screen|)`, which is dwell per row for
+  a single segment. The `1 +` is not a guard against a division: a flat segment — span 0, the
+  commonest case in a sparse window — must be the *brightest* tier, and this makes the measure
+  dimensionless and **absolute**. There is no per-column peak to normalise against down here, and
+  that is an improvement: a sparse frame's tiers mean the same thing from frame to frame, so
+  panning does not reshade the trace.
+- **No gather mode is excluded.** The reduction is `Envelope`-only, because turning a bucket's
+  min/max into a band answers a different question from the one a `Nearest` or `Mean` host asked.
+  A segment's slope is a property of the polyline itself, so `grade` is not reused as the gate —
+  only `intensity_grading` and `intensity_steps > 1` are.
+- **The geometry is bit-for-bit the ungraded polyline's**, staged exactly as `stage_xy()` stages
+  it, with the same `snap = false`; only the batch a segment lands in differs. A segment with one
+  non-finite end is dropped rather than clamped, which is the conclusion `add_polyline_xy()`
+  reaches too.
+- **`FrameStats::slope_traces` counts it, and it is disjoint from `column_traces`.** A window is
+  either dense enough to reduce onto the pixel grid or it is drawn as a polyline, never both — so
+  a host asserting `graded_traces == column_traces` keeps that reading unchanged.
+
+`a_sparse_trace_is_graded_by_slope_like_a_dense_one` is the guard: one window either side of the
+threshold over the same transition at the same place. The level reads **191 either way** (a flat
+segment dwells in its row, so it is the top tier and full ink) and the riser reads **71 either
+way**, against the 191 the sparse frame gave before. Across the whole sweep from 101 down to 0.1
+samples a pixel the riser holds 71 and the level holds 191, so there is no step at the threshold
+left to see.
+
+## A phosphor density is the trace, one grid per trace
+
+`Plot::set_density()` gives a plot a **phosphor density**: an image of how often its traces have
+passed, drawn *in place of them* -- one grid per trace, in that trace's own colour -- fading by a
+time constant or by an acquisition count. It is the library's because the library is the side that
+knows a trace's device geometry; a host that built one itself would be re-rasterising traces the
+renderer has already staged.
+
+The split from the grading above is what it costs: grading measures *one* frame's dwell and
+throws it away, while the density **keeps** what it measured — that is the whole point of it, and
+also why it cannot be a per-frame accumulator.
+
+- **The grid is the screen's, not the data's — bounded — and there is one per trace.** The axes
+  rect in device pixels (`DensityGrid`, `plot/plot/density.hpp`), one `f32` cell each, **up to
+  `kDensityCellCap` = 262 144 cells** (2^18, a mebibyte of counts): under the cap the grid *is* the
+  rect — the axes of a 640x360 viewport is a **573x313** grid of **179 349 cells** and **717 396
+  bytes**, and a thousand acquisitions through it cost the same — and past it the rect is scaled
+  down *uniformly*, so a cell stays square and the picture keeps the axes' aspect. A plot holds one
+  of these for **each trace it draws**, so the display's memory is that figure times the traces on
+  screen; the bound is per *grid*, so four traces hold at most 1 MiB each whatever the window is.
+  The colour is the reason for the per-trace split: a density that had one hue for the plot could
+  not say *which* trace put the ink there, and two signals agreeing in a cell would read as one
+  blended pixel. `Plot::density_grid(trace)` returns a trace's image; a trace with no series (an
+  unbound slot) holds no grid at all.
+
+  The cap is what keeps the resolution from following the window, and the window is not a fixed
+  thing: a 1520x850-logical window at 2x device scale has a 2877-pixel-wide axes rect, and four
+  rows of one trace are **4.5 M cells** — 18 MB of counts, every one of them walked per frame. The
+  pass is `O(cells)` in all three places it happens, so an unbounded image makes the *frame* cost a
+  function of the window: measured on llvmpipe (four traces, one a row, a 2 s window, a 3040x1700
+  framebuffer) the grid pass alone was **12.9 ms of tick and 12.8 ms of draw a frame** and 4.9 MB
+  uploaded, against **3.9 ms / 5.6 ms** and 1.0 MB at the cap. The renderer magnifies the capped
+  image back over the rect with a **linear** filter, because a cell is a *count* — a continuous
+  quantity — and a fragment between two of them is between their two ink levels, which is what a
+  linear tap returns and a point sample cannot (it would show the cell grid as blocks once a cell
+  is several pixels wide). A one-cell-tall feature is thereby spread over its neighbours, which is
+  what any magnification of an image does.
+- **A cell's value is a number of sweeps**, and a trace covering it during one
+  `Plot::accumulate_density()` leaves 1.0, **once however many of its own samples crossed it**.
+  Counting the hits instead puts a single dense sweep at the ceiling of the brightness scale and
+  hides the sweeps behind it, and a cell would then mean "how much the beam moved here" rather
+  than "how many acquisitions were here". The dedupe is a stamp per grid *row* (one `u64`, a few
+  kB, shared by every trace's deposit), keyed by (trace, column), so two sweeps agreeing on a cell
+  still count twice and the two segments that share a column boundary do not.
+- **The deposit is one pass per cell, not one per sample.** A trace's visible window is mapped to
+  sample indices and gathered exactly as `Renderer::draw_traces()` maps it (`neighbours()`, the
+  same 64-spp gate for the LOD level), then walked as a polyline: for each grid column the
+  segment covers, the rows it spans in that column get +1 each. A window of millions of samples
+  over hundreds of columns therefore costs *columns*, plus one row of ink per column the trace
+  crossed — the deposit is bounded by the screen, not by the data, which is what makes an
+  accumulation affordable at the trigger's own rate.
+- **The newest acquisition is deposited like every other, and no trace is drawn over the image.**
+  `Renderer::draw_traces()` returns at once while a density is on: the trace ink *is* the image, so
+  the acquisition just drawn is a sweep *inside* it and fades with the rest. Drawing the polyline
+  on top as well would put a solid, unfading stroke over its own faint ghost — the "persistent
+  image + last acquisition" a user reported, where the newest acquisition never faded.
+- **The brightness ceiling is the trace's own brightness, and the ramp is linear in sweeps.**
+  `DensityConfig::full_scale` defaults to **one sweep**, so a cell with one acquisition's ink is
+  drawn in its trace's colour at that colour's own alpha, and a signal crossing the same place
+  every acquisition settles *exactly* at the colour its trace would have drawn — the settlement is
+  a clamp, not a gain. `gamma` defaults to 1.0, because a cell's value is a count and half as many
+  sweeps must read as half the ink. A ceiling at the *fade's steady state* (`1/(1-0.5)=2`) was the
+  first default and is a legitimate alternative: it makes the newest sweep a fraction of the
+  settled brightness so the fade's ramp is visible, at the cost of a gain offset between the newest
+  sweep and the image behind it. The case that reads either one off the *screen* rather than the
+  grid is `a_phosphor_density_is_the_trace_in_its_own_colour`.
+- **The scale is applied once, on the CPU.** `DensityConfig::full_scale` and `gamma` map a cell's
+  count to a luminance byte when the grid changed, and the shaders (`kDensityVS`/`kDensityFS`)
+  only tint that byte with the trace's colour. The one derivation is deliberate: a value a host
+  reads back through `DensityGrid::ink()`/`peak()` and the picture it sees come from the same
+  numbers.
+- **Per frame, it is one texture upload and one draw call *per trace* — or one draw call each.**
+  The upload is one byte per cell (**179 kB** for the axes above, and at most 256 kB a trace at
+  `kDensityCellCap`, whatever the window); the one texture is re-filled per trace, and a frame whose
+  grids did not move skips the conversion and the uploads entirely and pays the quads alone
+  (`FrameStats::density_upload_bytes` reads 0 for it). The decay is what makes the grids move every
+  frame under `TimeConstant`, and what makes them stand still between acquisitions under
+  `PerAcquisition`.
+  A `TimeConstant` fade therefore does pay the conversion and the upload every frame, whatever the
+  bound — a *bounded* bill rather than a free one. Applying the fade on the GPU instead was
+  considered and is a **larger** change than this bound and was deliberately not bundled with it:
+  the image would have to live in a ping-pong target the decay multiplies in place, while the
+  *count* stays on the CPU, because that is what a host reads back through `ink()`/`peak()`, what
+  the deposit adds whole swaths to, and what the per-sweep dedupe keys on — so the two would have
+  to be reconciled per frame anyway. The bound is what makes that reconciliation a fixed cost.
+
+`a_density_grid_is_the_axes_in_device_pixels` reads the resolution and the memory back
+(**578x453 = 261 834 cells, 1 047 336 bytes** on its 640x480 viewport, which is past the cap, and
+the 320x240 leg it ends on is the axes rect *exactly*, one cell a device pixel —
+`ink=578 peak=1` for one flat sweep, the ink of one sweep *is* the columns it covers),
+`a_density_grid_is_capped_whatever_the_window` reads the bound itself off a 3840x2160 viewport
+(**681x384 = 261 504 cells = 1 046 016 bytes of a 3784x2138 axes**: the cells never exceed
+`kDensityCellCap`, the grid is within 1 % of the whole budget and its aspect is the axes' — the
+uniform scaling), and `a_capped_density_is_magnified_over_the_axes_rect` reads the *screen* side of
+it (**569x460 = 261 740 cells of an 832x673 axes**: the image covers all **832** of the rect's
+columns rather than the 569 cells it holds — the assertion a quad drawn at the grid's own size
+fails — the sweep stays on the row its transform maps it to, and its ink is most of the trace's own
+colour, `green=195` against a background of `65`, the rest being the magnification's blend),
+`a_density_halves_per_acquisition_and_keeps_the_newest_brightest` reads the count schedule
+(578 → 867 → 1012 on a 578-column grid, i.e. `1 + 1/2 + 1/4` of the width, `peak_steady=2.000`),
+`a_density_fades_by_its_time_constant` reads `exp(-dt/tau)` off the ink,
+`a_density_holds_one_grid_per_trace` reads two traces' grids apart (**261 834 cells each,
+ink 578/578**, in two different rows), and
+`a_phosphor_density_is_the_trace_in_its_own_colour` reads the frame: `cells=179349 uploaded=179349`
+on the frame the grid moved and `uploaded=0` on the identical one after it; a saturated cell is the
+trace's own colour exactly (`full=224`, the trace's `0xE0` green, against `bg=25`, where the old
+near-white tint read ~190 red); one time constant dims it (`faded=115`); and a steady state
+(`steady=224`) against a quarter of it (`quarter=138`) keeps the trace's hue, red near the
+background's.
+
 ## One sample or a statistic of many
 
 Every number the library reports is one the samples actually hold. What differs between

docs/interaction.md

@@ -192,6 +192,16 @@ without knowing what a pointer is. `hovered_cursor()`, `grabbed_cursor()`, `hove
 `grabbed_region()` and `region_grab(u32)` expose the same answers to a host (a resize cursor, a
 tooltip, a status line).
 
+The frame an open box zoom is drawing is published the same way and for the same reason
+(`Plot::set_selection_rect()`), and the plot still learns nothing about pointers: the host reads the
+rect off the controller -- `Controller::selection_preview()` -- on every frame of the drag and takes it
+off the plot when the gesture ends. The preview is deliberately not what the pointer swept. Shift
+frames both axes and its preview is the swept box; Ctrl frames x only, so its preview is widened to the
+full height of the axes, and Alt's to the full width. The swept sliver is the *gesture*; the widened
+rect is what the *release* will apply, which is the one worth showing while it is still only a
+gesture. Nothing is previewed until the drag has swept every axis the release will act on: an empty
+rect widened is a band the width of the plot, which would claim a range that does not exist yet.
+
 ## Live follow
 
 An x axis has a follow state, `XFollow::Off` (the default) or `XFollow::Live`

docs/styling.md

@@ -42,6 +42,8 @@ Colours (neither logical nor device — nothing to scale):
 | `axis_text` | `0xC8D0DC` | tick labels and axis titles |
 | `cursor` | `0xFFB020` | cursor markers; also the hovered/grab highlight |
 | `measure_fill` | `0xFFB020` at α 0.15 | the measurement band |
+| `invalid_fill` | `0x8A94A6` at α 0.18 | a span the host declared invalid (`Plot::set_invalid_spans()`) |
+| `invalid_repaired_fill` | `0x8A94A6` at α 0.08 | the same span once the host has marked it repaired |
 | `crosshair` | `0xE6EBF2` | crosshair lines and the readout panel's border (hue-neutral by design; trace markers keep each trace's own colour) |
 
 The scale:

include/plot/data/minmax_pyramid.hpp

@@ -76,6 +76,19 @@ class MinMaxPyramid {
   /// whose samples were all non-finite is stored as an empty aggregate
   /// (count 0, zero sums) that every reader treats as absent.
   void append(f32 v);
+  /// Folds a backfilled sample into every aggregate that covers absolute index
+  /// `absolute_sample`.
+  ///
+  /// **Precondition: the sample at that index was appended non-finite.** That is what makes
+  /// this purely additive -- min/max widen, sum/sumsq accumulate and count rises by one, at
+  /// every covering level -- so no bucket is ever recomputed and the cost is O(levels)
+  /// regardless of how wide the repaired span is. Amending a *finite* sample would need the
+  /// old value removed from sum/sumsq and could not restore min/max at all, which is why
+  /// this is a one-way NaN-to-value operation and not a general write.
+  ///
+  /// An index outside `[window_base(), window_end())` is a no-op: the window slides on the
+  /// consumer thread, so a caller cannot prove the slot is still held before asking.
+  void amend(u64 absolute_sample, f32 v);
   /// Slides the retained window's leading edge to absolute sample index
   /// `absolute_sample`, dropping every aggregate that covered a sample before it.
   /// Monotonic, and a no-op only when `absolute_sample <= window_base()`: an empty

include/plot/data/ring_buffer.hpp

@@ -64,6 +64,24 @@ class RingBuffer {
     for (u64 i = 0; i < n; ++i) push(vs[i]);
   }
 
+  /// Producer thread only: rewrites the slot at absolute index `absolute`, without pushing.
+  /// Returns false when that index is not retained -- already overwritten, or not yet
+  /// produced -- in which case nothing is written.
+  ///
+  /// This is for *backfill*: a slot pushed as a placeholder and corrected when the data that
+  /// belongs there arrives late. It is the same race class as `push()` -- one relaxed store
+  /// into a slot a consumer may be reading, and T is lock-free by the class's static_assert,
+  /// so a reader sees the old value or the new one and never a torn one. It deliberately does
+  /// not touch `produced_`: the count fixes which indices a snapshot reads, and an amend
+  /// changes a value inside that window rather than extending it.
+  bool amend(u64 absolute, T v) {
+    const u64 p = produced_.load(std::memory_order_relaxed);
+    if (absolute >= p) return false;
+    if (p > cap_ && absolute < p - cap_) return false;
+    buf_[static_cast<usize>(absolute & mask_)].store(v, std::memory_order_relaxed);
+    return true;
+  }
+
   /// Consumer: retained element count, saturating at capacity().
   u64 size() const noexcept {
     const u64 p = produced_.load(std::memory_order_acquire);
@@ -109,6 +127,18 @@ class RingBuffer {
   /// pushing).
   void clear() noexcept { produced_.store(0, std::memory_order_relaxed); }
 
+  /// Consumer thread only: discards every element and resumes the absolute count
+  /// at `absolute`, so the next push() lands there (not safe while a producer is
+  /// pushing).
+  ///
+  /// This is for a *recompute*: a ring whose contents are derived from another is
+  /// emptied and refilled from a given absolute origin, and it must come back
+  /// numbered as its source is. clear() would restart it at 0 and leave every
+  /// absolute index -- base(), produced(), copy_from() -- off by that origin.
+  void clear_to(u64 absolute) noexcept {
+    produced_.store(absolute, std::memory_order_relaxed);
+  }
+
  private:
   u64 cap_;
   u64 mask_;

include/plot/input/controller.hpp

@@ -229,6 +229,18 @@ class Controller {
   DragMode drag_mode() const noexcept { return mode_; }
   /// The current box-zoom selection in pixels; meaningful while BoxZoom.
   Rect selection_rect() const noexcept { return selection_; }
+
+  /// The rectangle a host should *draw* for the open box zoom: the swept area, widened to the full
+  /// axes along whichever axis the modifier's mask will not zoom. Ctrl frames the x range only, so its
+  /// preview is the band that spans the plot -- which is what the release will zoom -- where the area
+  /// a purely horizontal drag sweeps is a sliver a few pixels tall. Shift (and any other combo) frames
+  /// both, and gets the swept box itself.
+  ///
+  /// Meaningful while `BoxZoom`, like `selection_rect()`; the zero rect otherwise.
+  ///
+  /// Defined in the implementation: widening the preview to the axes needs the plot's layout, and
+  /// `Plot` is only forward-declared here.
+  Rect selection_preview() const noexcept;
   /// The cursor under the pointer -- a vertical marker or a horizontal ruler, whichever
   /// line the pointer is nearer -- or `kInvalid` when the pointer is outside the plot area
   /// or no cursor is within a few pixels.

include/plot/plot.hpp

@@ -54,6 +54,7 @@
 #include <plot/plot/axis.hpp>
 #include <plot/plot/crosshair.hpp>
 #include <plot/plot/cursor.hpp>
+#include <plot/plot/density.hpp>
 #include <plot/plot/figure.hpp>
 #include <plot/plot/grid.hpp>
 #include <plot/plot/legend.hpp>

include/plot/plot/density.hpp

@@ -0,0 +1,195 @@
+// SPDX-License-Identifier: MIT
+// SPDX-FileCopyrightText: 2026 Martino Ferrari
+
+#pragma once
+#include <span>
+#include <vector>
+
+#include <plot/core/types.hpp>
+
+namespace plot {
+
+/// The most cells one density grid may hold: **262 144**, a mebibyte of `f32` counts.
+///
+/// A grid is the axes rect in device pixels -- the screen's resolution and not the data's, which is
+/// the whole point of accumulating into a grid -- but the screen is not a fixed thing. A window can
+/// be dragged to any width, and at 2x device scale the axes rects of a 1520x850-logical window are
+/// 2877 device pixels wide each: four rows of one trace are **4.5 M cells**, 18 MB of counts
+/// between them, and every one of them is walked per frame. That walk is `O(cells)`: the fade
+/// multiplies every cell, a host's `ink()`/`peak()` read every cell, and a frame the fade moved
+/// converts and uploads every cell as one byte. So a resolution tied to the window is a per-frame
+/// cost tied to the window, with no ceiling -- measured headless on llvmpipe with four rows of one
+/// trace, a 2 s window and a 3040x1700 framebuffer: **4.5 M cells, 12.9 ms of tick and 12.8 ms of
+/// draw a frame, 4.9 MB uploaded**.
+///
+/// This is the ceiling, in **cells** rather than in pixels: the axes rect is scaled down, uniformly,
+/// until it fits, so a cell stays square and the picture keeps the axes' aspect (see `DensityGrid`).
+/// The number is a frame's budget read off that same measurement -- the same four rows at the cap
+/// are 1.05 M cells and **3.9 ms of tick and 5.6 ms of draw**, a third and a half of the unbounded
+/// grid's pass -- while the image is still 681 columns across on a 3784-pixel axes rect. It is a
+/// **cap** and not a resolution: a grid whose axes rect is under it is still exactly that rect in
+/// device pixels, and only an axes rect of more than a quarter of a megapixel -- a 4K window's, or
+/// one row of a tall one -- is scaled.
+inline constexpr usize kDensityCellCap = usize{1} << 18;
+
+/// Which way a plot's **phosphor density** fades between the acquisitions drawn into it.
+///
+/// The two are answers to two different questions, which is why the choice belongs to the
+/// caller rather than to a default: a bench scope's persistence is set by *time* -- "the trace
+/// is still visible a second after it was drawn" -- while a sweep-to-sweep accumulation is set
+/// by *count* -- "the tenth acquisition back is gone". The two agree only while the trigger
+/// rate is constant, and a rate that varies between runs is exactly when a caller has to pick.
+enum class DensityDecay {
+  /// `intensity *= exp(-dt / time_constant_s)` every time the grid is advanced
+  /// (`Plot::decay_density()`), so the image fades while you watch it whatever the trigger
+  /// rate -- a slow stream draws faint sweeps, a fast one bright ones, and both are still
+  /// legible a time constant later. A `time_constant_s <= 0` freezes the grid instead of
+  /// fading it.
+  TimeConstant,
+  /// `intensity *= per_acquisition` once per accumulated acquisition, applied by
+  /// `Plot::accumulate_density()` *before* the new acquisition is deposited, so the sweep just
+  /// drawn is the brightest and each older one is the factor down: the N-th back is gone
+  /// whatever the rate. It scales with the trigger rate by construction -- the record of the
+  /// last few sweeps is what the display holds -- which is what a caller wants when the
+  /// interesting comparison is between successive acquisitions and not between seconds.
+  PerAcquisition,
+};
+
+/// A plot's phosphor density: whether the grid is on, how it fades, and how a cell's count is
+/// turned into brightness. Plain data, replaced wholesale by `Plot::set_density()`.
+///
+/// The image is **one grid per trace**, drawn in that trace's own colour (`Trace::color`), because
+/// a density that had one hue for the whole plot could not say *which* trace put the ink there --
+/// two signals agreeing in a cell would be one blended pixel, and a display of several traces
+/// could not be read back to the trace it came from. A cell's brightness is a count of sweeps in
+/// *that trace's* colour: `full_scale` (default one sweep, the trace's own brightness) is where it
+/// saturates, and a signal crossing the same place every acquisition settles exactly at the colour
+/// its trace would have drawn.
+///
+/// Its reason to exist as a *plot* feature rather than a host's overlay is the same one
+/// `Plot::set_invalid_spans()` has: the plot is what knows a trace's device geometry -- the
+/// visible window about to be drawn, on the axes rect the layout settled -- so the host would
+/// otherwise have to rasterise traces the library has already staged, at a second derivation of
+/// the same mapping that could disagree with the first.
+struct DensityConfig {
+  /// Whether the grid is drawn *and* accumulated. Off is the default and costs nothing: no
+  /// grid is allocated, no frame uploads one, and the traces are drawn exactly as they were.
+  /// Turning it off drops what was accumulated --- a caller that has stopped paying is not
+  /// holding a stale image -- see `Plot::set_density()`.
+  bool enabled = false;
+  /// How the grid fades (see `DensityDecay`).
+  DensityDecay decay = DensityDecay::PerAcquisition;
+  /// `TimeConstant`'s constant, in **stream seconds** -- the same clock the x axis reads, so a
+  /// caller advancing the density by its frame's own `dt` gets a fade that does not depend on
+  /// the frame rate. `<= 0` freezes the grid.
+  f32 time_constant_s = 1.0f;
+  /// `PerAcquisition`'s factor, clamped to `[0, 1]` at use. 0.5 -- half per acquisition -- is
+  /// what a phosphor's afterglow looks like sweep to sweep: 1, 0.5, 0.25, 0.125 and by the
+  /// seventh the layer is under 1 %.
+  f32 per_acquisition = 0.5f;
+  /// The cell value that reads as **full brightness**, in accumulated sweeps -- and the one field
+  /// a caller reads *off its own trace* rather than off the fade. A cell at this value is drawn in
+  /// its trace's own colour at that colour's own alpha; the default of **one sweep** is therefore
+  /// the ink the newest acquisition leaves, so the acquisition just drawn reads exactly as the
+  /// trace it is a picture of (a signal crossing the same place every acquisition settles at the
+  /// trace's brightness, where a ceiling above one sweep would settle *brighter* than the trace and
+  /// leave a gain offset between the newest sweep and the image behind it). Everything above the
+  /// ceiling clamps to the same pixel: where several acquisitions agree, the cell is the trace's
+  /// colour at full strength and no brighter.
+  ///
+  /// A caller that wants the fade's own ramp on screen instead -- the newest sweep a *fraction* of
+  /// the steady state, so the eye can rank the sweeps -- sets this to the sum the fade settles at
+  /// (for `PerAcquisition`'s factor `f` that is `1/(1-f)`) and accepts the gain offset; that was
+  /// this field's first default, and it is a legitimate choice, not the one a phosphor makes.
+  f32 full_scale = 1.0f;
+  /// The gamma applied to the normalised cell value before it becomes a luminance. **1.0 by
+  /// default: linear in sweeps**, because that is what a count means -- a cell covered by half the
+  /// acquisitions is half the ink. Under 1 lifts the faint end, and that is what
+  /// `Style::intensity_gamma` is for where the value is a *dwell fraction* rather than a count;
+  /// here it flattens the top instead (0.45 maps a quarter of the scale to 0.54 and the ceiling to
+  /// 1.0, which is most of the ramp spent on the last sweep). Over 1 darkens the faint end for a
+  /// caller that wants only the strong agreement visible.
+  f32 gamma = 1.0f;
+};
+
+/// The density's own image: **the axes rect in device pixels, up to `kDensityCellCap` cells**, so
+/// its resolution is the screen's and not the data's -- the whole point of accumulating into a grid
+/// rather than keeping the acquisitions that were drawn into it -- while still being bounded by
+/// something other than the window a user has dragged. Under the cap the grid *is* the axes rect and
+/// a cell is a device pixel; past it the rect is scaled down uniformly (see `kDensityCellCap` for
+/// the number and the frame budget it comes from), and the renderer magnifies the image back over
+/// the rect with a linear filter, because a cell is a count of sweeps and not a pixel of a picture.
+///
+/// The bound is what makes the memory and the per-frame cost *numbers* rather than functions of the
+/// window: `columns() * rows() * 4` bytes whatever the trigger has done **and** whatever the
+/// window is, at most **262 144 cells, 1 048 576 bytes** a grid -- against the 4.5 MB a trace a
+/// 3040x1700 framebuffer's axes used to ask for, and the 26 ms of tick and draw a frame the pass
+/// over four of them then cost. A plot holds **one grid per trace** (see `DensityConfig`), so a
+/// display's memory is that figure times the traces actually drawn -- a plot's unbound slots hold no
+/// grid -- and four traces hold at most 4 MiB between them. The renderer adds one byte per cell as
+/// the luminance it uploads (`DensityGrid::cells()` is `f32` because a **count** is what decays and
+/// what `ink()`/`peak()` report; the byte is derived per changed frame, not stored here).
+///
+/// A cell's value is a **number of sweeps**: every visible trace of the plot that covers that cell
+/// during one `Plot::accumulate_density()` leaves 1.0 in it -- once, however many of that trace's
+/// own samples crossed it -- so brightness means how many acquisitions were here, and two traces
+/// agreeing in one cell is twice the ink. (What the *beam* did inside one column is a different
+/// question, and the library answers it elsewhere: `Style::intensity_grading`.) Decay multiplies
+/// the whole image, so a cell's value is a decaying count of sweeps and not a bounded score.
+///
+/// The grid is indexed row-major from the axes rect's **top-left** corner: cell `(c, r)` is at
+/// `r * columns() + c` and covers the device span `[axes.x + c*w/columns(), axes.x + (c+1)*w/columns())`
+/// by `[axes.y + r*h/rows(), axes.y + (r+1)*h/rows())` -- the device pixel `(axes.x + c, axes.y + r)`
+/// while the rect is under the cap, and a block of them when the plot scaled the image down.
+/// `revision()` moves on every change, which is what lets the renderer skip the upload -- and the
+/// whole conversion -- on a frame the grid did not move.
+class DensityGrid {
+ public:
+  /// Grid width in cells: the axes rect's width in device pixels, rounded up, scaled down when the
+  /// rect is past `kDensityCellCap` (see the class comment). 0 until the first accumulation on a
+  /// laid-out plot.
+  u32 columns() const noexcept { return columns_; }
+  /// Grid height in cells: the axes rect's height in device pixels, rounded up, scaled down with
+  /// `columns()`: `columns() * rows()` cells.
+  u32 rows() const noexcept { return rows_; }
+  usize cell_count() const noexcept {
+    return static_cast<usize>(columns_) * static_cast<usize>(rows_);
+  }
+  /// The cells, row-major from the top-left, one per cell of the axes rect -- see the class comment
+  /// for the resolution and what one cell's value means.
+  std::span<const f32> cells() const noexcept { return cells_; }
+  /// One cell, or 0.0 outside the grid.
+  f32 at(u32 column, u32 row) const noexcept {
+    if (column >= columns_ || row >= rows_) return 0.0f;
+    return cells_[static_cast<usize>(row) * columns_ + column];
+  }
+  /// The **total ink**: every cell's value summed. The reading that says how much has been
+  /// drawn into the grid at all -- it grows with each accumulation and falls with each decay,
+  /// and is 0 for a grid that is off or was just cleared.
+  f64 ink() const noexcept {
+    f64 total = 0.0;
+    for (const f32 v : cells_) total += static_cast<f64>(v);
+    return total;
+  }
+  /// The **peak**: the brightest cell's value, 0 for an empty grid. It is the reading that
+  /// says whether the accumulation is saturating (at or past `DensityConfig::full_scale`, which
+  /// reads as full brightness) and whether the decay has reached the sweep behind the newest.
+  f32 peak() const noexcept {
+    f32 top = 0.0f;
+    for (const f32 v : cells_) top = v > top ? v : top;
+    return top;
+  }
+  /// How many times the image changed: bumped by every accumulation, decay, clear and resize.
+  /// The renderer compares it with the revision it last uploaded, so a frame that changed
+  /// nothing uploads nothing.
+  u64 revision() const noexcept { return revision_; }
+
+ private:
+  friend class Plot;
+  std::vector<f32> cells_;
+  u32 columns_ = 0;
+  u32 rows_ = 0;
+  u64 revision_ = 0;
+};
+
+}  // namespace plot

include/plot/plot/figure.hpp

@@ -27,8 +27,15 @@ struct FigureLayout {
   /// strips and axes come from its own `Plot::layout()` against this rect, so a row
   /// with a y title keeps its column and no two rows can disagree about chrome.
   std::vector<Rect> rows;
+  /// One rect per plot, flattened row-major (row 0's cells left to right, then row 1's,
+  /// ...): the **viewport** each `Plot` was given. A row of one cell has exactly its row
+  /// rect here; a row of several tiles its rect left to right with `col_gap` between
+  /// cells, the cells' widths summing to the row's less the gaps.
+  std::vector<Rect> cells;
   /// The strip the figure's one shared x axis is drawn in: the bottom row's own
-  /// `PlotLayout::x_label_area`, at the bottom of the bottom row's rect and so as
+  /// `PlotLayout::x_label_area` (for a bottom row split into several cells, only the **last
+  /// cell's** strip -- the others' strips are their own `plot(i).layout().x_label_area`, which
+  /// is where the controller's axis-zoom hit test reads each cell's gestures from), at the bottom of the bottom row's rect and so as
   /// wide as that row's axes rather than the whole figure. Read back from the row
   /// rather than derived here, so a host and the frame cannot disagree about where
   /// the axis is. It is nonzero whenever the figure has rows and the bottom row
@@ -44,6 +51,10 @@ struct FigureLayout {
   /// figure edge to edge, which is the default; it is dropped for a figure too
   /// short to hold it, so the rows never lose their height to a gap.
   f32 row_gap = 0.0f;
+  /// The horizontal gap between two cells of a row, in device pixels. `set_col_gap()`'s
+  /// value, or 0 when any row holding several cells was too narrow to hold it and
+  /// dropped it, so the cells never lose their width to a gap.
+  f32 col_gap = 0.0f;
 };
 
 /// Several plots stacked in one column, sharing one x axis.
@@ -94,13 +105,30 @@ class Figure {
   /// which is the *unlinked* group: rows that share nothing, each with the range
   /// its own plot was given.
   explicit Figure(u32 rows);
+  /// A figure of `cells_per_row.size()` rows, row `r` holding `cells_per_row[r]` plots side
+  /// by side (a count of 0 is clamped to 1). Every row of one cell makes this the same
+  /// figure as `Figure(rows)`. There is deliberately no `initializer_list` constructor, so
+  /// `Figure{3u}` keeps meaning three rows.
+  explicit Figure(std::span<const u32> cells_per_row);
 
-  u32 row_count() const noexcept { return static_cast<u32>(plots_.size()); }
+  /// The number of figure rows -- the bands stacked top to bottom -- which equals
-  /// One row's plot. A row that does not exist yields a default-constructed `Plot`
+  /// `plot_count()` for a figure no row of which is split.
-  /// rather than reading out of bounds -- the rule every accessor on `Plot` follows
+  u32 row_count() const noexcept { return static_cast<u32>(cells_per_row_.size()); }
-  /// -- so a stale row can only ever affect itself.
+  /// The number of plots, i.e. cells over all rows. `plot()`, `link_x()`, `x_link()` and
-  Plot& plot(u32 row) noexcept;
+  /// the hovered plot of `set_crosshair()` index this flattened (row-major) range.
-  const Plot& plot(u32 row) const noexcept;
+  u32 plot_count() const noexcept { return static_cast<u32>(plots_.size()); }
+  /// How many cells row `row` holds; 0 for a row that does not exist.
+  u32 cells_in_row(u32 row) const noexcept;
+  /// The flattened index of row `row`'s first cell; `plot_count()` for `row ==
+  /// row_count()` and for anything beyond.
+  u32 first_plot_of_row(u32 row) const noexcept;
+  /// The row that holds flattened plot `plot` (the last row for an index past the end).
+  u32 row_of_plot(u32 plot) const noexcept;
+  /// One plot, by flattened cell index. A plot that does not exist yields a
+  /// default-constructed `Plot` rather than reading out of bounds -- the rule every
+  /// accessor on `Plot` follows -- so a stale index can only ever affect itself.
+  Plot& plot(u32 index) noexcept;
+  const Plot& plot(u32 index) const noexcept;
 
   // --- geometry ---------------------------------------------------------
 
@@ -119,6 +147,21 @@ class Figure {
   void clear_row_weights() noexcept { row_weights_.clear(); }
   bool has_row_weights() const noexcept { return !row_weights_.empty(); }
 
+  /// How much of row `row`'s width each of its cells gets: `weights[i]` is cell i's
+  /// share of what is left after every cell has its floor width (64 logical pixels,
+  /// capped at an equal share of a narrow row). Normalised. Refused, changing nothing,
+  /// when the row does not exist, the count is not the row's cell count, or a weight is
+  /// not a positive finite number. A row with no weights divides equally.
+  Status set_cell_weights(u32 row, std::span<const f32> weights);
+  /// Back to an equal division of row `row`; a row that does not exist is ignored.
+  void clear_cell_weights(u32 row) noexcept;
+  bool has_cell_weights(u32 row) const noexcept;
+  /// The horizontal gap left between two cells of a row, in device pixels (0.0 by
+  /// default). Negative values are clamped to 0, and a gap too wide for a row to hold is
+  /// dropped for that layout rather than squeezing the cells to nothing.
+  void set_col_gap(f32 device_px) noexcept { col_gap_ = device_px > 0.0f ? device_px : 0.0f; }
+  f32 col_gap() const noexcept { return col_gap_; }
+
   /// The gap left between two rows, in device pixels (0.0 by default, so the rows
   /// tile the figure). Negative values are clamped to 0, and a gap too large for the
   /// figure to hold is dropped for that layout rather than squeezing the rows to
@@ -195,17 +238,18 @@ class Figure {
   /// is not a number; such a call therefore leaves every row's crosshair as it was.
   void set_crosshair(f64 x, bool active);
 
-  /// Places the crosshair with the pointer's **row** and that row's local y (spec §17): the
+  /// Places the crosshair with the pointer's **plot** and that plot's local y (spec §17): the
-  /// shared x goes to every row -- vertical lines everywhere, as the plain overload does -- and
+  /// shared x goes to every plot -- vertical lines everywhere, as the plain overload does -- and
-  /// the horizontal line is drawn **only in `hovered_row`**, where its y is a value of *that*
+  /// the horizontal line is drawn **only in `hovered_row`** -- the **flattened plot index**, not
-  /// row's own scale. It is the fix for the reported defect -- a figure showing no horizontal
+  /// the figure-row index; they differ when a row holds several cells -- where its y is a value of
+  /// *that* plot's own scale. It is the fix for the reported defect -- a figure showing no horizontal
   /// line at all -- without inventing a figure-wide y, which would mean a different value in
   /// every row: the line appears where the pointer is, and no row ever shows another row's y.
   ///
   /// `y_in_row` is a data coordinate on `hovered_row`'s y axis 0, exactly as `Crosshair::y`'s
   /// two-coordinate placement is; a host reads it from the row's own y transform at the
-  /// pointer's pixel row. `hovered_row` outside `[0, row_count())` is treated as "no row under
+  /// pointer's pixel row. `hovered_row` outside `[0, plot_count())` is treated as "no plot under
-  /// the pointer": every row gets the vertical line and none gets a horizontal one, the same
+  /// the pointer": every plot gets the vertical line and none gets a horizontal one, the same
   /// state the single-coordinate overload produces.
   ///
   /// Refused, changing nothing, when `x` is not a number -- matching `set_crosshair(x, active)`
@@ -226,9 +270,10 @@ class Figure {
   /// How many groups there are, excluding the unlinked group 0.
   u32 x_link_count() const noexcept { return static_cast<u32>(links_.size()); }
 
-  /// Moves one row into a link group and applies that group's range to it at once,
+  /// Moves one plot into a link group and applies that group's range to it at once; `row`
-  /// so the row is on the group's window from this call rather than from the next
+  /// is the **flattened plot index** (see `plot_count()`), which is the row index only for a
-  /// frame. `group` 0 takes the row back out of its group, leaving it with the range
+  /// figure with one cell per row. The plot is on the group's window from this call rather
+  /// than from the next frame. `group` 0 takes the plot back out of its group, leaving it with the range
   /// it holds now.
   ///
   /// A group with no range yet -- one that no row and no `set_x_link_range()` has
@@ -242,7 +287,7 @@ class Figure {
   /// per-row window. `XFollow::Off` is the group's to set
   /// (`set_x_link_follow()`), not the axis'.
   Status link_x(u32 row, u32 group);
-  /// The group a row is in, or 0 when it is in none.
+  /// The group the plot with flattened index `row` is in, or 0 when it is in none.
   u32 x_link(u32 row) const noexcept;
 
   /// Sets a group's shared range and pushes it to every member.
@@ -325,7 +370,18 @@ class Figure {
   /// a following group's window, push both to all members.
   void sync_x_links();
 
+  /// Fills the row bookkeeping (`cells_per_row_`, `row_first_`, `cell_weights_`) from a
+  /// per-row cell count, clamping each to at least one. Does not touch `plots_`, which the
+  /// constructors size from `total_cells()`.
+  void build_cells(std::span<const u32> cells);
+
   std::vector<Plot> plots_;
+  std::vector<u32> cells_per_row_;
+  /// Prefix sums of `cells_per_row_`: `rows + 1` entries, `row_first_[r]` the flattened
+  /// index of row r's first cell and the last entry the plot count.
+  std::vector<u32> row_first_;
+  std::vector<std::vector<f32>> cell_weights_;
+  f32 col_gap_ = 0.0f;
   /// What `plot()` yields for a row that does not exist, so a stale row can be used
   /// without reading out of bounds. Owned rather than a static, so one figure's
   /// stray row can never write into another's.

include/plot/plot/plot.hpp

@@ -2,6 +2,7 @@
 // SPDX-FileCopyrightText: 2026 Martino Ferrari
 
 #pragma once
+#include <span>
 #include <vector>
 
 #include <plot/core/rect.hpp>
@@ -11,6 +12,7 @@
 #include <plot/plot/axis.hpp>
 #include <plot/plot/crosshair.hpp>
 #include <plot/plot/cursor.hpp>
+#include <plot/plot/density.hpp>
 #include <plot/plot/grid.hpp>
 #include <plot/plot/legend.hpp>
 #include <plot/plot/measure.hpp>
@@ -49,6 +51,28 @@ constexpr bool x_strip_has_title(XStrip mode) noexcept {
   return mode == XStrip::Both || mode == XStrip::TitleOnly;
 }
 
+/// One span of the primary x axis the host has declared invalid, in **data** coordinates --
+/// `Region`'s convention. In udpscope's case a reserved hole: samples the stream's counter says
+/// exist and that have not been delivered.
+///
+/// `repaired` says the host has since filled the span's samples in. Such a span is **still
+/// reported**, because the shading is a record of what the window was missing, but it is drawn in
+/// the fainter of the two tints -- so a reader can distinguish a gap that is still empty from one
+/// that has since been repaired, and from a span that has left the list entirely.
+struct InvalidSpan {
+  f64 x0 = 0.0;
+  f64 x1 = 0.0;
+  bool repaired = false;
+};
+
+/// One invalid span's measured shading: the rect, clipped to the axes' columns, and the state that
+/// chooses its tint. A struct and not a bare `Rect` for `RegionLayout`'s reason -- the renderer
+/// draws exactly what the layout measured and derives nothing of its own.
+struct InvalidSpanLayout {
+  Rect fill;
+  bool repaired = false;
+};
+
 /// Pixel geometry of a plot's chrome, all of it in the same pixel space as
 /// `Rect` (origin top-left) and therefore in **device** pixels: everything here is
 /// what the renderer draws with, already converted from the logical metrics in
@@ -105,6 +129,15 @@ struct PlotLayout {
   /// controller's hit test reads the very same rects, so where a region is drawn and
   /// where a pointer can grab it cannot drift apart.
   std::vector<RegionLayout> regions;
+  /// Every invalid span's shading, in `Plot::invalid_spans()` order and clipped to the axes'
+  /// columns. Measured here for the regions' first reason -- the frame draws exactly these
+  /// numbers -- and reserving nothing, so a hole cannot move the strips the labels were
+  /// measured into. A span entirely outside the window contributes no rect at all, so this is
+  /// not index-aligned with `invalid_spans()` and nothing needs it to be: there is no hit test
+  /// on a band and no label beside it. Each entry carries the span's `repaired` state alongside
+  /// its rect, so the tint is chosen where the geometry is measured rather than looked up again
+  /// at draw time.
+  std::vector<InvalidSpanLayout> invalid_spans;
   /// The crosshair's geometry, when one is active: the two lines' stroke boxes, the
   /// readout panel and one row per visible trace with the value of the sample nearest the
   /// pointer. Placed here rather than derived by the renderer, exactly as the legend and
@@ -112,6 +145,13 @@ struct PlotLayout {
   /// clamped against the rect it was measured for, so nothing of the readout can be drawn
   /// over a label strip or into a figure's neighbouring row.
   CrosshairLayout crosshair;
+  /// The box-zoom frame, when a modified drag has one open: the area the gesture is framing, in
+  /// viewport pixels, already widened along whichever axis the modifier will *not* zoom (see
+  /// `input::Controller::selection_preview()`, which is where that is decided). Here rather than
+  /// derived by the renderer, for the regions' reason -- the frame draws exactly these numbers -- and
+  /// left as the zero rect whenever no gesture is open, which is what both the fill and the four
+  /// border segments read as "draw nothing".
+  Rect selection;
 };
 
 /// What a pointer is on, as of the last pointer event: the cursor marker under it, the
@@ -525,6 +565,104 @@ class Plot {
   void set_x_note(std::string text);
   const std::string& x_note() const noexcept { return x_note_; }
 
+  /// Spans of the primary x axis the host has declared invalid -- in udpscope's case a reserved
+  /// hole: samples the stream's counter says exist and that have not been delivered. Each span's
+  /// `x0`/`x1` are in **data** coordinates, `Region`'s convention, and is shaded behind
+  /// the traces and over the grid.
+  ///
+  /// Deliberately *not* a `Region`: a region is interactive -- draggable bounds, hot zones, a
+  /// label, a cached statistic, a controller hit test -- and a plot can carry dozens of holes at
+  /// once, which would put a hundred-odd grab targets in the way of every pointer event for
+  /// marks nobody can usefully drag. This is passive shading and nothing else.
+  ///
+  /// The span is copied, so the caller's storage need not outlive the call. Spans need not be
+  /// sorted and may overlap; an empty call clears the shading.
+  ///
+  /// A span whose `repaired` flag is set is shaded more faintly (`Style::invalid_repaired_fill`
+  /// against `Style::invalid_fill`). Clearing the shading is the host's decision and nothing
+  /// here retires a span on its own: a repaired span is drawn until the host stops sending it.
+  void set_invalid_spans(std::span<const InvalidSpan> spans);
+  std::span<const InvalidSpan> invalid_spans() const noexcept { return invalid_spans_; }
+
+  // --- phosphor density --------------------------------------------------
+
+  /// Turns this plot's **phosphor density** on or off, and states how it fades. Off -- the
+  /// default -- is the plot exactly as it was: no grid is allocated, no geometry is deposited
+  /// and no frame uploads anything.
+  ///
+  /// On, the plot keeps an intensity grid behind each of its traces, in that trace's own colour
+  /// (see `DensityGrid` for the resolution, the bound on it and the per-cell meaning, and
+  /// `DensityConfig` for the per-trace colour and the memory the grids cost), and deposits the
+  /// acquisition on screen into it with `accumulate_density()`. While a density is on the
+  /// renderer draws **no solid trace** over it: the trace ink *is* the image, so the newest
+  /// acquisition is deposited like every other and fades with the rest -- a trace left drawn on
+  /// top of its own density could never fade, which is what a report of "the last acquisition
+  /// never fades" was. It is deliberately *not* a set of retained traces -- the library has the
+  /// trace geometry in hand, so a density costs one grid per trace whatever the trigger has done,
+  /// where retaining the acquisitions would cost a window copy each.
+  ///
+  /// Like `set_invalid_spans()` it reserves **no layout space** and nothing on it can be picked:
+  /// it is drawn inside the axes it was sized to, and a pointer neither finds it nor is found by
+  /// it. A cell is a device pixel of that axes rect while the rect is under `kDensityCellCap` and
+  /// a block of them past it, which the renderer scales back up with a linear filter -- the image
+  /// reserves no space either way, so the bound changes its resolution and nothing about the
+  /// layout.
+  ///
+  /// **Disabling drops what was accumulated at once**, not at the next acquisition: a caller who
+  /// has stopped paying for the display is not left holding a stale image of it, which is the
+  /// rule the app's own `set_persist_depth()` follows for the very same reason. Re-enabling
+  /// starts from an empty grid -- the image is sized to the screen, and a screen it has not been
+  /// sized against yet is a screen it has nothing to say about.
+  void set_density(const DensityConfig& config);
+  /// The configuration, as set.
+  const DensityConfig& density() const noexcept { return density_; }
+  /// The accumulated image **of a trace**, for a host that wants to draw it or read it back. There
+  /// is one per trace, in trace order, because each is drawn in that trace's own colour (see
+  /// `DensityConfig`); an out-of-range trace reads an empty (0x0) image. Empty until the first
+  /// `accumulate_density()` on a laid-out plot, and dropped by `set_density()` off.
+  const DensityGrid& density_grid(u32 trace) const noexcept {
+    return trace < density_grids_.size() ? density_grids_[trace] : empty_density_grid();
+  }
+
+  /// Deposits **the acquisition on screen** into each trace's grid: every visible trace of this
+  /// plot, the newest acquisition included, over the x window its own axis is showing, 1.0 into
+  /// every cell it covers -- **once per cell per sweep**, however many of that trace's own samples
+  /// crossed it, so a cell's value is how many traces have covered it since the last decay and not
+  /// how much the beam moved (see `DensityGrid`; the dwell question is
+  /// `Style::intensity_grading`'s). Called once per *acquisition*, which is the cadence the grids
+  /// count in: a caller that deposited every frame would add one sweep sixty times a second, and
+  /// the per-acquisition fade would have nothing to measure itself against. The renderer draws no
+  /// polyline for a trace whose density is on (see `set_density()`), so this deposit is the whole
+  /// of what the newest acquisition looks like -- and it fades with the rest.
+  ///
+  /// The geometry is the frame's own. The visible x range is mapped onto sample indices through
+  /// the series' own x (`Series::neighbours()`), never the `dx()` grid, and never the whole
+  /// series -- exactly as `Renderer::draw_traces()` maps it -- and the gathered points are taken
+  /// to pixels through the transforms the plot's last `layout()` pinned. So this belongs *after*
+  /// a layout: a plot that has never been laid out has no axes rect to size the grid to and
+  /// deposits nothing.
+  ///
+  /// The grid is sized to that axes rect, **the rect in device pixels up to `kDensityCellCap`
+  /// cells** (`DensityGrid`), and a grid of the wrong size is reallocated -- which drops what it
+  /// held, because the image is of the axes rect and a new rect is a new image. Under
+  /// `DensityDecay::PerAcquisition` the fade happens here, before the deposit, so the acquisition
+  /// just drawn is the brightest. A NaN sample is a gap: it deposits nothing and joins nothing,
+  /// the library-wide policy.
+  void accumulate_density();
+
+  /// Fades the grid by `dt_s` of **stream seconds** -- the clock the x axis reads, so a caller
+  /// advancing the display by its frame's own `dt` gets a fade that does not depend on the frame
+  /// rate. Only `DensityDecay::TimeConstant` fades here: `PerAcquisition`'s factor is applied by
+  /// `accumulate_density()`, because there is no acquisition in a frame that merely passed.
+  /// A non-positive `dt_s` and a non-positive `time_constant_s` are both no-ops, so a caller that
+  /// has not measured a frame yet cannot wipe the grid by accident.
+  void decay_density(f64 dt_s);
+
+  /// Empties the grid (and leaves the configuration alone). What a caller does when the data
+  /// under the image is replaced: the screen-relative image of another stream's sweeps says
+  /// nothing about this one.
+  void clear_density() noexcept;
+
   /// The measurement for `id`. Re-evaluated only when a cursor moved, when the
   /// measure was added, or when the series underneath it changed: a different
   /// series, a longer one, or a sliding window whose sample count stayed the same
@@ -702,6 +840,21 @@ class Plot {
   /// calls this when the pointer leaves the axes.
   void clear_crosshair() noexcept { crosshair_.active = false; }
 
+  /// The box-zoom frame the host is showing, in **viewport pixels**, or the zero rect for none.
+  ///
+  /// Set by the host from `input::Controller::selection_preview()` while a modified left drag is
+  /// choosing a range, and taken off when it ends. It is the *host's* job and not the plot's because
+  /// the plot has no controller and learns nothing about pointer, button or modifier (see
+  /// `plot::input`): this is the receiving end of that boundary, exactly as `set_hot_handles()` is.
+  /// Drawn as a frame -- a slightly opaque fill under a light border -- over everything else inside
+  /// the axes, so the area being framed stays legible against the traces it covers.
+  void set_selection_rect(Rect rect) noexcept { selection_ = rect; }
+  /// Takes the frame off, leaving the same state as before any drag: the next one starts from nothing.
+  void clear_selection_rect() noexcept { selection_ = Rect{}; }
+  /// The frame as set -- what `layout()` measures into `PlotLayout::selection`, and what a host or a
+  /// test reads back without paying a layout.
+  Rect selection_rect() const noexcept { return selection_; }
+
   /// Switches the readout panel off -- or back on -- without moving the crosshair: the lines and
   /// the per-trace markers stay, the panel is not measured and no row is listed. A host that wants
   /// the pointer's column marked but not a panel over its data sets this once; it is deliberately
@@ -852,6 +1005,30 @@ class Plot {
   /// region's pixel geometry is derived -- the controller hit-tests what this
   /// measured instead of mapping the bounds through the transform again.
   void build_regions();
+  /// Measures every invalid span into `layout_.invalid_spans`: its interval clipped to the axes'
+  /// columns, with a one-device-pixel floor, and the state that picks its tint. Here and not in
+  /// the renderer for `build_regions()`' reason -- one x mapping, the frame's own.
+  void build_invalid_spans();
+  /// Deposits one trace's visible window into its own density grid: the same index window
+  /// `Renderer::draw_traces()` maps -- `neighbours()` for the ends, the 64-spp gate for the LOD
+  /// level -- gathered into `density_points_`, mapped to pixels through the transforms of the
+  /// plot's last layout, and left with `deposit_density_segment()`. A trace with no series, no
+  /// visible window or non-positive `dx()` deposits nothing.
+  void deposit_density_trace(const Trace& trace, DensityGrid& grid);
+  /// Deposits one already-mapped segment of a trace polyline into `grid`: for every grid column
+  /// the segment crosses, the rows it covers in that column, +1 each. The columns it also *clips*:
+  /// a column whose slice of the segment lies entirely outside the axes is skipped, so a trace off
+  /// the top of the plot deposits nothing rather than a band along the edge, and a segment with
+  /// both ends past an edge keeps the part that is inside. A degenerate segment (`x0 == x1`, or a
+  /// non-finite coordinate) fills the single column it is in.
+  void deposit_density_segment(f32 x0, f32 y0, f32 x1, f32 y1, DensityGrid& grid) noexcept;
+  /// Grows `density_grids_` -- one grid per trace -- to the last layout's axes rect in device
+  /// pixels, clearing a grid when the size moved (a *different* screen is a different image), and
+  /// returns whether any grid is usable. The one place the grids are allocated.
+  bool size_density_grids();
+  /// The image an out-of-range trace reads (see `density_grid()`): a shared empty grid, so the
+  /// accessor need not hand back a reference into nothing.
+  static const DensityGrid& empty_density_grid() noexcept;
   /// Exact statistics of `region` over `series`, or an invalid result when the
   /// interval covers no sample. The one place the region arithmetic lives.
   static RegionStats evaluate_region_stats(const Region& region, const data::Series& series);
@@ -899,6 +1076,28 @@ class Plot {
   std::vector<MeasureSlot> measures_;
   std::vector<Annotation> annotations_;
   std::vector<Region> regions_;
+  std::vector<InvalidSpan> invalid_spans_;
+  /// The phosphor density: its configuration, the grids it accumulates into, and the scratch the
+  /// one visible window being deposited is gathered into. **One grid per trace** -- the image is of
+  /// the axes rect but each trace's is tinted with that trace's own colour (see `DensityConfig`), so
+  /// the memory is `traces * columns * rows * 4` bytes and not one plot's worth -- and each is
+  /// bounded by `kDensityCellCap`. The vector tracks `traces_` and outlives the frames its images
+  /// were drawn in, which is the whole point of accumulating into an image rather than retaining
+  /// traces.
+  DensityConfig density_{};
+  std::vector<DensityGrid> density_grids_;
+  /// Scratch for `deposit_density_trace()`: interleaved (x, y) of one gathered window, re-used
+  /// across traces and frames so a steady-state accumulation allocates nothing. Bounded by the
+  /// window, not the series, as `Renderer::gather_` is.
+  std::vector<f32> density_points_;
+  /// The per-sweep dedupe's stamps, one per grid **row** and shared by every trace's deposit: the
+  /// key of the last (trace, column) to deposit at that row, so one acquisition's own samples
+  /// cannot count a cell twice (see `deposit_density_segment()`). One `u64` a row -- a few kB at
+  /// any window -- and not one per cell, which would double a grid's memory for a comparison.
+  std::vector<u64> density_stamp_;
+  /// The sweep's own number, bumped once per trace deposited: the high half of every stamp key, so
+  /// every trace of a plot, and every acquisition, deposits exactly once per cell it covers.
+  u32 density_trace_ = 0;
   /// The (region, trace) statistics cache, filled on demand by `region_stats()`
   /// and so mutable: a lookup on a const Plot may cache, exactly as `measures_`
   /// does. Entries are created for the pairs a caller actually asks about, never
@@ -913,6 +1112,11 @@ class Plot {
   /// The crosshair's state (see Crosshair): at most one per plot, placed by
   /// `set_crosshair()` and read back by `crosshair()` and `layout()`.
   Crosshair crosshair_{};
+
+  /// The host's box-zoom frame (`set_selection_rect()`): viewport pixels, the zero rect when no
+  /// modified drag is choosing a range. State rather than a `PlotLayout` field alone because a host
+  /// sets it on every drag motion and reads it back; `layout()` only carries it through.
+  Rect selection_{};
   /// The samples `crosshair_value()` reads a span through: `Series::gather()` appends
   /// `(x, y)` pairs and never clears, so the lookup clears this and refills it with the at
   /// most two samples a span covers. Sized to hold them from construction -- four floats is

include/plot/render/program.hpp

@@ -84,4 +84,37 @@ class TextProgram {
   gl::Program program_;
 };
 
+/// Linked phosphor-density program and its uniform surface: one textured quad over a plot's
+/// axes rect. It fails exactly the way the two above do, propagating `Unsupported` and
+/// `GLFailure`.
+///
+/// It is the one pipeline with **no vertex data**: the quad's four corners come from
+/// `gl_VertexID`, so a draw is one four-vertex strip whatever the grid's size and there is no
+/// buffer to stage or upload. The density itself reaches the GPU as a texture -- one texel per
+/// cell -- which is the one thing this pipeline has that the others do not.
+///
+/// `create()` also points the `u_density` sampler at texture unit 0, which is the unit
+/// `plot::gl::Texture::bind()` defaults to, and leaves this program bound. The texture stays
+/// with the caller, who owns its lifetime.
+class DensityProgram {
+ public:
+  bool create(Status* st = nullptr) noexcept;
+  bool valid() const noexcept { return program_.id() != 0; }
+  void bind() const noexcept { program_.use(); }
+
+  /// `u_viewport`: render target size in pixels.
+  void set_viewport(Vec2 px) const noexcept;
+  /// `u_origin` and `u_size`: the quad in `Rect` pixels -- the axes rect's top-left corner and its
+  /// size, which is the area the image is drawn over (its own grid may hold fewer cells than the
+  /// rect has pixels: see `kDensityCellCap`). They are two uniforms rather than a rect because a
+  /// `vec4` uniform would need a fourth setter shape for one caller; a corner and a size are what
+  /// the vertex shader builds the quad from anyway.
+  void set_rect(Vec2 origin, Vec2 size) const noexcept;
+  /// `u_color`: the tint the cells' luminances are multiplied into.
+  void set_color(Color color) const noexcept;
+
+ private:
+  gl::Program program_;
+};
+
 }  // namespace plot::render

include/plot/render/renderer.hpp

@@ -29,10 +29,37 @@ namespace plot {
 struct FrameStats {
   u32 raw_traces = 0;        ///< traces drawn from raw samples (level 0)
   u32 lod_traces = 0;        ///< traces drawn from a min/max pyramid level
+  /// Traces whose geometry was reduced onto the pixel grid: one vertical segment
+  /// per column, lit from that column's own extremes. Counts a trace from either
+  /// path above -- the reduction is about the *density* of the gathered points,
+  /// not about which level produced them.
+  u32 column_traces = 0;
+  /// Traces whose columns were graded by dwell rather than drawn as one flat band
+  /// (`Style::intensity_grading`). A subset of `column_traces`: grading is a way of
+  /// drawing the reduction, not a third path.
+  u32 graded_traces = 0;
+  /// Traces drawn as a polyline whose *segments* were graded by slope -- the sparse
+  /// half of the same phosphor model (`Renderer::stage_trace_slopes`). **Disjoint from
+  /// `column_traces`**, and therefore from `graded_traces`: a window is either dense
+  /// enough to reduce onto the pixel grid or it is drawn as a polyline, never both. A
+  /// host asserting `graded_traces == column_traces` keeps that reading unchanged.
+  u32 slope_traces = 0;
   u64 visible_samples = 0;   ///< samples the gathered windows covered, summed
   u32 staged_segments = 0;   ///< line segments staged, all colour groups
   u32 staged_markers = 0;    ///< marker shapes staged over the traces
   u32 draw_calls = 0;        ///< draw calls issued, line and text
+  /// The phosphor density's own cells, when one was drawn: the **sum** of every trace's
+  /// `Plot::density_grid()` resolution, zero for a plot with the density off. It is what the
+  /// *frame* drew, so a host reading the density's cost off a frame reads it here rather than off
+  /// the grids, which say what is accumulated and not what was spent -- and it is the number that
+  /// scales with the trace count, since the image is one grid per trace (see `DensityConfig`).
+  u32 density_cells = 0;
+  /// The bytes of that image the frame **uploaded**: `columns * rows` when the grid had changed
+  /// since the last frame and 0 when it had not. It is the one field that separates the two
+  /// costs of a density -- the conversion and upload on the frame that moved, the single draw
+  /// call on the frames that did not -- which is exactly the pair a host comparing frame times
+  /// with the display on and off needs to tell apart.
+  u32 density_upload_bytes = 0;
 };
 
 /// Draws a `Plot` into whatever framebuffer is bound.
@@ -78,8 +105,8 @@ class Renderer {
   Renderer(const Renderer&) = delete;
   Renderer& operator=(const Renderer&) = delete;
 
-  /// Destroys every GL object this renderer created: both programs, both vertex
+  /// Destroys every GL object this renderer created: all three programs, the vertex arrays and
-  /// arrays and their instance buffers, and the glyph atlas texture. The
+  /// their instance buffers, the glyph atlas texture and the density's own texture. The
   /// renderer is left uninitialised (`ready() == false`) and `init()` can be
   /// called again on the same object.
   ///
@@ -404,6 +431,13 @@ class Renderer {
   /// axis-aligned line by up to half a pixel. Set on every flush, like `dash`.
   void flush_lines(const Mapping& map, Color color, f32 width, Vec2 dash = Vec2{},
                    bool snap = false) noexcept;
+  /// The same, for a batch other than the renderer's own `lines_`. The graded trace
+  /// pass stages one batch per alpha step, and a step has to be a draw call of its
+  /// own because the line pipeline takes its colour from a uniform -- so it needs to
+  /// flush a batch it chose rather than the member one. Every other caller flushes
+  /// `lines_` and uses the overload above.
+  void flush_lines(render::LineBatch& batch, const Mapping& map, Color color, f32 width,
+                   Vec2 dash = Vec2{}, bool snap = false) noexcept;
   /// Draws every staged glyph in `batch` -- each instance carries its own tint
   /// (`a_colour`) -- and empties the batch. Text is texture-bound, so this runs
   /// once per text batch, after the line geometry it belongs over.
@@ -491,6 +525,34 @@ class Renderer {
   void draw_plot(Plot& plot, const PlotLayout& layout);
 
   void draw_grid(const Plot& plot);
+  /// The plot's **phosphor density** (`Plot::set_density()`), when one is on: one textured quad per
+  /// trace over the axes rect, each in **that trace's own colour** -- a saturated cell is the trace
+  /// at its own brightness -- drawn over the grid and the invalid-span bands. The traces themselves
+  /// are not drawn while it is on (`draw_traces()` returns), so this is the whole of the data ink
+  /// and the newest acquisition is inside it.
+  ///
+  /// Each trace's image reaches the GPU as an `GL_R8` texture, one texel per cell, converted here
+  /// from the grid's counts -- the scale and the gamma are the plot's and this stage derives
+  /// neither, so the numbers a host reads back and the picture it sees are one derivation. The
+  /// texture is magnified over the axes rect with a linear filter, because past `kDensityCellCap` a
+  /// cell is several device pixels across. A frame whose grids did not change skips the conversion
+  /// *and* the uploads and costs the draw calls, which `FrameStats::density_upload_bytes` says per
+  /// frame.
+  void draw_density(const Plot& plot, const PlotLayout& layout);
+  /// One grid's quad: fills the shared `GL_R8` texture from `grid` (skipping when its revision and
+  /// address are the ones already uploaded) and draws it over the axes rect in `tint` -- the rect,
+  /// and not the grid's own cell count, so a capped grid is scaled back over the area it is an
+  /// image of. The one place the density conversion lives, shared by every trace of
+  /// `draw_density()`.
+  void draw_density_grid(const DensityConfig& config, const DensityGrid& grid, Color tint,
+                         const PlotLayout& layout);
+  /// `Plot::invalid_spans()`, as `PlotLayout::invalid_spans` measured them: one fill per span,
+  /// in `style_.invalid_fill` or — for a span the host has marked repaired —
+  /// `style_.invalid_repaired_fill`. Over the grid and under everything else inside the axes, so
+  /// a hole reads as a property of the plot's background -- the grid shows through it and a trace
+  /// that does have data in those columns is drawn on top, which is what distinguishes a reserved
+  /// hole from a trace that has gone quiet.
+  void draw_invalid_spans(const PlotLayout& layout);
   void draw_axis_lines(const Plot& plot);
   /// The chrome helpers take the frame's layout: `Plot::layout()` recomputes the
   /// ticks, the strips and the grid, so it is computed once, in `draw()`, and handed
@@ -500,6 +562,53 @@ class Renderer {
   /// The data helpers take it too; they read the axes rect and the transforms it
   /// pins.
   void draw_traces(const Plot& plot, const PlotLayout& layout);
+  /// One gathered window reduced onto the pixel grid and staged in framebuffer
+  /// pixels: for each integer column of `layout.axes`, one exactly vertical
+  /// segment from the lowest to the highest screen y any gathered point put in
+  /// it. Returns how many columns were staged (0 stages nothing); the caller
+  /// flushes with `pixel_mapping()` and `snap = true`.
+  ///
+  /// `gather_` is the input, read with the same origin `draw_traces` asked the
+  /// series for. See `draw_traces` for when this path is taken and why.
+  u32 stage_trace_columns(const Plot& plot, const PlotLayout& layout, const Trace& trace,
+                          f64 x_origin, u32 points);
+  /// The same reduction, graded by **dwell**: a column is drawn as a stack of runs,
+  /// each at the alpha step its own share of the column's samples earns, so a flat
+  /// top is bright and the edge leading to it is faint (`Style::intensity_grading`).
+  ///
+  /// Stages into `steps_`, one `LineBatch` per alpha step, which the caller flushes
+  /// in turn -- the line pipeline's colour is a uniform, so a step is a draw call.
+  /// Returns the segments staged across all steps (0 stages nothing).
+  ///
+  /// `gather_` is the input and must have been asked for at the *finer* level
+  /// `Style::intensity_sub_columns` implies; a column's dwell is not recoverable
+  /// from its own min and max (see `Style::intensity_grading`).
+  u32 stage_trace_density(const Plot& plot, const PlotLayout& layout, const Trace& trace,
+                          f64 x_origin, u32 points);
+  /// The **sparse** window's polyline, graded by the same measure: each segment is
+  /// staged into the step its own *slope* earns, so a near-vertical segment between two
+  /// adjacent samples -- a discontinuity, which the signal crossed without dwelling
+  /// anywhere in it -- is faint and a near-flat one is bright.
+  ///
+  /// It exists because grading used to be gated on the column reduction, and that
+  /// reduction is gated on a *density* (two gathered points per pixel column) whose only
+  /// purpose is removing the moire beat. Dwell has nothing to do with that density, so
+  /// zooming in past it switched the whole phosphor model off and drew an edge as
+  /// brightly as a flat top -- the edge got brighter the further in you zoomed.
+  ///
+  /// The measure agrees with `stage_trace_density()`'s at the boundary but is **absolute
+  /// rather than per column**: below two points a column there is no column peak to
+  /// normalise against, so a segment's dwell is `1 / (1 + rows it spans)` outright. A
+  /// flat segment earns the top step and one crossing the whole axis earns
+  /// `Style::intensity_floor`, which is what a riser's column already gets on the dense
+  /// side.
+  ///
+  /// Geometry is staged exactly as `stage_xy()` stages it -- in the pre-affine space,
+  /// relative to `x_origin` -- so only *which batch* a segment lands in differs from the
+  /// ungraded polyline, and the caller flushes with the trace's own `Mapping` and
+  /// `snap = false`. Returns the segments staged across all steps (0 stages nothing).
+  u32 stage_trace_slopes(const Plot& plot, const Trace& trace, const f32* xy, u32 points,
+                         f64 x_origin, bool log_x, bool log_y);
   /// The cursors, both orientations: one stroke per cursor, placed at the coordinate its own
   /// orientation owns (`Plot::cursor_screen_coordinate()`) and spanning the other axis' whole
   /// range, in its own colour -- or in the accent at handle width while it is hovered or
@@ -578,6 +687,11 @@ class Renderer {
   /// pointer is on: a readout the legend covered would be the feature failing at its one job.
   void draw_crosshair_readout(const Plot& plot, const PlotLayout& layout);
 
+  /// The host's box-zoom frame (`PlotLayout::selection`): a fill at `selection_fill` under a border at
+  /// `selection_edge`, or nothing at all when nothing was swept. Drawn last of the interior passes, so
+  /// the area being framed is legible over the traces, the regions and the readout alike.
+  void draw_selection_frame(const PlotLayout& layout);
+
   /// One marker shape (`Marker`) at a viewport-pixel centre: `Cross` two
   /// segments, `Circle` an 8-gon, `Square` four. Staged into the line batch in
   /// pixel space, at `size_px` half-extent, so a marker's size is device pixels
@@ -598,6 +712,27 @@ class Renderer {
   render::TextAtlas atlas_;
   render::LineProgram line_program_;
   render::TextProgram text_program_;
+  /// The phosphor density's pipeline, its one attribute-less vertex array and the texture a grid is
+  /// uploaded into. The texture is `GL_R8`, one texel per cell of the plot's grid, and is re-filled
+  /// for each trace in turn -- a trace's grid is drawn before the next trace's replaces it -- so a
+  /// row of several traces still costs the one texture. It is re-created when the grid's size moves
+  /// (a resized plot is a differently sized image, and the plot has already dropped what the old one
+  /// held).
+  render::DensityProgram density_program_;
+  gl::VertexArray density_vao_;
+  gl::Texture density_texture_;
+  /// The luminance image as uploaded, re-used across frames so a steady-state frame reallocates
+  /// nothing: one byte per cell.
+  std::vector<u8> density_pixels_;
+  u32 density_w_ = 0;
+  u32 density_h_ = 0;
+  /// The grid the texture currently holds, by address, and its revision. Compared per frame and per
+  /// trace, so a frame whose grids did not move skips the conversion *and* the upload -- the pause
+  /// in a persistence display. The address is part of the key because the texture is shared: two
+  /// traces of one plot have two grids with two revisions, and without the address a skip would
+  /// draw one trace's image under another's colour.
+  const DensityGrid* density_uploaded_grid_ = nullptr;
+  u64 density_uploaded_revision_ = 0;
   render::LineVertexArray line_vao_;
   render::TextVertexArray text_vao_;
 
@@ -611,7 +746,25 @@ class Renderer {
   render::TextBatch glyphs_under_;
   render::TextBatch glyphs_over_;
   std::vector<f32> gather_;   ///< scratch for one gathered window, re-used
-  std::vector<f32> staged_;   ///< scratch for one staged window, re-used
+  /// One (lowest y, highest y) pair per pixel column of the axes, re-used:
+  /// `stage_trace_columns()`'s working set. Two floats per column, so an 8K-wide
+  /// axis is 64 kB -- bounded by the *screen*, where `gather_` is bounded by the
+  /// window.
+  std::vector<f32> columns_;
+  /// `stage_trace_density()`'s working set, and deliberately **one column wide**: the
+  /// gathered points arrive in x order, so a column can be accumulated, read and
+  /// cleared before the next one starts. A full-axes density image would be
+  /// `axes.w * axes.h` (33 MB at 4K); this is `axes.h` (a few kB) and stays in L1.
+  ///
+  /// Each sub-bucket's span is written as a +1 at its first row and a -1 one past
+  /// its last, so accumulating a span costs two writes whatever its height; the
+  /// running sum over the column is then how many sub-buckets cover each row, which
+  /// is the dwell.
+  std::vector<f32> column_rows_;
+  /// One batch per alpha step of the grading (`Style::intensity_steps`), re-used
+  /// across frames: the line pipeline takes its colour from a uniform, so segments
+  /// at different alphas cannot share a draw call and must be staged apart.
+  std::vector<render::LineBatch> steps_;
   mutable std::vector<u8> readback_;  ///< dump_frame_ppm's row buffer
 
   /// The host's `GL_COLOR_CLEAR_VALUE`, queried on the first `begin_frame()` (GL

include/plot/render/shaders.hpp

@@ -68,4 +68,26 @@ extern const char* const kLineFS;
 extern const char* const kTextVS;
 extern const char* const kTextFS;
 
+/// GLSL source of the phosphor-density pipeline: one textured quad over the axes rect.
+///
+/// The vertex shader builds the quad from `gl_VertexID` -- a four-vertex `GL_TRIANGLE_STRIP`
+/// like the other two pipelines, and the only one with **no vertex attributes at all**: the
+/// image is one rectangle whose corners are uniform state, so there is no geometry to stage and
+/// nothing to upload (the density's own bytes go to a texture, not to a buffer).
+///
+/// Uniforms: `u_viewport` (vec2, pixels), `u_origin` (vec2, the quad's top-left corner in `Rect`
+/// pixels), `u_size` (vec2, its size in pixels -- the axes rect the image is drawn over, which the
+/// texture's cells are spread across: one texel a cell while the rect is under `kDensityCellCap`,
+/// and a filtered magnification past it), `u_color` (vec4), `u_density` (sampler2D, unit 0).
+///
+/// The fragment shader multiplies the sampled single-channel image into `u_color`'s alpha, which
+/// is the whole of the brightness mapping: a cell's count was turned into a luminance byte on the
+/// CPU (`Plot`), where the count, the decay and the gamma live, so this stage has no scale of its
+/// own to get out of step with the numbers a host reads back.
+///
+/// `Rect` is top-left origin while GL is bottom-left, so the y axis is flipped exactly once,
+/// here, as in the line pipeline.
+extern const char* const kDensityVS;
+extern const char* const kDensityFS;
+
 }  // namespace plot::render

include/plot/render/style.hpp

@@ -55,6 +55,28 @@ struct Style {
   Color axis_text = Color::hex(0xC8D0DC);
   Color cursor = Color::hex(0xFFB020);
   Color measure_fill = Color::hex(0xFFB020, 0.15f);
+  /// The box-zoom selection's frame, drawn while a modified left drag is choosing a range: a light
+  /// neutral near full alpha for the border and the same neutral at a low one for the fill. Neutral
+  /// and not a trace colour, on `invalid_fill`'s argument -- the frame says "this is the area", and a
+  /// tint a trace could have would read as data. The fill's alpha is chosen against the same floor:
+  /// low enough that what is under the frame stays readable, because the point is to show what is
+  /// being selected, not to hide it.
+  Color selection_fill = Color::hex(0xC8D0DC, 0.12f);
+  Color selection_edge = Color::hex(0xC8D0DC, 0.85f);
+  /// The shading over a span the host has declared invalid (`Plot::set_invalid_spans()`): the
+  /// axis furniture's own neutral grey at a low alpha, on the same model as `measure_fill`
+  /// above. Neutral and not a trace colour on purpose -- a band is the *absence* of data, and
+  /// one in a hue a trace could have would read as a signal rather than as a gap. The alpha is
+  /// low enough that the grid under it stays legible, which is what makes the band read as a
+  /// region of the plot rather than as a panel laid over it.
+  Color invalid_fill = Color::hex(0x8A94A6, 0.18f);
+  /// The same shading for a span whose samples have since arrived and been written in, at well
+  /// under half the alpha. The gap is still reported -- the window was drawn without that data --
+  /// but a reader can tell a hole that is still empty from one that has been filled. Fainter by
+  /// alpha alone and not by hue, so the two read as two depths of one mark rather than as two
+  /// different kinds of thing; and still above the threshold where the difference from *no* band
+  /// is visible, which is the floor this alpha is chosen against.
+  Color invalid_repaired_fill = Color::hex(0x8A94A6, 0.08f);
   /// The crosshair's colour: its two lines and the readout panel's border (spec §15). Markers are
   /// deliberately *not* this colour -- they carry each trace's own, because a marker says *which*
   /// trace and the line says *where*.
@@ -177,6 +199,90 @@ struct Style {
                                    ///< sides draw through the one instanced
                                    ///< anti-aliased quad path.
 
+  // --- intensity grading: counts and ratios, never sizes -------------------
+
+  /// Draw a dense trace's pixel columns **graded by how long the signal dwells at
+  /// each height**, the way a digital-phosphor scope does, instead of as one flat
+  /// band per column: bright where samples pile up (a flat top, a peak), faint
+  /// where they only pass through (an edge, a noise excursion).
+  ///
+  /// Off by default, because it is a change of *look* and not a correction: the
+  /// flat band is the honest answer to "what did this column reach", and a host
+  /// that wants that -- or that draws few enough samples never to take the column
+  /// path at all -- should not have its traces restyled by an upgrade. A scope-like
+  /// host turns it on.
+  ///
+  /// It is not derivable from the flat band. A column's min and max are the same
+  /// whether its samples fill the span or sit piled at its two ends, which is
+  /// exactly the difference between a ramp and a pulse -- so grading needs the
+  /// gather asked at a *finer* level than the pixel grid (`intensity_sub_columns`)
+  /// and reads the distribution from those sub-buckets.
+  ///
+  /// The measure is *dwell per row*, and the weighting is the whole of it: each
+  /// sub-column segment deposits **one unit spread over the rows it spans**, so a
+  /// tall crossing leaves a thin smear and a short one at a turning point leaves a
+  /// bright mark. Counting a row at +1 per segment that touches it instead -- the
+  /// obvious thing -- grades a sine's fast middle as brightly as its rails, which
+  /// is the pattern inverted.
+  ///
+  /// Below `dense_threshold_spp`, where there are no columns to reduce, this grades
+  /// the **polyline** by each segment's own slope instead (`FrameStats::slope_traces`
+  /// against `graded_traces`) -- the same measure for a sparse window, where a
+  /// segment *is* the sub-column. One switch covers both because the alternative was
+  /// a defect: gated on the reduction, the model switched off as a window narrowed
+  /// past the threshold, and an edge drawn at a third of a flat top's ink jumped to
+  /// all of it in one pixel of zoom.
+  bool intensity_grading = false;
+
+  /// Sub-buckets per pixel column the gather is asked for when grading: the level
+  /// is chosen for `samples_per_pixel / intensity_sub_columns`, so a column's
+  /// density is read from this many envelopes instead of from one.
+  ///
+  /// It buys resolution in *dwell*, linearly, for the same factor in gathered
+  /// points -- and the points stay bounded by the screen, which is the property
+  /// that matters (8 of them over a 1000 px axis is 16 000 points whatever the
+  /// window holds). Below about 4 a pulse's flat levels and its edge are too few
+  /// samples apart to separate.
+  ///
+  /// It is a *want*, not a promise: the renderer floors the level it asks for at the
+  /// pyramid's coarsest bucket level, so a window too sparse to hold this many buckets
+  /// a column is graded from however many it does hold. Without that floor `level_for`
+  /// answers 0 -- raw samples -- the moment a sub-column falls under one bucket, which
+  /// turns a frame the flat path draws off the pyramid into an O(visible) gather. So
+  /// raising this past about 8 costs resolution nothing and buys it nothing either: the
+  /// bucket size is the limit, not this number.
+  u32 intensity_sub_columns = 8;
+
+  /// Quantisation of the grading, in alpha steps. Each step is one draw call (the
+  /// line pipeline's colour is a uniform, so a per-segment alpha would mean a
+  /// per-instance one), and the segments are bounded by the columns, so the cost
+  /// of a step is a draw call over a few hundred instances.
+  ///
+  /// Four is enough to read a waveform's structure and few enough that a step is a
+  /// visible tier rather than a gradient -- the point is to separate "dwelt here"
+  /// from "passed through", not to measure.
+  u32 intensity_steps = 4;
+
+  /// Alpha the faintest graded step is drawn at, as a fraction of the trace's own.
+  ///
+  /// Not 0: a column the signal merely passed through is still a column the signal
+  /// *reached*, and a riser dimmed out of existence is a square wave drawn as two
+  /// disconnected lines. This is the floor that keeps the trace continuous.
+  f32 intensity_floor = 0.3f;
+
+  /// Exponent the normalised dwell is raised to before it is quantised. Below 1 it
+  /// lifts the faint end, which is what makes a fast edge visible beside a flat top
+  /// whose dwell is three orders of magnitude greater.
+  ///
+  /// The dwell is normalised **against the column's own peak**, not against a scale
+  /// for the whole frame, so the steps spend their range on the structure *inside*
+  /// each column. One scale for the frame needs the whole `w * h` density image
+  /// (33 MB at 4K, which is why the accumulator is one column wide) and reads
+  /// worse: a column the signal flew straight through holds little dwell at any
+  /// height, so it would grade uniformly faint -- a trace that fades out exactly
+  /// where it moves fastest.
+  f32 intensity_gamma = 0.45f;
+
   /// `logical` in device pixels: the single conversion point for every logical
   /// metric above, so the arithmetic appears once per consumer instead of a `*
   /// ui_scale` scattered over the renderer and the layout.

src/data/minmax_pyramid.cpp

@@ -179,6 +179,43 @@ void MinMaxPyramid::append(f32 v) {
   }
 }
 
+void MinMaxPyramid::amend(u64 absolute_sample, f32 v) {
+  if (!std::isfinite(v)) return;
+  if (absolute_sample < base_ || absolute_sample >= count_) return;
+
+  const f64 vd = f64(v);
+  const auto fold = [&](Entry& e) {
+    // An empty bucket's `mm` is meaningless (see the Entry note), so the first finite
+    // sample *sets* the extremes instead of widening from a zero that was never a sample.
+    if (e.count == 0) {
+      e.mm.min = v;
+      e.mm.max = v;
+    } else {
+      e.mm.min = std::min(e.mm.min, v);
+      e.mm.max = std::max(e.mm.max, v);
+    }
+    e.sum += vd;
+    e.sumsq += vd * vd;
+    ++e.count;
+  };
+
+  // The in-progress level-0 bucket, when the index lies inside it. It is not an entry yet,
+  // so the loop below cannot reach it; leaving it out would lose the amendment for a hole
+  // whose tail is still filling, which is exactly the hole a prompt backfill arrives into.
+  if (count_ % kBucket != 0 && absolute_sample >= (count_ / kBucket) * kBucket) {
+    fold(pending_);
+  }
+
+  // Every level independently: min/max/sum/sumsq/count are each associative, so folding the
+  // value into a parent gives the same aggregate as re-merging its children would.
+  for (u32 l = 0; l < static_cast<u32>(levels_.size()); ++l) {
+    const u64 i = absolute_sample / level_span(l);
+    if (i < levels_[l].base) continue;
+    if (i - levels_[l].base >= static_cast<u64>(levels_[l].entries.size())) continue;
+    fold(levels_[l].entries[static_cast<usize>(i - levels_[l].base)]);
+  }
+}
+
 void MinMaxPyramid::drop_before(u64 absolute_sample) {
   if (absolute_sample <= base_) return;
   if (absolute_sample > count_) {

src/input/controller.cpp

@@ -751,6 +751,31 @@ void Controller::pan(const PointerEvent& e) {
   }
 }
 
+Rect Controller::selection_preview() const noexcept {
+  // Nothing to preview off a box zoom: the mask bits outlive the gesture -- `end_drag()` clears the
+  // selection, not them -- so widening without this guard would hand out a full-band rect for a drag
+  // that finished minutes ago.
+  if (mode_ != DragMode::BoxZoom) return Rect{};
+  // And nothing has been framed until the drag has swept every axis the release will apply: at the
+  // press instant the selection is an empty rect at the pointer, and the *widened* form of that is a
+  // band the width of the plot, which is a claim about a range that does not exist yet. Ctrl's other
+  // axis is deliberately not required: a drag with no vertical movement at all is a band across the
+  // plot, which is exactly what Ctrl is for.
+  if ((box_zoom_x_ && !(selection_.w > 0.0f)) || (box_zoom_y_ && !(selection_.h > 0.0f))) return Rect{};
+  Rect preview = selection_;
+  if (box_zoom_x_ && box_zoom_y_) return preview;
+  const Rect& axes = plot_->layout().axes;
+  if (!box_zoom_x_) {
+    preview.x = axes.x;
+    preview.w = axes.w;
+  }
+  if (!box_zoom_y_) {
+    preview.y = axes.y;
+    preview.h = axes.h;
+  }
+  return preview;
+}
+
 void Controller::box_zoom_update(const PointerEvent& e) {
   const f32 x = std::min(origin_x_, e.x);
   const f32 y = std::min(origin_y_, e.y);

src/plot/figure.cpp

@@ -23,6 +23,56 @@ namespace {
 /// wants a taller floor gives the figure a taller viewport, or gives the rows weights.
 constexpr f32 kMinRowHeightLogical = 24.0f;
 
+/// The width a cell never drops below, in logical pixels, converted exactly as the row
+/// height floor is. It yields to the row -- capped at an equal share of the width there
+/// is -- so a row too narrow for its cells still tiles instead of overflowing.
+constexpr f32 kMinCellWidthLogical = 64.0f;
+
+/// The number of plots a per-row cell count asks for, each row holding at least one.
+u32 total_cells(std::span<const u32> cells) noexcept {
+  u32 total = 0;
+  for (const u32 c : cells) total += std::max<u32>(c, 1u);
+  return total;
+}
+
+/// Splits the row rect `r` into `n` cells in `out[0..n)` and returns the gap actually used.
+/// The cells tile `r` exactly: the gap is dropped when `r` cannot hold it, every cell first
+/// gets the floor width and then its weight's share of what is left, and the last cell
+/// closes the row on its right edge, absorbing the rounding of the ones before it.
+f32 place_cells(const Rect& r, u32 n, const std::vector<f32>& weights, f32 col_gap,
+                f32 ui_scale, Rect* out) {
+  if (n == 1u) {
+    out[0] = r;
+    return col_gap;
+  }
+  f32 gap = col_gap;
+  f32 usable = r.w - gap * static_cast<f32>(n - 1u);
+  if (usable <= 0.0f) {
+    gap = 0.0f;
+    usable = r.w;
+  }
+  usable = std::max(0.0f, usable);
+  const f32 floor_device = ui_scale > 0.0f ? kMinCellWidthLogical * ui_scale
+                                           : kMinCellWidthLogical;
+  const f32 floor_px = std::min(floor_device, usable / static_cast<f32>(n));
+  const f32 extra = usable - floor_px * static_cast<f32>(n);
+  f32 total = 0.0f;
+  const bool weighted = weights.size() == n;
+  if (weighted) {
+    for (const f32 w : weights) total += w;
+  }
+  f32 x = r.x;
+  f32 consumed = 0.0f;
+  for (u32 i = 0; i < n; ++i) {
+    const f32 share = weighted && total > 0.0f ? weights[i] / total : 1.0f / static_cast<f32>(n);
+    const f32 end = i + 1u == n ? usable : consumed + floor_px + extra * share;
+    out[i] = Rect{x, r.y, end - consumed, r.h};
+    consumed = end;
+    x = out[i].right() + gap;
+  }
+  return gap;
+}
+
 /// A coordinate in the shared axis' **axis space**: `log10` when the figure's one
 /// x axis -- the bottom row's, the row the shared strip belongs to -- is
 /// logarithmic, the value itself otherwise. A following group's span and offset
@@ -41,18 +91,72 @@ f64 from_link_space(f64 v, bool log) noexcept {
 
 }  // namespace
 
-Figure::Figure(u32 rows) : plots_(rows) {}
+Figure::Figure(u32 rows) : plots_(rows) {
-
+  const std::vector<u32> ones(rows, 1u);
-Plot& Figure::plot(u32 row) noexcept {
+  build_cells(std::span<const u32>(ones));
-  return row < plots_.size() ? plots_[row] : fallback_;
 }
 
-const Plot& Figure::plot(u32 row) const noexcept {
+Figure::Figure(std::span<const u32> cells_per_row) : plots_(total_cells(cells_per_row)) {
-  return row < plots_.size() ? plots_[row] : fallback_;
+  build_cells(cells_per_row);
+}
+
+void Figure::build_cells(std::span<const u32> cells) {
+  cells_per_row_.assign(cells.begin(), cells.end());
+  for (u32& c : cells_per_row_) c = std::max<u32>(c, 1u);
+  row_first_.assign(cells_per_row_.size() + 1u, 0u);
+  for (std::size_t r = 0; r < cells_per_row_.size(); ++r) {
+    row_first_[r + 1u] = row_first_[r] + cells_per_row_[r];
+  }
+  cell_weights_.assign(cells_per_row_.size(), {});
+}
+
+u32 Figure::cells_in_row(u32 row) const noexcept {
+  return row < cells_per_row_.size() ? cells_per_row_[row] : 0u;
+}
+
+u32 Figure::first_plot_of_row(u32 row) const noexcept {
+  return row < cells_per_row_.size() ? row_first_[row] : plot_count();
+}
+
+u32 Figure::row_of_plot(u32 plot) const noexcept {
+  u32 r = 0;
+  while (r + 1u < cells_per_row_.size() && row_first_[r + 1u] <= plot) ++r;
+  return r;
+}
+
+Plot& Figure::plot(u32 index) noexcept {
+  return index < plots_.size() ? plots_[index] : fallback_;
+}
+
+const Plot& Figure::plot(u32 index) const noexcept {
+  return index < plots_.size() ? plots_[index] : fallback_;
+}
+
+Status Figure::set_cell_weights(u32 row, std::span<const f32> weights) {
+  if (row >= cells_per_row_.size() || weights.size() != cells_per_row_[row]) {
+    return Status{ErrorCode::InvalidArgument, "cell weights must name every cell of an existing row"};
+  }
+  for (const f32 w : weights) {
+    if (!std::isfinite(w) || !(w > 0.0f)) {
+      return Status{ErrorCode::InvalidArgument,
+                    "cell weights must be positive finite numbers: a weight is a share of "
+                    "the row, and a cell with none of it has no rect"};
+    }
+  }
+  cell_weights_[row].assign(weights.begin(), weights.end());
+  return Status{};
+}
+
+void Figure::clear_cell_weights(u32 row) noexcept {
+  if (row < cell_weights_.size()) cell_weights_[row].clear();
+}
+
+bool Figure::has_cell_weights(u32 row) const noexcept {
+  return row < cell_weights_.size() && !cell_weights_[row].empty();
 }
 
 Status Figure::set_row_weights(std::span<const f32> weights) {
-  if (weights.size() != plots_.size()) {
+  if (weights.size() != cells_per_row_.size()) {
     return Status{ErrorCode::InvalidArgument, "row weights must name every row"};
   }
   f32 total = 0.0f;
@@ -369,6 +473,8 @@ void Figure::sync_x_links() {
 const FigureLayout& Figure::layout() {
   const u32 rows = row_count();
   layout_.rows.assign(rows, Rect{});
+  layout_.cells.clear();
+  layout_.col_gap = 0.0f;
   layout_.row_gap = row_gap_;
   layout_.x_axis_strip = Rect{};
   if (rows == 0u) {
@@ -441,20 +547,35 @@ const FigureLayout& Figure::layout() {
   // short to hold the one asked for.
   layout_.row_gap = gap;
 
+  // Each row rect is split into its cells; a one-cell row's cell is the rect itself, so an
+  // unsplit figure lays out exactly as it always did.
+  layout_.cells.assign(plots_.size(), Rect{});
+  layout_.col_gap = col_gap_;
+  for (u32 row = 0; row < rows; ++row) {
+    const u32 n = cells_per_row_[row];
+    const f32 used = place_cells(layout_.rows[row], n, cell_weights_[row], col_gap_,
+                                 floor_scale, &layout_.cells[row_first_[row]]);
+    if (n > 1u && used < col_gap_) layout_.col_gap = 0.0f;
+  }
+
   const u32 bottom_row = rows - 1u;
   for (u32 row = 0; row < rows; ++row) {
-    Plot& p = plots_[row];
+    // One x axis for the whole figure, and it is the bottom row's: every plot keeps its
-    p.set_viewport(layout_.rows[row]);
-    // One x axis for the whole figure, and it is the bottom row's: every row keeps its
     // x chrome -- labels, title and the strip the controller's axis zoom is found in --
-    // and every other row gives all of it to that one, so the labels and the title are
+    // and every plot above the bottom row gives all of it to that row, so the labels and
-    // not drawn once per row. A figure told to label every row keeps them everywhere,
+    // the title are not drawn once per row. A figure told to label every row keeps them
-    // and then there is no shared axis to speak of: each row has its own.
+    // everywhere, and then there is no shared axis to speak of: each plot has its own. A
-    p.set_x_strip_mode(labels_bottom_only_ && row != bottom_row ? XStrip::None : XStrip::Both);
+    // split bottom row labels each of its cells, each against its own x axis.
-    // Before either pass below, and the same value for every row: nothing is measured on
+    const XStrip strip = labels_bottom_only_ && row != bottom_row ? XStrip::None : XStrip::Both;
-    // the right, so unlike the left gutter this needs no measurement pass -- the rows end
+    for (u32 i = row_first_[row]; i < row_first_[row + 1u]; ++i) {
-    // on a common column because they are all told the one width.
+      Plot& p = plots_[i];
-    p.set_right_gutter(right_gutter_);
+      p.set_viewport(layout_.cells[i]);
+      p.set_x_strip_mode(strip);
+      // Before either pass below, and the same value for every plot: nothing is measured on
+      // the right, so unlike the left gutter this needs no measurement pass -- the plots
+      // end on a common column because they are all told the one width.
+      p.set_right_gutter(right_gutter_);
+    }
   }
   // After the viewports, so a row's ticks and grid -- built from its axes rect -- and
   // its transforms describe this frame's rects; and before the rows lay themselves
@@ -486,18 +607,21 @@ const FigureLayout& Figure::layout() {
   // `set_min_y_gutter()` seeds the maximum rather than being imposed on a row before the
   // measurement, so a reserved floor cannot widen what a row reports and then be widened
   // by its own reservation on the next frame.
+  //
+  // Over the flattened plots: every cell of every row takes part, so the y axes of a split
+  // row line up with each other and with the rows above and below.
   f32 gutter = min_y_gutter_;
-  for (u32 row = 0; row < rows; ++row) {
+  for (Plot& p : plots_) {
-    plots_[row].set_min_y_gutter(0.0f);
+    p.set_min_y_gutter(0.0f);
-    const PlotLayout& row_layout = plots_[row].layout();
+    const PlotLayout& row_layout = p.layout();
     gutter = std::max(gutter, row_layout.y_axis_width + row_layout.y_title_width);
   }
   // A one-row figure imposes exactly what that row measured, so it lays out as the plot
   // would on its own; a figure whose rows all need the same strip imposes that, which is
   // also what each would have done alone.
-  for (u32 row = 0; row < rows; ++row) {
+  for (Plot& p : plots_) {
-    plots_[row].set_min_y_gutter(gutter);
+    p.set_min_y_gutter(gutter);
-    plots_[row].layout();
+    p.layout();
   }
 
   // The figure's one x axis is the bottom row's, so the strip it is drawn in is that

src/plot/plot.cpp

@@ -344,6 +344,311 @@ void Plot::set_y_axis_origin_from_range(u32 axis, bool on) {
 
 void Plot::set_x_note(std::string text) { x_note_ = std::move(text); }
 
+void Plot::set_invalid_spans(std::span<const InvalidSpan> spans) {
+  invalid_spans_.assign(spans.begin(), spans.end());
+}
+
+// --- phosphor density ---------------------------------------------------------
+
+void Plot::set_density(const DensityConfig& config) {
+  // Disabling is a caller asking to stop paying for the display, and a trigger that has stopped
+  // firing never reaches another accumulation -- so the image goes now rather than at an event
+  // that may not come. The same rule, for the same reason, as the app's `set_persist_depth()`.
+  if (density_.enabled && !config.enabled) {
+    for (DensityGrid& grid : density_grids_) {
+      grid.cells_.clear();
+      grid.cells_.shrink_to_fit();
+      grid.columns_ = 0u;
+      grid.rows_ = 0u;
+      ++grid.revision_;
+    }
+    density_grids_.clear();
+    density_grids_.shrink_to_fit();
+  }
+  // The two fields the renderer turns a cell's count into a luminance with: a change to either is
+  // a change to every cell's *byte*, and a grid's own revision does not see it. A host that states
+  // its configuration every frame (udpscope does) must not force a re-upload per frame, so this
+  // bumps only when one of the two actually moved -- and then a re-upload is owed.
+  const bool rescale = density_.enabled && config.enabled &&
+                       (density_.full_scale != config.full_scale || density_.gamma != config.gamma);
+  density_ = config;
+  if (rescale) {
+    for (DensityGrid& grid : density_grids_) ++grid.revision_;
+  }
+}
+
+void Plot::decay_density(f64 dt_s) {
+  if (!density_.enabled || density_.decay != DensityDecay::TimeConstant) return;
+  // A non-positive frame and a non-positive time constant are both "do not fade": the first is a
+  // caller that has not measured a frame yet, and the second is a caller asking for a grid that
+  // is drawn and never fades.
+  if (!(dt_s > 0.0) || !(density_.time_constant_s > 0.0f)) return;
+  const f32 factor =
+      static_cast<f32>(std::exp(-dt_s / static_cast<f64>(density_.time_constant_s)));
+  if (!(factor < 1.0f)) return;
+  for (DensityGrid& grid : density_grids_) {
+    if (grid.cells_.empty()) continue;
+    for (f32& cell : grid.cells_) cell *= factor;
+    ++grid.revision_;
+  }
+}
+
+void Plot::clear_density() noexcept {
+  for (DensityGrid& grid : density_grids_) {
+    if (grid.cells_.empty()) continue;
+    std::fill(grid.cells_.begin(), grid.cells_.end(), 0.0f);
+    ++grid.revision_;
+  }
+}
+
+bool Plot::size_density_grids() {
+  const Rect& axes = layout_.axes;
+  if (!(axes.w >= 1.0f) || !(axes.h >= 1.0f)) return false;
+  u32 columns = static_cast<u32>(std::ceil(axes.w));
+  u32 rows = static_cast<u32>(std::ceil(axes.h));
+  if (columns == 0u || rows == 0u) return false;
+  // **The grid is the axes rect in device pixels, up to `kDensityCellCap`.** Beyond it the rect is
+  // scaled down *uniformly*, so the cells stay square in device pixels and the picture keeps the
+  // axes' aspect: a cap on one axis alone would stretch a cell, and a density smeared in one
+  // direction only reads as a bug in the data rather than as a coarse image. The cells are then no
+  // longer one device pixel across, which is why the renderer magnifies the image with a linear
+  // filter instead of a point sample -- see `Renderer::draw_density_grid()`.
+  //
+  // The floor of the product is what makes the cap hold: `floor(w*s) * floor(h*s) <= w*s * h*s
+  // <= cap` for the `s` chosen, and the two `max(1, ...)` keep a very thin axes rect from
+  // rounding to nothing.
+  const u64 pixels = static_cast<u64>(columns) * static_cast<u64>(rows);
+  if (pixels > static_cast<u64>(kDensityCellCap)) {
+    const f64 scale = std::sqrt(static_cast<f64>(kDensityCellCap) / static_cast<f64>(pixels));
+    columns = std::max(1u, static_cast<u32>(static_cast<f64>(columns) * scale));
+    rows = std::max(1u, static_cast<u32>(static_cast<f64>(rows) * scale));
+  }
+  // **One grid per trace**, because a density is drawn in the colour of the trace that laid it
+  // down (see `DensityConfig`). The vector tracks the trace list, so a trace added after the first
+  // accumulation gets its own empty grid here while the grids already sized keep what they held.
+  if (density_grids_.size() != traces_.size()) density_grids_.resize(traces_.size());
+  // The per-sweep dedupe's stamps are one per grid **row** and shared by every trace's deposit:
+  // the key a cell is deduped against carries the trace's number (see
+  // `deposit_density_segment()`), so a stamp left by one trace's sweep never matches another's, and
+  // a zeroed stamp -- every key has a non-zero trace number in its high half -- matches nothing.
+  if (density_stamp_.size() != rows) density_stamp_.assign(rows, 0u);
+  bool usable = false;
+  for (usize i = 0u; i < traces_.size(); ++i) {
+    DensityGrid& grid = density_grids_[i];
+    if (!traces_[i].visible()) {
+      // A trace with nothing to draw gets no image: the grid is per *trace*, and a slot with no
+      // series is not one. Dropping it here is also what keeps the display's memory proportional
+      // to the traces actually on screen rather than to a plot's fixed trace slots -- a row of four
+      // signals out of eight slots holds four grids, not eight.
+      if (!grid.cells_.empty()) {
+        grid.cells_.clear();
+        grid.cells_.shrink_to_fit();
+        grid.columns_ = 0u;
+        grid.rows_ = 0u;
+        ++grid.revision_;
+      }
+      continue;
+    }
+    if (columns != grid.columns_ || rows != grid.rows_) {
+      // A grid of another size is another image, and there is nothing honest to carry over from
+      // one to the other: the cells are device pixels, so a resize moves every one of them. Drop
+      // what it held rather than resample it -- the display restarts, which is what a scope does
+      // when its screen changes.
+      grid.cells_.assign(static_cast<usize>(columns) * rows, 0.0f);
+      grid.columns_ = columns;
+      grid.rows_ = rows;
+      ++grid.revision_;
+    }
+    usable = usable || !grid.cells_.empty();
+  }
+  return usable;
+}
+
+void Plot::accumulate_density() {
+  if (!density_.enabled) return;
+  if (!size_density_grids()) return;
+  // The fade before the deposit, never after: under `PerAcquisition` the acquisition just drawn
+  // is the brightest one and each older one is the factor down, which is what "the N-th back is
+  // gone" means. TimeConstant fades in `decay_density()` instead, because its fade is the clock's
+  // and not the acquisition's.
+  if (density_.decay == DensityDecay::PerAcquisition) {
+    const f32 factor = std::clamp(density_.per_acquisition, 0.0f, 1.0f);
+    for (DensityGrid& grid : density_grids_) {
+      if (grid.cells_.empty()) continue;
+      for (f32& cell : grid.cells_) cell *= factor;
+      ++grid.revision_;
+    }
+  }
+  // **Every visible trace of the acquisition on screen, the newest included.** The current
+  // acquisition is deposited here like any other, so it is inside the image and fades with it --
+  // there is no second, solid trace drawn over the density (see `Renderer::draw_traces()`), which
+  // is what a report of "the last acquisition never fades" turned out to be. One grid each, so two
+  // traces that agree read as two colours at full strength where they overlap and not as one
+  // blended one.
+  const usize n = std::min(density_grids_.size(), traces_.size());
+  for (usize i = 0u; i < n; ++i) deposit_density_trace(traces_[i], density_grids_[i]);
+}
+
+void Plot::deposit_density_trace(const Trace& trace, DensityGrid& grid) {
+  if (!trace.visible()) return;
+  const data::Series& series = *trace.series;
+  const u64 n = series.size();
+  if (!(series.dx() > 0.0) || n == 0u) return;
+
+  // The same index window `Renderer::draw_traces()` maps, by the same calls: `neighbours()` on
+  // the series' own stamps -- never the `(x - x0()) / dx()` grid, which is a nominal spacing and
+  // would lose the segments entering and leaving the frame -- with one sample of slack on each
+  // side and clamped to the series.
+  const Range window = x_range(trace.axis_x);
+  u64 first = 0u;
+  u64 last = n;
+  u64 i0 = 0u;
+  u64 i1 = 0u;
+  if (series.neighbours(window.min, i0, i1)) first = i0 > 0u ? i0 - 1u : 0u;
+  if (series.neighbours(window.max, i0, i1)) last = std::min(n, i1 + 1u);
+  if (last <= first) return;
+
+  // The same level gate the renderer uses, and for the same reason: a window denser than the
+  // pixel grid is a *reduction*, and the density is a reduction of it too -- one pass per cell
+  // the column's own envelope crosses. The levels agree because the ask is the same ask.
+  const f64 samples_per_pixel =
+      static_cast<f64>(last - first) / static_cast<f64>(layout_.axes.w);
+  const u32 level = samples_per_pixel >= static_cast<f64>(style_.dense_threshold_spp)
+                        ? series.pyramid().level_for(n, samples_per_pixel)
+                        : 0u;
+
+  density_points_.clear();
+  series.gather(level, first, last, window.min, density_points_, trace.mode);
+  if (density_points_.size() < 2u) return;
+
+  // A fresh stamp for this trace's part of this acquisition: the key a cell is deduped against is
+  // `(this, column)`, so every trace of a plot deposits once per cell it covers even where they
+  // overlap, and a cell one trace crosses twice in one sweep deposits once.
+  ++density_trace_;
+  const Transform tx = x_transform(trace.axis_x);
+  const Transform ty = y_transform(trace.axis_y);
+  f32 px = 0.0f;
+  f32 py = 0.0f;
+  u32 run = 0u;  // points in the current unbroken run
+  // A run's *first* point is not deposited on its own: the segment that leaves it already puts
+  // ink in that cell, and depositing both would count the pen's arrival twice -- a single pass
+  // would read as two in the cell every trace starts in, which is exactly the cell a peak
+  // reading is taken from. A run of one point -- a lone visible sample, or one isolated by a
+  // gap -- is deposited as a degenerate segment instead, because a place a trace *was* is ink
+  // however short its stay.
+  const auto flush_run = [&]() {
+    if (run == 1u) deposit_density_segment(px, py, px, py, grid);
+  };
+  for (usize k = 0; k + 1u < density_points_.size(); k += 2u) {
+    // x is gathered relative to the visible range's minimum (see `Series::gather()`), so the
+    // absolute x is reconstructed in f64 before it is mapped -- the same reconstruction, and the
+    // same reason, as the staging paths.
+    const f64 x_abs = window.min + static_cast<f64>(density_points_[k]);
+    const f64 y_abs = static_cast<f64>(density_points_[k + 1u]);
+    if (!std::isfinite(x_abs) || !std::isfinite(y_abs)) {
+      flush_run();  // a NaN is a gap: it joins nothing, so the trace is deposited in pieces
+      run = 0u;
+      continue;
+    }
+    const f32 sx = static_cast<f32>(tx.to_screen_x(x_abs));
+    const f32 sy = static_cast<f32>(ty.to_screen_y(y_abs));
+    if (!std::isfinite(sx) || !std::isfinite(sy)) {
+      flush_run();
+      run = 0u;
+      continue;
+    }
+    if (run > 0u) deposit_density_segment(px, py, sx, sy, grid);
+    px = sx;
+    py = sy;
+    ++run;
+  }
+  flush_run();
+  ++grid.revision_;
+}
+
+void Plot::deposit_density_segment(f32 x0, f32 y0, f32 x1, f32 y1, DensityGrid& grid) noexcept {
+  const u32 columns = grid.columns_;
+  const u32 rows = grid.rows_;
+  if (columns == 0u || rows == 0u) return;
+  if (density_stamp_.size() < rows) return;  // sized with the grid; nothing deposits before that
+  if (!std::isfinite(x0) || !std::isfinite(y0) || !std::isfinite(x1) || !std::isfinite(y1)) return;
+  const Rect& axes = layout_.axes;
+  // **The image's footprint is the axes rect rounded up to whole device pixels** -- the rect
+  // `size_density_grids()` counted the cells on -- so `sx`/`sy` are exactly **1** while that rect is
+  // under `kDensityCellCap`: a cell *is* a device pixel and this is the arithmetic the density has
+  // always used. Past the cap they are a fraction of one, and the cell index is read through the
+  // scale rather than straight off the pixel. (The rounding is why the footprint, not the
+  // fractional rect, is the reference: a cell is defined on whole pixels, and a grid of `ceil(w)` of
+  // them covers the rect the axes was laid out with.)
+  const f32 sx = axes.w > 0.0f ? static_cast<f32>(columns) / std::ceil(axes.w) : 1.0f;
+  const f32 sy = axes.h > 0.0f ? static_cast<f32>(rows) / std::ceil(axes.h) : 1.0f;
+  const f32 lo_x = std::min(x0, x1);
+  const f32 hi_x = std::max(x0, x1);
+  i32 c0 = static_cast<i32>(std::floor((lo_x - axes.x) * sx));
+  i32 c1 = static_cast<i32>(std::floor((hi_x - axes.x) * sx));
+  // Clipped to the axes' columns *and* to the grid: a segment reaching past the right edge keeps
+  // the part that is inside, and one entirely outside deposits nothing at all. The clamp is what
+  // keeps ink off the edge column when a trace leaves the frame sideways.
+  c0 = std::max(c0, 0);
+  c1 = std::min(c1, static_cast<i32>(columns) - 1);
+  if (c1 < c0) return;
+
+  const f32 span = hi_x - lo_x;
+  const f32 denom = x1 - x0;
+  const i32 last_row = static_cast<i32>(rows) - 1;
+  // The segment's y span inside one column's own slice of x: the two ends of the slice taken
+  // along the segment. Every column's span meets its neighbour's end exactly (the y is linear in
+  // x), so the deposit is a continuous trace and not a dotted one.
+  const auto column_y_span = [&](i32 column, f32& out_lo, f32& out_hi) {
+    const f32 ca = axes.x + static_cast<f32>(column) / sx;
+    f32 ya = y0;
+    f32 yb = y1;
+    if (span > 0.0f && denom != 0.0f) {
+      const f32 a = std::max(ca, lo_x);
+      const f32 b = std::min(ca + 1.0f / sx, hi_x);
+      ya = y0 + (a - x0) / denom * (y1 - y0);
+      yb = y0 + (b - x0) / denom * (y1 - y0);
+    }
+    out_lo = std::min(ya, yb);
+    out_hi = std::max(ya, yb);
+  };
+  for (i32 c = c0; c <= c1; ++c) {
+    f32 y_lo = 0.0f;
+    f32 y_hi = 0.0f;
+    column_y_span(c, y_lo, y_hi);
+    // A column whose slice of the segment lies wholly outside the axes deposits nothing: without
+    // this, a trace above the top of the plot would paint a band along the top row, which is the
+    // one thing a density must not do -- it would say the trace was there.
+    if (!(y_hi >= axes.y) || !(y_lo <= axes.bottom())) continue;
+    const f32 top = std::max(y_lo, axes.y);
+    // One ULP inside the bottom edge, so a segment ending exactly on it lands in the last row
+    // rather than one past the end.
+    const f32 bottom = std::min(y_hi, std::nextafter(axes.bottom(), axes.y));
+    i32 r0 = std::clamp(static_cast<i32>(std::floor((top - axes.y) * sy)), 0, last_row);
+    i32 r1 = std::clamp(static_cast<i32>(std::floor((bottom - axes.y) * sy)), 0, last_row);
+    // **One pass per cell per sweep, not per hit.** A column of a dense window is crossed hundreds
+    // of times by one acquisition's own samples, and counting each crossing would put a single
+    // sweep at the ceiling of the brightness scale: the newer sweeps behind it would be invisible,
+    // and a cell's value would mean "how much the beam moved here" instead of "how many
+    // acquisitions were here" -- which is what a persistence display is. The stamp is per
+    // *(trace, column)*, so two sweeps that agree on a cell still count twice, and the two segments
+    // that share a column's boundary do not.
+    const u64 key = (static_cast<u64>(density_trace_) << 32) | static_cast<u64>(static_cast<u32>(c));
+    f32* column_cells = grid.cells_.data() + static_cast<usize>(c);
+    for (i32 r = r0; r <= r1; ++r) {
+      const usize row = static_cast<usize>(r);
+      if (density_stamp_[row] == key) continue;  // this sweep has already put its ink here
+      density_stamp_[row] = key;
+      column_cells[row * static_cast<usize>(columns)] += 1.0f;
+    }
+  }
+}
+
+const DensityGrid& Plot::empty_density_grid() noexcept {
+  static const DensityGrid empty{};
+  return empty;
+}
+
 f64 Plot::x_axis_origin(u32 axis) const {
   return axis < x_axes_.size() ? x_axes_[axis].origin : 0.0;
 }
@@ -1091,11 +1396,16 @@ const PlotLayout& Plot::layout() {
   // measured from the *placed* live windows, which is what makes a region's data
   // interval map to the pixel columns the frame will actually use.
   build_regions();
+  build_invalid_spans();
   build_legend();
   // The crosshair last: its panel is fitted into `axes` and its lines are held inside it, and
   // its rows are the sample values nearest a data x -- so it wants the transforms the
   // settled layout pins, exactly as the legend and the regions do.
   build_crosshair();
+  // The box-zoom frame is not measured, only carried: the host already has it in viewport pixels from
+  // the controller that produced it, and re-deriving it here would be a second rounding of the same
+  // rectangle -- and a second place for it to disagree with what the gesture is doing.
+  layout_.selection = selection_;
   return layout_;
 }
 
@@ -1358,6 +1668,41 @@ void Plot::build_regions() {
   }
 }
 
+void Plot::build_invalid_spans() {
+  layout_.invalid_spans.clear();
+  if (invalid_spans_.empty()) return;
+
+  const Rect& axes = layout_.axes;
+  // The primary x axis' transform, taken here for `build_regions()`' reason: after the live
+  // windows have been placed and the strips have settled, so these are the columns the frame
+  // draws with and a band is anchored to the data by construction rather than by a second
+  // mapping that would have to be kept in step with this one.
+  const Transform tx = x_transform(0u);
+  // A hole can be narrower than a column -- one missing sample in a window of hundreds of
+  // thousands -- and a fill rounded to zero width would draw nothing, losing exactly the case
+  // the band is most needed for. One device pixel is the floor.
+  const f32 min_w = std::max(1.0f, style_.device(1.0f));
+
+  for (const InvalidSpan& span : invalid_spans_) {
+    const f64 a = std::min(span.x0, span.x1);
+    const f64 b = std::max(span.x0, span.x1);
+    if (!std::isfinite(a) || !std::isfinite(b)) continue;
+    const f32 lo = static_cast<f32>(tx.to_screen_x(a));
+    const f32 hi = static_cast<f32>(tx.to_screen_x(b));
+    // Scrolled out of the window: nothing to shade. Tested before the floor is applied, so a
+    // span off the left edge is dropped rather than pinned to it as a one-pixel band that
+    // accuses the samples at the window's start.
+    if (hi < axes.x || lo > axes.right()) continue;
+    const f32 first = std::clamp(lo, axes.x, axes.right());
+    const f32 last = std::clamp(hi, axes.x, axes.right());
+    const f32 w = std::min(std::max(last - first, min_w), axes.w);
+    // Widening a band at the right edge would run it over the axis line, so the floor is taken
+    // out of the left instead: the span's own edge is kept wherever there is room for it.
+    const f32 x = std::clamp(first, axes.x, axes.right() - w);
+    layout_.invalid_spans.push_back(InvalidSpanLayout{Rect{x, axes.y, w, axes.h}, span.repaired});
+  }
+}
+
 // --- crosshair (spec §15) --------------------------------------------------
 
 CrosshairSpan crosshair_span(const data::Series& series, f64 x) noexcept {

src/render/program.cpp

@@ -60,4 +60,27 @@ void TextProgram::set_texture_size(Vec2 texels) const noexcept {
   program_.set_uniform("u_tex_size", texels);
 }
 
+bool DensityProgram::create(Status* st) noexcept {
+  program_ = gl::Program::from_source(kDensityVS, kDensityFS, st);
+  if (program_.id() == 0) {
+    return false;
+  }
+  // The grid texture is bound to texture unit 0 by plot::gl::Texture::bind(), so the sampler
+  // has to point there. Set once, here, not per frame -- the same shape as the text program's.
+  program_.use();
+  program_.set_uniform_int("u_density", 0);
+  return true;
+}
+
+void DensityProgram::set_viewport(Vec2 px) const noexcept { program_.set_uniform("u_viewport", px); }
+
+void DensityProgram::set_rect(Vec2 origin, Vec2 size) const noexcept {
+  program_.set_uniform("u_origin", origin);
+  program_.set_uniform("u_size", size);
+}
+
+void DensityProgram::set_color(Color color) const noexcept {
+  program_.set_uniform("u_color", color);
+}
+
 }  // namespace plot::render

src/render/renderer.cpp

@@ -193,14 +193,23 @@ Renderer::~Renderer() {
 void Renderer::release_gl() noexcept {
   ready_ = false;
   // Assigning fresh objects releases every GL name through the handles'
-  // destructors: both programs, both vertex arrays and their instance buffers,
+  // destructors: all three programs, the vertex arrays and their instance
-  // and the atlas texture. Safe to call more than once; every assignment is a
+  // buffers, the glyph atlas texture and the density's own texture. Safe to call
-  // no-op while the renderer is uninitialised.
+  // more than once; every assignment is a no-op while the renderer is
+  // uninitialised.
   atlas_ = render::TextAtlas{};
   line_program_ = render::LineProgram{};
   text_program_ = render::TextProgram{};
+  density_program_ = render::DensityProgram{};
   line_vao_ = render::LineVertexArray{};
   text_vao_ = render::TextVertexArray{};
+  density_vao_ = gl::VertexArray{};
+  density_texture_ = gl::Texture{};
+  density_pixels_.clear();
+  density_w_ = 0;
+  density_h_ = 0;
+  density_uploaded_grid_ = nullptr;
+  density_uploaded_revision_ = 0;
   lines_.clear();
   glyphs_under_.clear();
   glyphs_over_.clear();
@@ -252,10 +261,10 @@ bool Renderer::init(Status* st) noexcept {
     return false;
   }
 
-  if (!line_program_.create(st) || !text_program_.create(st)) {
+  if (!line_program_.create(st) || !text_program_.create(st) || !density_program_.create(st)) {
     return false;
   }
-  if (!line_vao_.create(st, mode) || !text_vao_.create(st, mode)) {
+  if (!line_vao_.create(st, mode) || !text_vao_.create(st, mode) || !density_vao_.create(st)) {
     return false;
   }
   ready_ = true;
@@ -462,7 +471,7 @@ void Renderer::draw(Figure& figure) {
   // Every row is prepared before the figure lays itself out, because a row's strips
   // are measured from the metrics this installs: a row measuring with one backend and
   // drawing with another is the defect the propagation point exists to prevent.
-  const u32 rows = figure.row_count();
+  const u32 rows = figure.plot_count();
   for (u32 row = 0; row < rows; ++row) prepare_plot(figure.plot(row));
 
   // The figure's one layout for the frame. It hands every row its rect and its
@@ -516,6 +525,13 @@ void Renderer::draw_plot(Plot& plot, const PlotLayout& layout) {
   // against the line passes would not change a pixel.)
   set_clip(layout.axes);
   draw_grid(plot);
+  // The holes over the grid and under the data: a band is chrome of the *background*, not an
+  // overlay, so everything a frame draws inside the axes is drawn on top of it.
+  draw_invalid_spans(layout);
+  // ... the density included: it is trace ink and not chrome, so it goes over the bands exactly
+  // where the traces did -- and, while it is on, *instead* of them (`draw_traces()` returns) -- and
+  // under them for the same reason they are under the data.
+  draw_density(plot, layout);
   clear_clip();
   draw_axis_lines(plot);
   set_clip(layout.axes);
@@ -542,6 +558,9 @@ void Renderer::draw_plot(Plot& plot, const PlotLayout& layout) {
   // panel is drawn over the legend and every other overlay rather than under them, and its
   // text joins the frame's over flush with the tick labels and titles.
   draw_crosshair_readout(plot, layout);
+  // The selection frame last of all: it is the gesture still in progress, and nothing inside the axes
+  // should be able to sit on top of the area being chosen.
+  draw_selection_frame(layout);
   clear_clip();
   draw_tick_labels(plot, layout);
   draw_titles(plot, layout);
@@ -616,9 +635,14 @@ void Renderer::upload_text_vertices(std::span<const f32> interleaved) noexcept {
 
 void Renderer::flush_lines(const Mapping& map, Color color, f32 width, Vec2 dash,
                            bool snap) noexcept {
-  const u32 segments = lines_.segment_count();
+  flush_lines(lines_, map, color, width, dash, snap);
+}
+
+void Renderer::flush_lines(render::LineBatch& batch, const Mapping& map, Color color, f32 width,
+                           Vec2 dash, bool snap) noexcept {
+  const u32 segments = batch.segment_count();
   if (segments != 0 && ready_) {
-    upload_vertices(lines_.data());
+    upload_vertices(batch.data());
     line_program_.bind();
     line_program_.set_scale(map.scale);
     line_program_.set_offset(map.offset);
@@ -643,7 +667,7 @@ void Renderer::flush_lines(const Mapping& map, Color color, f32 width, Vec2 dash
     stats_.staged_segments += segments;
     ++stats_.draw_calls;
   }
-  lines_.clear();  // keeps the capacity, so the next group re-uses the store
+  batch.clear();  // keeps the capacity, so the next group re-uses the store
 }
 
 void Renderer::flush_text(render::TextBatch& batch) noexcept {
@@ -972,7 +996,388 @@ void Renderer::draw_titles(const Plot& plot, const PlotLayout& layout) {
 
 // ------------------------------------------------------------------- data
 
+u32 Renderer::stage_trace_columns(const Plot& plot, const PlotLayout& layout, const Trace& trace,
+                                  f64 x_origin, u32 points) {
+  const Transform xt = plot.x_transform(trace.axis_x);
+  const Transform yt = plot.y_transform(trace.axis_y);
+  const f32 left = layout.axes.x;
+  // One column per whole pixel of the axes, plus the partial one at the right-hand
+  // edge: `axes.w` is fractional, and the samples that land in that last fraction
+  // are inside the frame.
+  const u32 count = static_cast<u32>(layout.axes.w) + 1u;
+  constexpr f32 kInf = std::numeric_limits<f32>::infinity();
+  columns_.resize(2u * static_cast<usize>(count));
+  for (u32 c = 0; c < count; ++c) {
+    columns_[2u * c] = kInf;         // the lowest screen y seen in this column
+    columns_[2u * c + 1u] = -kInf;   // and the highest; `lo <= hi` is "present"
+  }
+
+  for (u32 k = 0; k < points; ++k) {
+    const f64 x_abs = x_origin + static_cast<f64>(gather_[2u * k]);
+    const f64 sx = xt.to_screen_x(x_abs);
+    const f64 sy = yt.to_screen_y(static_cast<f64>(gather_[2u * k + 1u]));
+    // A NaN sample, and a non-positive one on a log axis, have no position: both
+    // arrive here as a non-finite screen coordinate.
+    if (!std::isfinite(sx) || !std::isfinite(sy)) continue;
+    const f64 column = std::floor(sx - static_cast<f64>(left));
+    // Clamped, not dropped. The gathered window carries one sample of slack on each
+    // side, and that sample's ink belongs to the edge column -- it is what the
+    // polyline drew there, under the same clip. Nothing further out can arrive: the
+    // window is the visible range's.
+    const u32 c = !(column > 0.0)                           ? 0u
+                  : column >= static_cast<f64>(count - 1u)   ? count - 1u
+                                                            : static_cast<u32>(column);
+    const f32 y = static_cast<f32>(sy);
+    if (y < columns_[2u * c]) columns_[2u * c] = y;
+    if (y > columns_[2u * c + 1u]) columns_[2u * c + 1u] = y;
+  }
+
+  const f32 width = style_.device(trace.width);
+  u32 staged = 0;
+  f32 prev_lo = 0.0f;
+  f32 prev_hi = 0.0f;
+  bool joined = false;   // the column before this one is present, so there is a join to make
+  for (u32 c = 0; c < count; ++c) {
+    f32 lo = columns_[2u * c];
+    f32 hi = columns_[2u * c + 1u];
+    if (!(lo <= hi)) {
+      // No sample landed here. A hole in the data stays a hole: bridging it would
+      // draw a vertical line over x the series says nothing about, where the
+      // polyline drew a diagonal across the gap at most one pixel wide.
+      joined = false;
+      continue;
+    }
+    // Connectivity. Two columns' extremes need not overlap -- a fast edge rises
+    // through a whole column -- and two disjoint vertical segments read as a broken
+    // trace, which is exactly what the polyline's connecting segment prevented. The
+    // later column is extended to meet the earlier one's nearest bound, so the join
+    // is made inside the column that moved and no ink appears left of it.
+    if (joined) {
+      if (hi < prev_lo) {
+        hi = prev_lo;
+      } else if (lo > prev_hi) {
+        lo = prev_hi;
+      }
+    }
+    prev_lo = lo;
+    prev_hi = hi;
+    joined = true;
+    // A span shorter than the stroke is drawn *as* the stroke: the fragment shader
+    // ramps on the distance to the segment's axis and does not cap its ends, so a
+    // vertical segment shorter than its own width rasterises a sliver of itself --
+    // and a column of a flat trace, where `lo == hi`, nothing at all.
+    if (hi - lo < width) {
+      const f32 mid = 0.5f * (lo + hi);
+      lo = mid - 0.5f * width;
+      hi = mid + 0.5f * width;
+    }
+    // The column's centre, in framebuffer pixels. Every segment therefore shares one
+    // sub-pixel phase, which is the whole point (see `draw_traces`), and the flush's
+    // snap puts that one phase on the grid.
+    const f32 x = left + static_cast<f32>(c) + 0.5f;
+    lines_.add_segment({x, lo}, {x, hi});
+    ++staged;
+  }
+  return staged;
+}
+
+u32 Renderer::stage_trace_density(const Plot& plot, const PlotLayout& layout, const Trace& trace,
+                                  f64 x_origin, u32 points) {
+  if (points < 2u) return 0u;
+  // At least two steps, or there is nothing to grade and the faintest step is also
+  // the brightest -- a one-step grading is the flat band drawn dimmer, which is not
+  // what any host asking for this wants.
+  const u32 steps = std::max(2u, style_.intensity_steps);
+  // Exactly `steps`, never merely at least: the flush loop reads `steps_.size()` as the
+  // step count and divides by it, so a batch left over from a larger setting would be
+  // flushed at the wrong alpha -- or, being uncleared, at all.
+  steps_.resize(steps);
+  for (u32 t = 0; t < steps; ++t) steps_[t].clear();
+
+  const Transform xt = plot.x_transform(trace.axis_x);
+  const Transform yt = plot.y_transform(trace.axis_y);
+  const f32 left = layout.axes.x;
+  const f32 top = layout.axes.y;
+  const u32 columns = static_cast<u32>(layout.axes.w) + 1u;
+  // One accumulator row per whole pixel of the axes, plus the partial one at the
+  // bottom edge, plus one past the end for a span's closing delta.
+  const u32 rows = static_cast<u32>(layout.axes.h) + 1u;
+  column_rows_.assign(static_cast<usize>(rows) + 1u, 0.0f);
+
+  const f32 width = style_.device(trace.width);
+  const f32 gamma = style_.intensity_gamma > 0.0f ? style_.intensity_gamma : 1.0f;
+  const f32 bottom = top + layout.axes.h;
+
+  u32 staged = 0;
+  u32 column = 0;        // the column being accumulated
+  bool open = false;     // it has at least one segment
+  u32 prev_column = 0;   // the last column that emitted anything, for the join below
+  f32 prev_lo = 0.0f;
+  f32 prev_hi = 0.0f;
+  bool joined = false;
+  // The smallest deposit any segment made into the column being accumulated, which is
+  // what bounds the "lit at all" test below. Reset per column by `emit_column()`.
+  f32 w_min = std::numeric_limits<f32>::infinity();
+
+  // Reads one column's accumulator out as graded runs and clears it, so the next column
+  // starts empty. Two walks of it, which is nothing -- it is one column wide and in L1 --
+  // and the first is what makes the second's grading *relative to this column*:
+  //
+  // the brightest row of a column is always the top tier. That is deliberate and it is
+  // the difference between grading and dimming. The alternative, one scale for the whole
+  // frame, needs a pass over every column before any of them can be drawn (an
+  // `axes.w * axes.h` image, 33 MB at 4K) and makes a column the signal flew through
+  // *uniformly* faint -- a trace that fades out where it moves fastest, which is where a
+  // reader is most often looking. Per column, the dwell structure *inside* each one is
+  // what the tiers spend their range on: the rails of a sine are bright and its fast
+  // middle is faint, in every column.
+  //
+  // The runs are maximal stretches of equal tier, so this is O(rows) segments per column
+  // at worst and a handful in practice: a column of a clean waveform is a bright ridge
+  // and a faint tail.
+  const auto emit_column = [&]() {
+    const f32 x = left + static_cast<f32>(column) + 0.5f;
+    f32 peak = 0.0f;
+    {
+      f32 cover = 0.0f;
+      for (u32 r = 0; r < rows; ++r) {
+        cover += column_rows_[r];
+        if (cover > peak) peak = cover;
+      }
+    }
+    const f32 inv = peak > 0.0f ? 1.0f / peak : 0.0f;
+    // What counts as covered at all: **a row one segment covered is lit**. The deposits
+    // are fractions, so this cannot be an integer test, and it cannot be a share of the
+    // column's peak alone either -- that was this function's one real defect. A square
+    // wave's riser is a single segment spread over the whole axis, so it deposits
+    // `1/rows` per row, while a flat level in the same column is one deposit of 1.0 per
+    // sub-bucket piled on one row: at 105 samples a column the peak is ~50 and the share
+    // floor is ~0.5, eighty times the riser's own 0.006. Every row of the edge was
+    // unlit, and the connector could not bridge it either -- the two levels are both lit,
+    // so the column's band already spans the gap and neither gap test fires. Measured on
+    // a true square at 104.8 spp over a 312-row axis: 106 of 116 riser columns drawn as
+    // two disconnected marks with up to 311 dark rows between them, the other 10 kept by
+    // the phase that put the riser in a column of its own -- which is why it read as an
+    // edge *flickering* rather than as one missing. `intensity_floor` guards a lit row's
+    // alpha and was documented as preventing exactly this; it never got the chance.
+    //
+    // So the share term is kept only for what it is good for -- suppressing residue from
+    // the running-sum reconstruction -- and is capped by half the smallest deposit the
+    // column actually received, which no real segment's contribution can fall under.
+    const f32 lit_floor = std::min(0.01f * peak, 0.5f * w_min);
+    f32 cover = 0.0f;
+    bool in_run = false;
+    u32 run_tier = 0;
+    u32 run_start = 0;
+    f32 band_lo = 0.0f;
+    f32 band_hi = 0.0f;
+    bool any = false;
+    // One past the last row too: it closes a run that reaches the bottom edge.
+    for (u32 r = 0; r <= rows; ++r) {
+      cover += column_rows_[r];
+      column_rows_[r] = 0.0f;
+      const bool lit = r < rows && cover > lit_floor;
+      u32 tier = 0;
+      if (lit) {
+        const f32 share = std::min(1.0f, cover * inv);
+        const u32 t = static_cast<u32>(std::pow(share, gamma) * static_cast<f32>(steps));
+        tier = std::min(steps - 1u, t);
+      }
+      if (in_run && (!lit || tier != run_tier)) {
+        f32 lo = top + static_cast<f32>(run_start);
+        f32 hi = top + static_cast<f32>(r);
+        // A run shorter than the stroke is drawn *as* the stroke, for the reason
+        // `stage_trace_columns()` gives: the fragment shader ramps on the distance to
+        // the segment's axis and does not cap its ends.
+        if (hi - lo < width) {
+          const f32 mid = 0.5f * (lo + hi);
+          lo = mid - 0.5f * width;
+          hi = mid + 0.5f * width;
+        }
+        steps_[run_tier].add_segment({x, lo}, {x, hi});
+        ++staged;
+        in_run = false;
+      }
+      if (lit && !in_run) {
+        run_start = r;
+        run_tier = tier;
+        in_run = true;
+      }
+      if (lit) {
+        if (!any) {
+          band_lo = top + static_cast<f32>(r);
+          any = true;
+        }
+        band_hi = top + static_cast<f32>(r) + 1.0f;
+      }
+    }
+    open = false;
+    w_min = std::numeric_limits<f32>::infinity();
+    if (!any) {
+      joined = false;   // nothing visible here: a hole, like an uncovered column
+      return;
+    }
+    // Connectivity, the same rule as the flat path: two columns' bands need not
+    // overlap -- a fast edge rises through a whole column -- and two disjoint
+    // verticals read as a broken trace. The gap is bridged by a segment of its own at
+    // the **faintest** tier rather than by extending a run, because a connector is
+    // inferred geometry and not a place the signal was measured to dwell: grading it
+    // bright would claim the opposite of what it is.
+    if (joined && column == prev_column + 1u) {
+      if (band_hi < prev_lo) {
+        steps_[0].add_segment({x, band_hi}, {x, prev_lo});
+        ++staged;
+      } else if (band_lo > prev_hi) {
+        steps_[0].add_segment({x, prev_hi}, {x, band_lo});
+        ++staged;
+      }
+    }
+    prev_lo = band_lo;
+    prev_hi = band_hi;
+    prev_column = column;
+    joined = true;
+  };
+
+  f64 px = 0.0;
+  f64 py = 0.0;
+  bool have_prev = false;
+  for (u32 k = 0; k < points; ++k) {
+    const f64 x_abs = x_origin + static_cast<f64>(gather_[2u * k]);
+    const f64 sx = xt.to_screen_x(x_abs);
+    const f64 sy = yt.to_screen_y(static_cast<f64>(gather_[2u * k + 1u]));
+    // A NaN sample, and a non-positive one on a log axis, have no position -- and it
+    // breaks the chain as well as skipping the point: a segment from the sample
+    // before it to the one after would cross x the series says nothing about.
+    if (!std::isfinite(sx) || !std::isfinite(sy)) {
+      have_prev = false;
+      continue;
+    }
+    if (have_prev) {
+      // The *segment*, not the point, is what carries dwell: it is a stretch of the
+      // waveform, and where it went slowly it covers few rows and where it went fast it
+      // covers many. This is where a height-based heuristic cannot reach -- a column's
+      // min and max cannot tell a ramp from a pulse, and a column's segments can (see
+      // `Style::intensity_grading`).
+      //
+      // It is charged to the column its earlier end falls in. The gather is asked at
+      // `intensity_sub_columns` buckets per column, so a segment is a fraction of a
+      // column wide and splitting one across a boundary would buy a fraction of one
+      // sub-bucket's dwell.
+      const f64 c = std::floor(px - static_cast<f64>(left));
+      // Clamped, not dropped, for the reason `stage_trace_columns()` gives: the
+      // gathered window carries one sample of slack on each side and that sample's
+      // ink belongs to the edge column.
+      const u32 ci = !(c > 0.0)                                 ? 0u
+                     : c >= static_cast<f64>(columns - 1u)      ? columns - 1u
+                                                               : static_cast<u32>(c);
+      if (open && ci != column) emit_column();   // x is increasing, so ci > column
+      if (!open) {
+        column = ci;
+        open = true;
+      }
+      const f64 lo = std::min(py, sy);
+      const f64 hi = std::max(py, sy);
+      // Wholly outside the axes is wholly clipped, and a clamp would move its ink to
+      // the edge and invent a ridge there. A segment that *crosses* the edge is
+      // clamped instead, which is the coverage the clip leaves -- so a column's shares
+      // are shares of what is visible in it, which is what is being graded.
+      if (hi >= static_cast<f64>(top) && lo <= static_cast<f64>(bottom)) {
+        const f64 ra = std::floor(lo - static_cast<f64>(top));
+        const f64 rb = std::floor(hi - static_cast<f64>(top));
+        const u32 r0 = !(ra > 0.0) ? 0u
+                       : ra >= static_cast<f64>(rows - 1u) ? rows - 1u
+                                                          : static_cast<u32>(ra);
+        const u32 r1 = !(rb > 0.0) ? 0u
+                       : rb >= static_cast<f64>(rows - 1u) ? rows - 1u
+                                                          : static_cast<u32>(rb);
+        // A segment deposits one unit of dwell, **spread over the rows it covers** --
+        // which is the whole measurement, and counting the rows instead was wrong in a
+        // way worth recording: a sub-bucket holds about as many samples as any other, so
+        // a segment crossing a hundred rows is those samples *passing through* each of
+        // them, while one covering two rows is the same samples *sitting* in them. Giving
+        // each crossed row a full unit makes a sine's fast middle as bright as its rails,
+        // which is the pattern grading exists to show.
+        //
+        // Two writes whatever the height: the running sum over the column is then the
+        // dwell at each row.
+        const f32 w = 1.0f / static_cast<f32>(r1 - r0 + 1u);
+        if (w < w_min) w_min = w;
+        column_rows_[r0] += w;
+        column_rows_[r1 + 1u] -= w;
+      }
+    }
+    px = sx;
+    py = sy;
+    have_prev = true;
+  }
+  if (open) emit_column();
+  return staged;
+}
+
+u32 Renderer::stage_trace_slopes(const Plot& plot, const Trace& trace, const f32* xy, u32 points,
+                                 f64 x_origin, bool log_x, bool log_y) {
+  if (points < 2u) return 0u;
+  // At least two, for the reason `stage_trace_density()` gives: a one-step grading is
+  // the whole trace drawn dimmer, which is not what a host asking for this wants.
+  const u32 steps = std::max(2u, style_.intensity_steps);
+  steps_.resize(steps);
+  for (u32 t = 0; t < steps; ++t) steps_[t].clear();
+
+  const Transform yt = plot.y_transform(trace.axis_y);
+  const f32 gamma = style_.intensity_gamma > 0.0f ? style_.intensity_gamma : 1.0f;
+  const f32 fsteps = static_cast<f32>(steps);
+
+  u32 staged = 0;
+  for (u32 i = 0; i + 1u < points; ++i) {
+    const f64 y0 = static_cast<f64>(xy[2u * i + 1u]);
+    const f64 y1 = static_cast<f64>(xy[2u * i + 3u]);
+    const f64 s0 = yt.to_screen_y(y0);
+    const f64 s1 = yt.to_screen_y(y1);
+    // A NaN sample, and a non-positive one on a log axis, have no position, and the
+    // *segment* is what is being staged -- so one unplaceable end drops it entirely
+    // rather than being clamped to somewhere the series says nothing about. The
+    // ungraded polyline reaches the same conclusion through `add_polyline_xy()`, which
+    // a non-finite vertex excludes from both of its segments.
+    if (!std::isfinite(s0) || !std::isfinite(s1)) continue;
+
+    // Dwell, the same quantity `stage_trace_density()` deposits and for the same
+    // reason: a segment is a stretch of the waveform, and the rows it spans are the
+    // rows the signal crossed *on its way* rather than sat in. `1 + span` so a flat
+    // segment -- span 0, the commonest case in a sparse window -- is 1 and not a
+    // division by zero, which also makes the measure dimensionless and absolute: no
+    // per-column peak exists to normalise against down here.
+    const f32 span = static_cast<f32>(std::fabs(s1 - s0));
+    const f32 dwell = 1.0f / (1.0f + span);
+    const u32 t = std::min(steps - 1u, static_cast<u32>(std::pow(dwell, gamma) * fsteps));
+
+    // Staged exactly as `stage_xy()` does, so the geometry is bit-for-bit the ungraded
+    // polyline's and only the batch differs. The linear case needs no mapping at all --
+    // the gather already emitted x relative to this origin.
+    if (!log_x && !log_y) {
+      steps_[t].add_segment(Vec2{xy[2u * i], xy[2u * i + 1u]},
+                            Vec2{xy[2u * i + 2u], xy[2u * i + 3u]});
+    } else {
+      const f64 ox = space(x_origin, log_x);
+      steps_[t].add_segment(
+          Vec2{static_cast<f32>(space(static_cast<f64>(xy[2u * i]) + x_origin, log_x) - ox),
+               static_cast<f32>(space(y0, log_y))},
+          Vec2{static_cast<f32>(space(static_cast<f64>(xy[2u * i + 2u]) + x_origin, log_x) - ox),
+               static_cast<f32>(space(y1, log_y))});
+    }
+    ++staged;
+  }
+  return staged;
+}
+
 void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
+  // **No solid trace while the density is on.** The trace ink *is* the density image (see
+  // `Plot::set_density()` and `draw_density()`): every visible trace was deposited, the newest
+  // acquisition included, so drawing the polyline as well would put a solid, unfading stroke over
+  // its own faint image -- the "persistent image + last acquisition" a report described, where the
+  // newest acquisition never faded because it was never only the image. The traces still exist --
+  // the legend, the crosshair readout and the measurements read them -- they are simply not drawn
+  // as lines.
+  if (plot.density().enabled) return;
   // Both dimensions: a zero-width rect selects no level, and a zero-height one
   // would flatten every trace onto a single row -- a frame that looks like a
   // rendering choice rather than the collapsed plot it is.
@@ -1013,9 +1418,30 @@ void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
     // This is the whole performance contract: the window, never the series.
     const u64 visible = last - first;
     const f64 samples_per_pixel = static_cast<f64>(visible) / static_cast<f64>(layout.axes.w);
-    const u32 level = samples_per_pixel >= static_cast<f64>(style_.dense_threshold_spp)
+    // Grading reads a column's *distribution*, which one envelope per column cannot
-                          ? series.pyramid().level_for(n, samples_per_pixel)
+    // carry (`Style::intensity_grading`), so the gather is asked for the level a
-                          : 0u;
+    // fraction of a column implies. The *gate* is still the pixel grid's density: a
+    // window sparse enough to be drawn as a polyline is drawn as one, graded or not.
+    const bool grade = style_.intensity_grading && trace.mode == data::GatherMode::Envelope &&
+                       style_.intensity_sub_columns > 1u && style_.intensity_steps > 1u;
+    const u32 flat_level = samples_per_pixel >= static_cast<f64>(style_.dense_threshold_spp)
+                               ? series.pyramid().level_for(n, samples_per_pixel)
+                               : 0u;
+    // The finer level, floored at the pyramid's coarsest bucket level. Grading asks for a
+    // fraction of a column and `level_for` answers 0 -- raw samples -- as soon as that
+    // fraction falls under one bucket, so an unfloored ask turns every moderately dense
+    // frame into an O(visible) gather: measured at 1.3 MS/s over a 2 s window, 172 samples
+    // a pixel, where the flat path sits on the pyramid and grading dropped the whole figure
+    // to raw (`raw=1154 lod=0` against `raw=710 lod=453`) and cost 2.3 -> 6.4 ms a frame.
+    // The floor degrades the *look* instead: fewer sub-columns than asked for, down to
+    // whatever the coarsest buckets give, which at 64 samples a bucket is still two or three
+    // per column. Grading is a way of drawing a reduction and may not undo it.
+    const u32 level =
+        grade && flat_level > 0u
+            ? std::max(1u, series.pyramid().level_for(
+                               n, samples_per_pixel /
+                                      static_cast<f64>(style_.intensity_sub_columns)))
+            : flat_level;
 
     gather_.clear();
     // The visible range's minimum is the gather origin: the emitted f32 is then O(the span on
@@ -1111,8 +1537,97 @@ void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
     // trace/axis hierarchy on a high-DPI panel. `width == 0` is scatter: the
     // markers below are the whole trace.
     if (trace.width > 0.0f) {
-      stage_xy(gather_.data(), points, x_range.min, log_x, log_y);
+      // A window denser than two gathered points per pixel column is drawn as *columns*
-      flush_lines(map, trace.color, style_.device(trace.width), dash);
+      // rather than as a polyline: one exactly vertical, pixel-snapped segment per column,
+      // spanning what that column's own points reach.
+      //
+      // The polyline's geometry at this density is a stack of near-vertical hairlines at
+      // *fractional* x -- an envelope bucket spans (spp/2, spp] samples, so there are one to
+      // two buckets per column, each emitting its own min->max hairline plus a connector to
+      // the next, about three and a half per column. Each is composited with its own
+      // sub-pixel coverage, so a column's brightness is a non-linear function of those
+      // phases; the phases repeat at the beat between the bucket pitch and the pixel pitch,
+      // which is a **moire** across the trace, and panning sweeps the beat so the pattern
+      // crawls. It is strongest exactly where a scope is used hardest: a high sample rate, a
+      // high signal frequency, or a noisy signal, all of which make the ribbon thin enough
+      // for its per-column coverage to be visible as texture.
+      //
+      // Reducing to one segment per column removes the cause rather than the symptom: there
+      // is one phase on the whole trace (and the snap puts it on the grid), so there is
+      // nothing left to beat. It is also O(axes.w) geometry instead of O(buckets), and it
+      // loses nothing a reader could have seen -- a column cannot show more than the extremes
+      // of what it covers, which is what the band is.
+      //
+      // Two conditions, and each refuses a case this would damage.
+      // - `Envelope` only. `Nearest` and `Mean` are one-point-per-bucket modes chosen so the
+      //   trace reads as *samples* or as a smoothed line; a min/max band would answer a
+      //   different question from the one the host asked.
+      // - Two points per column. Below that the gather is sparser than the grid, and the
+      //   polyline's segments are the shape: `Series::gather()` also falls back to raw samples
+      //   when no complete bucket fits the range, and that window's trace is drawn by the two
+      //   segments that enter and leave the frame (see
+      //   `a_sparse_window_between_samples_still_inks_both_margins`). The real envelope path
+      //   emits two to four points per column by construction, so the test holds exactly when
+      //   it ran.
+      const bool columns = trace.mode == data::GatherMode::Envelope &&
+                           static_cast<f64>(points) >= 2.0 * static_cast<f64>(layout.axes.w);
+      // `snap = true` on geometry that is not chrome, which is the one carve-out in that
+      // uniform's rule ("a line that reports a data position may not be moved off it"): a
+      // column *is* a pixel column, and its x is already a screen coordinate derived from
+      // one -- there is no data position to move it off. The y bounds, which are what the
+      // segment reports, are untouched by the snap. It holds for both staging paths.
+      const u32 staged =
+          !columns ? 0u
+          : grade  ? stage_trace_density(plot, layout, trace, x_range.min, points)
+                   : stage_trace_columns(plot, layout, trace, x_range.min, points);
+      if (staged != 0u && grade) {
+        // One draw call per alpha step, faintest first: the line pipeline's colour is a
+        // uniform, so a per-segment alpha is not expressible and a step is a batch. They
+        // are flushed in order so the bright ridge composites over the faint tail rather
+        // than under it -- the runs within a column do not overlap, but their AA fringes
+        // do, and that is the order a phosphor display puts them in.
+        for (u32 t = 0; t < steps_.size(); ++t) {
+          if (steps_[t].segment_count() == 0u) continue;
+          Color color = trace.color;
+          color.a *= style_.intensity_floor +
+                     (1.0f - style_.intensity_floor) * static_cast<f32>(t) /
+                         static_cast<f32>(steps_.size() - 1u);
+          flush_lines(steps_[t], pixel_mapping(), color, style_.device(trace.width), dash, true);
+        }
+        ++stats_.column_traces;
+        ++stats_.graded_traces;
+      } else if (staged != 0u) {
+        flush_lines(pixel_mapping(), trace.color, style_.device(trace.width), dash, true);
+        ++stats_.column_traces;
+      } else {
+        // The sparse half of the phosphor model. `grade` is not reused as the gate: it
+        // requires `Envelope`, because the *column reduction* turns a bucket's min/max
+        // into a band and that answers a different question from the one a `Nearest` or
+        // `Mean` host asked. A segment's slope is a property of the polyline itself, so
+        // no gather mode is excluded here.
+        const u32 sparse =
+            style_.intensity_grading && style_.intensity_steps > 1u
+                ? stage_trace_slopes(plot, trace, gather_.data(), points, x_range.min, log_x,
+                                     log_y)
+                : 0u;
+        if (sparse != 0u) {
+          // Faintest first, and `snap = false` -- the same order as the graded columns
+          // for the same compositing reason, but these segments sit at *data* positions
+          // and the snap uniform's rule applies to them in full.
+          for (u32 t = 0; t < steps_.size(); ++t) {
+            if (steps_[t].segment_count() == 0u) continue;
+            Color color = trace.color;
+            color.a *= style_.intensity_floor +
+                       (1.0f - style_.intensity_floor) * static_cast<f32>(t) /
+                           static_cast<f32>(steps_.size() - 1u);
+            flush_lines(steps_[t], map, color, style_.device(trace.width), dash, false);
+          }
+          ++stats_.slope_traces;
+        } else {
+          stage_xy(gather_.data(), points, x_range.min, log_x, log_y);
+          flush_lines(map, trace.color, style_.device(trace.width), dash);
+        }
+      }
     }
 
     // Markers, staged as line segments through this same batch in *pixel* space
@@ -1240,6 +1755,123 @@ void Renderer::draw_cursor_label(const Plot& plot, const PlotLayout& layout, con
   }
 }
 
+void Renderer::draw_invalid_spans(const PlotLayout& layout) {
+  for (const InvalidSpanLayout& band : layout.invalid_spans) {
+    fill_pixels(band.fill, band.repaired ? style_.invalid_repaired_fill : style_.invalid_fill);
+  }
+}
+
+void Renderer::draw_density(const Plot& plot, const PlotLayout& layout) {
+  const DensityConfig& config = plot.density();
+  if (!config.enabled) {
+    // A plot that has stopped drawing a density is not holding a stale one: forget what the shared
+    // texture holds, so a re-enable -- which drops the grids and rebuilds them, possibly at the same
+    // addresses and with fresh revisions -- re-uploads rather than trusting a cache entry that
+    // happens to match.
+    density_uploaded_grid_ = nullptr;
+    return;
+  }
+  if (!(layout.axes.w > 0.0f) || !(layout.axes.h > 0.0f)) return;
+  if (!density_program_.valid()) return;  // a pipeline that never linked draws nothing
+  // One quad per trace, in that trace's own colour: the plot holds one grid per trace (see
+  // `DensityConfig`), so where two traces agree the viewer sees both colours, and a saturated cell
+  // is the colour of the trace whose ink filled it and not a blend. A trace with no visible series
+  // was deposited into nothing (its grid is empty), so it is skipped.
+  for (u32 i = 0u; i < plot.trace_count(); ++i) {
+    const Trace& trace = plot.trace(i);
+    if (!trace.visible()) continue;
+    draw_density_grid(config, plot.density_grid(i), trace.color, layout);
+  }
+}
+
+void Renderer::draw_density_grid(const DensityConfig& config, const DensityGrid& grid, Color tint,
+                                 const PlotLayout& layout) {
+  const u32 columns = grid.columns();
+  const u32 rows = grid.rows();
+  if (columns == 0u || rows == 0u) return;
+
+  // The image as the shader reads it: one byte per cell, `full_scale` and `gamma` already
+  // applied. The conversion lives here rather than in the fragment shader so that a cell's
+  // *count* has exactly one reading -- the plot's, which is also what a host reads back through
+  // `DensityGrid::ink()`/`peak()`, and which decays once per frame on the CPU anyway.
+  //
+  // **One texture, re-filled per trace.** The cache is keyed by the grid's own address as well as
+  // its revision, so a plot drawn twice with nothing changed (the steady state of a display that
+  // has stopped being swept) skips the conversion *and* the upload -- while a row of several traces
+  // re-fills the one texture once per trace, which is what a figure of several rows already cost
+  // before the density was per trace.
+  const bool resized = columns != density_w_ || rows != density_h_;
+  if (resized) {
+    if (!density_texture_.create_r8(columns, rows, nullptr)) {
+      gl_error_ = true;
+      return;
+    }
+    // **Linear, and it used to be a point sample.** The filter is the thing that makes a cell
+    // bigger than a pixel acceptable: a cell is a *count*, a continuous quantity, so a fragment
+    // between two of them is between their two ink levels -- which is exactly what a linear tap
+    // returns, and what a `GL_NEAREST` fetch cannot (it would show the grid's own steps as blocks
+    // once the image is scaled up, `kDensityCellCap` cells spread across a wider axes rect). The
+    // nearest tap was right only while a cell *was* a device pixel and every fragment landed in
+    // its own; minification interpolates for the same reason, so a plot whose rect is under the
+    // cap (cell and pixel one and the same, up to the rounding of `ceil`) reads as it always did.
+    density_texture_.set_filter(gl::GL_LINEAR, gl::GL_LINEAR);
+    density_w_ = columns;
+    density_h_ = rows;
+    density_uploaded_grid_ = nullptr;  // a fresh texture holds nothing
+  }
+  if (resized || density_uploaded_grid_ != &grid || grid.revision() != density_uploaded_revision_) {
+    const f32 full = config.full_scale > 0.0f ? config.full_scale : 1.0f;
+    const f32 gamma = config.gamma > 0.0f ? config.gamma : 1.0f;
+    // The gamma through a 256-entry table rather than a `pow` per cell: the output *is* eight
+    // bits, so quantising the count first and lifting the quantised value costs nothing a
+    // per-cell `pow` would have bought, and it keeps the per-frame pass a loop of multiplies.
+    u8 lut[256];
+    for (u32 i = 0u; i < 256u; ++i) {
+      const f32 v = static_cast<f32>(i) / 255.0f;
+      lut[i] = static_cast<u8>(std::clamp(std::pow(v, gamma), 0.0f, 1.0f) * 255.0f + 0.5f);
+    }
+    density_pixels_.resize(grid.cell_count());
+    const f32* cells = grid.cells().data();
+    for (usize i = 0; i < density_pixels_.size(); ++i) {
+      const f32 v = cells[i] / full;
+      const u32 quantised =
+          static_cast<u32>(std::clamp(v, 0.0f, 1.0f) * 255.0f + 0.5f);
+      density_pixels_[i] = lut[std::min(quantised, 255u)];
+    }
+    // `upload_r8` sets GL_UNPACK_ALIGNMENT to 1 and leaves it there (see gl::Texture), so the
+    // host's own value is saved and put back -- the same care `TextAtlas::sync()` takes around
+    // its own upload, since the two share a context and a frame.
+    gl::GLint alignment = 4;
+    gl::glGetIntegerv(gl::GL_UNPACK_ALIGNMENT, &alignment);
+    density_texture_.upload_r8(columns, rows, density_pixels_.data());
+    gl::glPixelStorei(gl::GL_UNPACK_ALIGNMENT, alignment);
+    density_uploaded_grid_ = &grid;
+    density_uploaded_revision_ = grid.revision();
+    // += and not =: a figure draws a density per trace per row, and what this field reports is the
+    // frame's upload, not the last one's.
+    stats_.density_upload_bytes += columns * rows;
+  }
+
+  // The quad covers the image's own **footprint**: the axes rect rounded up to whole device pixels,
+  // the rect `Plot::size_density_grids()` counted the cells on. While that rect is under
+  // `kDensityCellCap` it is exactly `columns` by `rows` pixels -- one texel a pixel, the mapping
+  // this has always had -- and past the cap the grid is smaller and the image is magnified back
+  // over it. The uv still runs 0..1 over the quad, so a fragment between two cells is a linear
+  // blend of them: the filter the texture was created with.
+  density_program_.bind();
+  density_program_.set_viewport({viewport_.w, viewport_.h});
+  density_program_.set_rect({layout.axes.x, layout.axes.y},
+                            {std::ceil(layout.axes.w), std::ceil(layout.axes.h)});
+  // The tint is the trace's own colour: its alpha is the trace's, so a saturated cell reads as the
+  // trace at its own brightness, and the shader multiplies it by the cell's luminance.
+  density_program_.set_color(tint);
+  density_texture_.bind();
+  density_vao_.bind();
+  gl::glDrawArrays(gl::GL_TRIANGLE_STRIP, 0, 4);
+  stats_.density_cells += columns * rows;
+  ++stats_.draw_calls;
+}
+
 void Renderer::draw_regions(const Plot& plot, const PlotLayout& layout) {
   const HotHandles hot = plot.hot_handles();
   const f32 edge_w = style_.device(style_.line_width_px);
@@ -1463,6 +2095,27 @@ void Renderer::stage_marker(plot::Marker marker, Vec2 centre_px, f32 size_px) {
   }
 }
 
+void Renderer::draw_selection_frame(const PlotLayout& layout) {
+  const Rect& frame = layout.selection;
+  // Two guards, not one: a drag swept flat in one direction has a real extent on one axis and none on
+  // the other, and a border on that is still the gesture's own answer -- the fill is what a zero
+  // extent has nothing of.
+  if (!(frame.w > 0.0f) && !(frame.h > 0.0f)) return;
+  if (frame.w > 0.0f && frame.h > 0.0f) fill_pixels(frame, style_.selection_fill);
+  // The border frames the pixels the fill covers and not the measured rect's own fractional edges:
+  // the readout panel's rounding and the readout panel's reason, since a hairline straddling a
+  // fractional edge is a frame bright on two sides and dim on the others.
+  const f32 left = std::ceil(frame.x - 0.5f) + 0.5f;
+  const f32 right = std::ceil(frame.right() - 0.5f) - 0.5f;
+  const f32 top = std::ceil(frame.y - 0.5f) + 0.5f;
+  const f32 bottom = std::ceil(frame.bottom() - 0.5f) - 0.5f;
+  lines_.add_segment({left, top}, {right, top});
+  lines_.add_segment({left, bottom}, {right, bottom});
+  lines_.add_segment({left, top}, {left, bottom});
+  lines_.add_segment({right, top}, {right, bottom});
+  flush_lines(pixel_mapping(), style_.selection_edge, style_.device(1.0f));
+}
+
 void Renderer::draw_readout_panel(const Rect& panel, Color border) {
   if (!(panel.w > 0.0f) || !(panel.h > 0.0f)) return;
   // The frame's own background at a partial alpha, which dims whatever it covers instead of erasing

src/render/shaders.cpp

@@ -235,4 +235,48 @@ void main() {
 }
 )";
 
+const char* const kDensityVS = R"(#version 330 core
+// No vertex attributes at all: the image is one axis-aligned rectangle whose corners are
+// uniform state, so the quad comes from gl_VertexID alone and there is no vertex buffer to
+// fill. The density's own bytes go to a texture (see kDensityFS), never to a buffer.
+uniform vec2 u_viewport;  // render target size, pixels
+uniform vec2 u_origin;    // the quad's top-left corner in Rect pixels
+uniform vec2 u_size;      // the quad's size in pixels -- the axes rect, which the image fills
+
+out vec2 v_uv;
+
+void main() {
+  // A four-vertex triangle strip, like the line and text pipelines: the corner index is the
+  // vertex id's two bits, so 0,1,2,3 are (0,0), (1,0), (0,1), (1,1).
+  vec2 corner = vec2(float(gl_VertexID & 1), float((gl_VertexID >> 1) & 1));
+  vec2 px = u_origin + corner * u_size;
+  // Rect is top-left origin, GL is bottom-left: the one and only y flip.
+  vec2 ndc = vec2(px.x / u_viewport.x * 2.0 - 1.0, 1.0 - px.y / u_viewport.y * 2.0);
+  gl_Position = vec4(ndc, 0.0, 1.0);
+  // uv runs 0..1 across the whole image, so a fragment lands wherever the axes rect puts it
+  // between the grid's cells: one texel a cell while the rect is under the cap (a cell a device
+  // pixel, the sampling all but a point sample) and a linear magnification of the image past it.
+  v_uv = corner;
+}
+)";
+
+const char* const kDensityFS = R"(#version 330 core
+in vec2 v_uv;  // cell coordinate in [0,1] across the quad
+
+uniform sampler2D u_density;  // GL_R8 luminance, one texel per cell, GL_LINEAR
+uniform vec4 u_color;
+
+out vec4 o_color;
+
+void main() {
+  // The cell's count was already turned into a luminance on the CPU, where the count, the
+  // decay and the gamma live -- so this stage has no scale of its own that a host reading the
+  // grid's numbers back could disagree with. All that is left is the tint: the density is drawn
+  // once per trace, in that trace's own colour (the caller's `u_color`), so a saturated cell is
+  // the trace at its own brightness and a faint one is the same hue at a lower alpha.
+  float ink = texture(u_density, v_uv).r;
+  o_color = vec4(u_color.rgb, u_color.a * ink);
+}
+)";
+
 }  // namespace plot::render

tests/harness.hpp

@@ -3,6 +3,7 @@
 
 #pragma once
 #include <cstdio>
+#include <cstdlib>
 #include <cmath>
 #include <chrono>
 #include <algorithm>
@@ -57,7 +58,9 @@ inline void check_near(double a, double b, const char* file, int line, const cha
 
 inline int run_all() {
   int failed = 0;
+  const char* only = std::getenv("PLOT_TEST_FILTER");
   for (auto& c : cases()) {
+    if (only != nullptr && std::string(c.name).find(only) == std::string::npos) continue;
     try {
       c.fn();
       std::printf("[ ok ] %s\n", c.name);

tests/test_controller.cpp

@@ -2403,3 +2403,54 @@ PLOT_TEST(an_unselectable_cursor_is_neither_hovered_nor_grabbed) {
   PLOT_CHECK_NEAR(p.cursor(readout).x, before, 1e-12);
   PLOT_CHECK(c.grabbed_cursor() == normal);
 }
+
+PLOT_TEST(a_ctrl_box_zoom_previews_the_band_it_will_zoom) {
+  // What a host draws for an open box zoom is not always the area the pointer swept. Ctrl frames the
+  // x range only, so what its release will change is a *band* across the plot -- and a pointer dragged
+  // straight across sweeps a sliver a couple of pixels tall, which would be the frame showing the
+  // gesture instead of its effect. Shift frames both axes and gets the swept box itself; Alt is the
+  // other single-axis mask, and gets the other frame.
+  plot::Plot p;
+  p.set_viewport({0, 0, 800, 400});
+  p.add_x_axis({"t", {0.0, 800.0}, true, plot::AxisPlace::Bottom, false});
+  const plot::Rect axes = p.layout().axes;
+  constexpr plot::u32 kAlt = static_cast<plot::u32>(plot::input::Mod::Alt);
+  plot::input::Controller c(p);
+  c.set_viewport({0, 0, 800, 400});
+
+  c.on_pointer({100, 200, 0, 0, plot::input::Button::Left, kCtrl, true, true, false});
+  // Nothing framed until something was swept: the press alone is an empty rect at the pointer, and a
+  // full-width band derived from it would claim a range that does not exist yet.
+  PLOT_CHECK_NEAR(c.selection_preview().w, 0.0, 1e-6);
+  c.on_pointer({300, 202, 200, 2, plot::input::Button::Left, kCtrl, true, false, false});
+  const plot::Rect ctrl = c.selection_preview();
+  PLOT_CHECK_NEAR(ctrl.x, 100.0, 1e-6);
+  PLOT_CHECK_NEAR(ctrl.w, 200.0, 1e-6);
+  PLOT_CHECK_NEAR(ctrl.y, axes.y, 1e-6);
+  PLOT_CHECK_NEAR(ctrl.h, axes.h, 1e-6);
+  // The gesture's own geometry is untouched: the widening happens in the preview, so the range the
+  // release computes is still the one the pointer described.
+  PLOT_CHECK_NEAR(c.selection_rect().h, 2.0, 1e-6);
+  c.on_pointer({300, 202, 0, 0, plot::input::Button::Left, kCtrl, false, false, true});
+
+  c.on_pointer({100, 50, 0, 0, plot::input::Button::Left, kShift, true, true, false});
+  c.on_pointer({400, 150, 300, 100, plot::input::Button::Left, kShift, true, false, false});
+  const plot::Rect both = c.selection_preview();
+  PLOT_CHECK_NEAR(both.x, 100.0, 1e-6);
+  PLOT_CHECK_NEAR(both.y, 50.0, 1e-6);
+  PLOT_CHECK_NEAR(both.w, 300.0, 1e-6);
+  PLOT_CHECK_NEAR(both.h, 100.0, 1e-6);
+  c.on_pointer({400, 150, 0, 0, plot::input::Button::Left, kShift, false, false, true});
+
+  c.on_pointer({100, 50, 0, 0, plot::input::Button::Left, kAlt, true, true, false});
+  c.on_pointer({110, 150, 10, 100, plot::input::Button::Left, kAlt, true, false, false});
+  const plot::Rect alt = c.selection_preview();
+  PLOT_CHECK_NEAR(alt.x, axes.x, 1e-6);
+  PLOT_CHECK_NEAR(alt.w, axes.w, 1e-6);
+  PLOT_CHECK_NEAR(alt.y, 50.0, 1e-6);
+  PLOT_CHECK_NEAR(alt.h, 100.0, 1e-6);
+  c.on_pointer({110, 150, 0, 0, plot::input::Button::Left, kAlt, false, false, true});
+  // Closed: a frame on a finished gesture would claim the old selection is still open.
+  PLOT_CHECK(c.drag_mode() == plot::input::DragMode::None);
+  PLOT_CHECK_NEAR(c.selection_preview().w, 0.0, 1e-6);
+}

tests/test_figure.cpp

@@ -16,6 +16,7 @@
 #include <plot/render/embedded_mono_font.hpp>
 
 #include <cmath>
+#include <span>
 #include <vector>
 
 namespace {
@@ -1141,3 +1142,136 @@ PLOT_TEST(figure_crosshair_draws_a_horizontal_line_only_in_the_hovered_row) {
   PLOT_CHECK(figure.plot(1u).layout().crosshair.vertical.w > 0.0f);
   PLOT_CHECK(figure.plot(1u).layout().crosshair.horizontal.h == 0.0f);
 }
+
+// ------------------------------------------------------------------ cell grid
+
+namespace {
+
+/// A figure whose rows hold `cells[r]` plots each (the flattened plots in row-major
+/// order), with an x and a y axis on every plot unless `axes` is off.
+plot::Figure split_figure(const std::vector<plot::u32>& cells, bool axes = true) {
+  plot::Figure figure{std::span<const plot::u32>(cells)};  // braces: parentheses would be a vexing parse
+  figure.set_viewport(whole_figure());
+  if (axes) {
+    for (plot::u32 i = 0; i < figure.plot_count(); ++i) {
+      figure.plot(i).add_x_axis({"t", {0.0, 100.0}, false, plot::AxisPlace::Bottom, false});
+      figure.plot(i).add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+    }
+  }
+  return figure;
+}
+
+}  // namespace
+
+PLOT_TEST(figure_cells_all_ones_equals_rows) {
+  plot::Figure split = split_figure({1, 1, 1});
+  plot::Figure plain = figure_with_axes(3u);
+  const plot::FigureLayout& sl = split.layout();
+  const plot::FigureLayout& pl = plain.layout();
+  PLOT_CHECK(split.row_count() == 3u && split.plot_count() == 3u);
+  PLOT_CHECK(sl.cells.size() == 3u);
+  for (plot::u32 i = 0; i < 3u; ++i) {
+    PLOT_CHECK_NEAR(sl.cells[i].y, pl.rows[i].y, 0.01);
+    PLOT_CHECK_NEAR(sl.cells[i].h, pl.rows[i].h, 0.01);
+    PLOT_CHECK_NEAR(sl.cells[i].w, pl.rows[i].w, 0.01);
+  }
+}
+
+PLOT_TEST(figure_cells_tile_exactly) {
+  plot::Figure figure = split_figure({1, 2, 1});
+  figure.set_col_gap(10.0f);
+  const plot::FigureLayout& fl = figure.layout();
+  PLOT_CHECK(figure.row_count() == 3u && figure.plot_count() == 4u);
+  PLOT_CHECK(figure.cells_in_row(1u) == 2u);
+  PLOT_CHECK(figure.first_plot_of_row(1u) == 1u && figure.first_plot_of_row(3u) == 4u);
+  PLOT_CHECK(figure.row_of_plot(2u) == 1u);
+  PLOT_CHECK_NEAR(fl.cells[2].x - fl.cells[1].right(), 10.0, 0.01);
+  PLOT_CHECK_NEAR(fl.cells[2].right(), fl.rows[1].right(), 0.001);
+  PLOT_CHECK_NEAR(fl.cells[1].x, fl.rows[1].x, 0.001);
+  PLOT_CHECK_NEAR(fl.cells[1].y, fl.cells[2].y, 0.001);
+  PLOT_CHECK_NEAR(fl.cells[1].h, fl.cells[2].h, 0.001);
+  PLOT_CHECK_NEAR(fl.cells[1].w, fl.cells[2].w, 0.01);
+  PLOT_CHECK_NEAR(fl.col_gap, 10.0, 0.001);
+}
+
+PLOT_TEST(figure_cell_weights_and_floor) {
+  plot::Figure figure = split_figure({2});
+  figure.set_col_gap(0.0f);
+  const std::vector<plot::f32> w{3.0f, 1.0f};
+  PLOT_CHECK(figure.set_cell_weights(0u, w));
+  PLOT_CHECK(figure.has_cell_weights(0u));
+  {
+    const auto& c = figure.layout().cells;
+    PLOT_CHECK_NEAR((c[0].w - 64.0), (c[1].w - 64.0) * 3.0, 0.01);
+  }
+  const std::vector<plot::f32> tiny{1000.0f, 0.001f};
+  PLOT_CHECK(figure.set_cell_weights(0u, tiny));
+  PLOT_CHECK(figure.layout().cells[1].w >= 64.0f - 0.001f);
+  const std::vector<plot::f32> three{1.0f, 1.0f, 1.0f};
+  const std::vector<plot::f32> zero{1.0f, 0.0f};
+  PLOT_CHECK(!figure.set_cell_weights(0u, three));
+  PLOT_CHECK(!figure.set_cell_weights(0u, zero));
+  PLOT_CHECK(!figure.set_cell_weights(5u, w));
+  figure.clear_cell_weights(0u);
+  PLOT_CHECK(!figure.has_cell_weights(0u));
+  const auto& c = figure.layout().cells;
+  PLOT_CHECK_NEAR(c[0].w, c[1].w, 0.01);
+}
+
+PLOT_TEST(figure_cells_narrow_degrades) {
+  plot::Figure figure = split_figure({4}, false);
+  figure.set_viewport(plot::Rect{0.0f, 0.0f, 20.0f, 100.0f});
+  for (plot::u32 i = 0; i < 4u; ++i) {
+    figure.plot(i).add_x_axis({"t", {0.0, 100.0}, false, plot::AxisPlace::Bottom, false});
+    figure.plot(i).add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+  }
+  figure.set_col_gap(10.0f);
+  const plot::FigureLayout& fl = figure.layout();
+  double sum = 0.0;
+  for (const plot::Rect& c : fl.cells) {
+    PLOT_CHECK(c.w >= 0.0f && c.h >= 0.0f);
+    PLOT_CHECK_NEAR(c.h, 100.0, 0.01);
+    sum += c.w;
+  }
+  PLOT_CHECK_NEAR(sum, 20.0, 0.01);
+  PLOT_CHECK_NEAR(fl.col_gap, 0.0, 0.001);
+}
+
+PLOT_TEST(figure_cells_share_x_link_and_crosshair) {
+  plot::Figure figure = split_figure({2, 1});
+  const plot::u32 group = figure.add_x_link();
+  for (plot::u32 i = 0; i < 3u; ++i) PLOT_CHECK(figure.link_x(i, group));
+  figure.plot(1u).set_x_range(0u, {3.0, 9.0});
+  figure.layout();
+  for (plot::u32 i = 0; i < 3u; ++i) {
+    PLOT_CHECK_NEAR(figure.plot(i).x_range(0u).min, 3.0, 1e-9);
+    PLOT_CHECK_NEAR(figure.plot(i).x_range(0u).max, 9.0, 1e-9);
+  }
+  figure.set_crosshair(4.0, true);
+  for (plot::u32 i = 0; i < 3u; ++i) {
+    PLOT_CHECK(figure.plot(i).crosshair().active);
+    PLOT_CHECK_NEAR(figure.plot(i).crosshair().x, 4.0, 1e-9);
+  }
+  figure.clear_crosshair();
+  for (plot::u32 i = 0; i < 3u; ++i) PLOT_CHECK(!figure.plot(i).crosshair().active);
+}
+
+PLOT_TEST(figure_cells_x_labels_bottom_row_only) {
+  plot::Figure figure = split_figure({1, 2});
+  const plot::FigureLayout& fl = figure.layout();
+  PLOT_CHECK(figure.plot(0u).layout().x_label_area.h == 0.0f);
+  PLOT_CHECK(figure.plot(1u).layout().x_label_area.h > 0.0f);
+  PLOT_CHECK(figure.plot(2u).layout().x_label_area.h > 0.0f);
+  PLOT_CHECK_NEAR(fl.x_axis_strip.h, figure.plot(2u).layout().x_label_area.h, 0.001);
+}
+
+PLOT_TEST(figure_cells_common_y_gutter) {
+  plot::Figure figure = split_figure({2}, false);
+  give_magnitude_row(figure.plot(0u), 0u);
+  give_magnitude_row(figure.plot(1u), 1u);
+  const plot::FigureLayout& fl = figure.layout();
+  const double g0 = figure.plot(0u).layout().axes.x - fl.cells[0].x;
+  const double g1 = figure.plot(1u).layout().axes.x - fl.cells[1].x;
+  PLOT_CHECK(g0 > 0.0);
+  PLOT_CHECK_NEAR(g0, g1, 0.01);
+}

tests/test_glfw_host.cpp

@@ -14,6 +14,9 @@
 #include <glfw/glfw_host.hpp>
 #include <plot/plot/figure.hpp>
 
+#include <span>
+#include <vector>
+
 namespace {
 
 /// A figure of `rows` rows over a known rect, with an x and a y axis in every row (so
@@ -315,3 +318,31 @@ PLOT_TEST(the_host_keeps_its_own_controller_while_no_figure_is_set) {
   PLOT_CHECK(host.row_controller(0u) == nullptr);
   PLOT_CHECK(&host.controller_at(10.0f, 10.0f) == &host.controller());
 }
+
+PLOT_TEST(glfw_host_routes_by_cell) {
+  // A figure of two rows, the first of one cell and the second of two side by side: the
+  // pointer's x as well as its y picks the plot, and the controllers are indexed by the
+  // flattened plot.
+  std::vector<plot::u32> cells{1, 2};
+  plot::Figure figure{std::span<const plot::u32>(cells)};
+  figure.set_viewport(plot::Rect{0, 0, 300, 600});
+  figure.set_col_gap(6.0f);
+  for (plot::u32 i = 0; i < 3; ++i) {
+    figure.plot(i).add_x_axis({"t", {0.0, 1.0}, false, plot::AxisPlace::Bottom, false});
+    figure.plot(i).add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+  }
+  plot::glfw::Host host;
+  host.set_figure(&figure);
+  const std::vector<plot::Rect> c = figure.layout().cells;
+  PLOT_CHECK(c.size() == 3u);
+  for (plot::u32 i = 0; i < 3; ++i) {
+    PLOT_CHECK(host.row_controller(i) != nullptr);
+    const double cx = c[i].x + c[i].w * 0.5, cy = c[i].y + c[i].h * 0.5;
+    PLOT_CHECK(&host.controller_at(static_cast<plot::f32>(cx), static_cast<plot::f32>(cy)) ==
+               host.row_controller(i));
+  }
+  PLOT_CHECK(host.row_controller(3u) == nullptr);
+  // in the column gap: the nearest cell wins
+  PLOT_CHECK(&host.controller_at(c[1].right() + 1.0f, c[1].y + 5.0f) == host.row_controller(1));
+  PLOT_CHECK(&host.controller_at(c[2].x - 1.0f, c[2].y + 5.0f) == host.row_controller(2));
+}

tests/test_minmax_pyramid.cpp

@@ -6,6 +6,7 @@
 #include <plot/data/detail/merge_count.hpp>
 #include <plot/data/minmax_pyramid.hpp>
 #include <algorithm>
+#include <limits>
 #include <random>
 
 using plot::data::kBucket;
@@ -342,3 +343,69 @@ PLOT_TEST(pyramid_level_cap_keeps_the_span_shift_defined) {
   p.append(1.0f);
   PLOT_CHECK(p.level_count() >= 1);
 }
+
+PLOT_TEST(amend_folds_a_backfilled_sample_into_every_covering_level) {
+  // A hole is appended as NaN -- which the pyramid already stores as an empty aggregate --
+  // and amended later when the packet that owned it finally arrives. The amendment has to
+  // reach every level that covers the index, because the renderer reads whichever level the
+  // zoom picked: repairing level 0 alone would make a trace whole when zoomed in and still
+  // broken when zoomed out.
+  MinMaxPyramid p;
+  p.reserve(8 * kBucket);
+  for (u64 i = 0; i < 8 * kBucket; ++i) {
+    // One NaN, at an index comfortably inside the first bucket of every level.
+    p.append(i == 5 ? std::numeric_limits<f32>::quiet_NaN() : 1.0f);
+  }
+  // Before: every covering bucket aggregates kBucket-1 ones and knows nothing of index 5.
+  PLOT_CHECK(p.bucket_count(0, 0) == kBucket - 1);
+  PLOT_CHECK_NEAR(p.bucket(0, 0).max, 1.0);
+
+  p.amend(5, 7.0f);
+
+  // Level 0 gained the sample.
+  PLOT_CHECK(p.bucket_count(0, 0) == kBucket);
+  PLOT_CHECK_NEAR(p.bucket(0, 0).max, 7.0);
+  PLOT_CHECK_NEAR(p.bucket_sum(0, 0), f64(kBucket - 1) + 7.0);
+  PLOT_CHECK_NEAR(p.bucket_sumsq(0, 0), f64(kBucket - 1) + 49.0);
+  // And so did every coarser level that covers it.
+  for (u32 l = 1; l < p.level_count(); ++l) {
+    if (p.level_size(l) == 0) continue;
+    const u64 span = u64{kBucket} << l;
+    const u64 b = 5 / span;
+    if (b < p.level_base(l) || b - p.level_base(l) >= p.level_size(l)) continue;
+    PLOT_CHECK_NEAR(p.bucket(l, b).max, 7.0);
+    PLOT_CHECK(p.bucket_count(l, b) == span);
+  }
+}
+
+PLOT_TEST(amend_makes_an_all_nan_bucket_present_again) {
+  // A bucket whose every sample was non-finite is stored with count 0, which every reader
+  // treats as absent. One amendment has to make it present -- min and max become the value
+  // rather than widening from a meaningless zero, which is the case a plain fold gets wrong.
+  MinMaxPyramid p;
+  p.reserve(4 * kBucket);
+  const f32 nan = std::numeric_limits<f32>::quiet_NaN();
+  for (u64 i = 0; i < 2 * kBucket; ++i) p.append(i < kBucket ? nan : 1.0f);
+  PLOT_CHECK(p.bucket_count(0, 0) == 0);
+
+  p.amend(3, -2.0f);
+
+  PLOT_CHECK(p.bucket_count(0, 0) == 1);
+  PLOT_CHECK_NEAR(p.bucket(0, 0).min, -2.0);
+  PLOT_CHECK_NEAR(p.bucket(0, 0).max, -2.0);
+}
+
+PLOT_TEST(amend_outside_the_window_is_a_no_op) {
+  // An index the window has already dropped, or one not yet appended, has nowhere to go.
+  // Silently ignoring it is what lets the caller amend without first proving the ring still
+  // holds the slot -- a race it cannot win, because the window slides on the other thread.
+  MinMaxPyramid p;
+  p.reserve(4 * kBucket);
+  for (u64 i = 0; i < 4 * kBucket; ++i) p.append(1.0f);
+  p.drop_before(2 * kBucket);
+  const u64 before = p.bucket_count(0, 2);
+  p.amend(5, 99.0f);                 // dropped
+  p.amend(100 * kBucket, 99.0f);     // never appended
+  PLOT_CHECK(p.bucket_count(0, 2) == before);
+  PLOT_CHECK_NEAR(p.bucket(0, 2).max, 1.0);
+}

tests/test_plot.cpp

@@ -2789,3 +2789,425 @@ PLOT_TEST(an_annotation_can_be_moved_by_id) {
   p.set_annotation(42u, other);
   PLOT_CHECK_NEAR(p.annotation(id).x, 3.5, 1e-12);
 }
+
+PLOT_TEST(the_selection_frame_is_carried_and_taken_off) {
+  // The box-zoom frame is the host's to set -- the plot has no controller and learns nothing about
+  // pointers -- so what it owes is to carry it: out through `layout()` unchanged, because it is
+  // already in viewport pixels and a second derivation would be a second rounding of the same
+  // rectangle, and gone when the host takes it off, because a frame left behind claims the selection
+  // is still open.
+  plot::Plot p;
+  p.set_viewport({0, 0, 800, 400});
+  PLOT_CHECK(p.layout().selection.w == 0.0f && p.layout().selection.h == 0.0f);  // nothing swept
+  p.set_selection_rect({10.0f, 20.0f, 30.0f, 40.0f});
+  PLOT_CHECK_NEAR(p.selection_rect().x, 10.0, 1e-6);
+  PLOT_CHECK_NEAR(p.layout().selection.y, 20.0, 1e-6);
+  PLOT_CHECK_NEAR(p.layout().selection.w, 30.0, 1e-6);
+  PLOT_CHECK_NEAR(p.layout().selection.h, 40.0, 1e-6);
+  p.clear_selection_rect();
+  PLOT_CHECK_NEAR(p.selection_rect().w, 0.0, 1e-6);
+  PLOT_CHECK_NEAR(p.layout().selection.h, 0.0, 1e-6);
+}
+
+// --- phosphor density -------------------------------------------------------
+
+namespace {
+
+/// A two-sample flat series: one segment across the whole window at y = 0, which is the
+/// simplest geometry a density can be read against -- one cell per column and nothing else.
+std::vector<f32> flat_pair() { return std::vector<f32>{0.0f, 0.0f}; }
+
+/// A plot with one flat trace over a 640x480 viewport, laid out. The axes rect it returns is
+/// the one `accumulate_density()` sizes the grid to, so a test reads both together.
+struct DensityFixture {
+  plot::data::ArraySeries series;
+  plot::Plot plot;
+  plot::u32 ax = 0;
+  plot::u32 ay = 0;
+
+  explicit DensityFixture(std::vector<f32> y = flat_pair(), plot::f64 dx = 1.0)
+      : series(std::move(y), 0.0, dx) {
+    plot.set_viewport({0.0f, 0.0f, 640.0f, 480.0f});
+    ax = plot.add_x_axis({"t", {0.0, 1.0}, false, plot::AxisPlace::Bottom, false});
+    ay = plot.add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+    PLOT_CHECK(plot.add_trace({&series, plot::Color::hex(0x00E070), 1.5f, ax, ay, "flat"}) == 0u);
+    plot.set_x_range(ax, {0.0, 1.0});
+    plot.set_y_range(ay, {-1.0, 1.0});
+    plot.layout();
+  }
+};
+
+}  // namespace
+
+/// The grid is the screen's, not the data's: one cell per device pixel of the axes rect **up to
+/// `kDensityCellCap`**, and nothing at all until the density is switched on. The figures here are
+/// the ones the API's memory claim rests on -- `cell_count * 4` bytes, whatever the trigger has
+/// done and whatever the window is.
+PLOT_TEST(a_density_grid_is_the_axes_in_device_pixels) {
+  DensityFixture f;
+  const plot::Rect axes = f.plot.layout().axes;
+  // The 640x480 viewport this fixture asks for is past the cap, so its grid is the axes rect
+  // *scaled down* -- the rule the library states, written out here so the assertion is arithmetic
+  // rather than a recorded number. A grid under the cap is the rect itself, which the 320x240 leg
+  // at the end reads.
+  const auto capped = [](plot::u32 w, plot::u32 h) {
+    std::pair<plot::u32, plot::u32> out{w, h};
+    const plot::u64 pixels = static_cast<plot::u64>(w) * static_cast<plot::u64>(h);
+    if (pixels > static_cast<plot::u64>(plot::kDensityCellCap)) {
+      const plot::f64 s = std::sqrt(static_cast<plot::f64>(plot::kDensityCellCap) /
+                                    static_cast<plot::f64>(pixels));
+      out.first = std::max(1u, static_cast<plot::u32>(static_cast<plot::f64>(w) * s));
+      out.second = std::max(1u, static_cast<plot::u32>(static_cast<plot::f64>(h) * s));
+    }
+    return out;
+  };
+  const auto [columns, rows] =
+      capped(static_cast<plot::u32>(std::ceil(axes.w)), static_cast<plot::u32>(std::ceil(axes.h)));
+  // The row a device y lands in is read through the grid's cells-per-*whole*-pixel, which is what
+  // the deposit uses (see `deposit_density_segment()`): 1 while the grid is the rect.
+  const plot::f32 sy = static_cast<plot::f32>(rows) / std::ceil(axes.h);
+  PLOT_CHECK(static_cast<plot::u64>(columns) * rows <= plot::kDensityCellCap);
+
+  // Off is the default, and off is *nothing*: no grid, no ink, and an accumulation that
+  // deposits nothing at all.
+  PLOT_CHECK(!f.plot.density().enabled);
+  f.plot.accumulate_density();
+  PLOT_CHECK(f.plot.density_grid(0u).cell_count() == 0u);
+  PLOT_CHECK(f.plot.density_grid(0u).ink() == 0.0);
+  PLOT_CHECK(f.plot.density_grid(0u).peak() == 0.0f);
+
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  f.plot.set_density(cfg);
+  PLOT_CHECK(f.plot.density().enabled);
+  f.plot.accumulate_density();
+
+  const plot::DensityGrid& grid = f.plot.density_grid(0u);
+  PLOT_CHECK(grid.columns() == columns);
+  PLOT_CHECK(grid.rows() == rows);
+  PLOT_CHECK(grid.cell_count() == static_cast<plot::usize>(columns) * rows);
+  // `4 bytes * cells`, and never more than the cap: the whole point of the bound.
+  const plot::usize bytes = grid.cell_count() * sizeof(plot::f32);
+  PLOT_CHECK(bytes <= static_cast<plot::usize>(plot::kDensityCellCap) * sizeof(plot::f32));
+  std::printf("[density] grid=%ux%u cells=%zu grid_bytes=%zu ink=%.0f peak=%.0f\n",
+              grid.columns(), grid.rows(), grid.cell_count(), bytes, grid.ink(),
+              static_cast<double>(grid.peak()));
+
+  // One flat trace over the whole window lights every column exactly once: one segment, no
+  // column reached twice, so the ink *is* the width and the peak is one pass.
+  PLOT_CHECK_NEAR(grid.ink(), static_cast<double>(columns), 1.0);
+  PLOT_CHECK_NEAR(grid.peak(), 1.0, 1e-4);
+
+  // ... and all of it in one row, the one y = 0 maps to.
+  const plot::Transform ty = f.plot.y_transform(f.ay);
+  const int row = static_cast<int>(std::floor((ty.to_screen_y(0.0) - axes.y) * sy));
+  plot::u32 lit = 0;
+  for (plot::u32 r = 0; r < grid.rows(); ++r) {
+    for (plot::u32 c = 0; c < grid.columns(); ++c) {
+      if (grid.at(c, r) <= 0.0f) continue;
+      ++lit;
+      PLOT_CHECK(static_cast<int>(r) == row);
+    }
+  }
+  PLOT_CHECK(lit == columns);
+
+  // The accumulation is a *screen* image: a plot that has moved to another axes rect gets a
+  // grid of that size and nothing carried over from the old one -- and that rect is under the
+  // cap, so the grid is it *exactly*: one cell a device pixel, no scaling at all.
+  f.plot.set_viewport({0.0f, 0.0f, 320.0f, 240.0f});
+  f.plot.layout();
+  f.plot.accumulate_density();
+  const plot::DensityGrid& small = f.plot.density_grid(0u);
+  const plot::Rect small_axes = f.plot.layout().axes;
+  PLOT_CHECK(small.columns() == static_cast<plot::u32>(std::ceil(small_axes.w)));
+  PLOT_CHECK(small.rows() == static_cast<plot::u32>(std::ceil(small_axes.h)));
+  PLOT_CHECK(small.cell_count() <= plot::kDensityCellCap);
+  PLOT_CHECK(small.columns() < columns);
+  PLOT_CHECK_NEAR(small.ink(), static_cast<double>(small.columns()), 1.0);
+}
+
+/// The cap is what keeps the resolution from following the window: a grid is never more than
+/// `kDensityCellCap` cells, whatever the axes rect is, so the memory a display holds and the frame
+/// pass over it are numbers and not functions of how wide the window was dragged. The scaling is
+/// **uniform**, so a cell stays square and the picture keeps the axes' aspect -- the reading that
+/// separates this from a cap on one axis, which would stretch every cell by the other one's ratio.
+PLOT_TEST(a_density_grid_is_capped_whatever_the_window) {
+  DensityFixture f;
+  f.plot.set_viewport({0.0f, 0.0f, 3840.0f, 2160.0f});
+  f.plot.layout();
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  f.plot.set_density(cfg);
+  f.plot.accumulate_density();
+
+  const plot::DensityGrid& grid = f.plot.density_grid(0u);
+  const plot::Rect axes = f.plot.layout().axes;
+  PLOT_CHECK(static_cast<plot::u64>(grid.columns()) * grid.rows() <= plot::kDensityCellCap);
+  PLOT_CHECK(grid.cell_count() * sizeof(plot::f32) <= 1'048'576u);
+  // ... and it is as large as the cap allows: flooring a uniform scale costs at most the two
+  // columns and rows the truncation drops, so the grid is within a hair of the whole budget.
+  PLOT_CHECK(static_cast<plot::f64>(grid.cell_count()) >
+             0.99 * static_cast<plot::f64>(plot::kDensityCellCap));
+  // Uniform: the grid's aspect is the axes rect's, to the rounding of the two floors.
+  PLOT_CHECK_NEAR(static_cast<plot::f64>(grid.columns()) / grid.rows(),
+                  static_cast<plot::f64>(axes.w) / axes.h, 0.01);
+
+  // A cap on the *cells* also returns a full sweep's worth of ink: one flat pass over the window
+  // is one per column however fine or coarse the grid is.
+  PLOT_CHECK_NEAR(grid.ink(), static_cast<double>(grid.columns()), 1.0);
+  PLOT_CHECK_NEAR(grid.peak(), 1.0, 1e-4);
+  std::printf("[density] capped grid=%ux%u cells=%zu bytes=%zu of a %ux%u axes\n", grid.columns(),
+              grid.rows(), grid.cell_count(), grid.cell_count() * sizeof(plot::f32),
+              static_cast<plot::u32>(std::ceil(axes.w)), static_cast<plot::u32>(std::ceil(axes.h)));
+}
+
+/// Per acquisition the image is multiplied by the factor *before* the new acquisition is
+/// deposited, so the sweep on screen is the brightest and the one behind it is the factor
+/// down: the schedule a phosphor's afterglow has, and the reading that says which way round
+/// the halving goes.
+PLOT_TEST(a_density_halves_per_acquisition_and_keeps_the_newest_brightest) {
+  DensityFixture f;
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  cfg.decay = plot::DensityDecay::PerAcquisition;
+  cfg.per_acquisition = 0.5f;
+  f.plot.set_density(cfg);
+
+  f.plot.accumulate_density();
+  // The grid is sized by the first accumulation, so the width is read after it -- and the ink
+  // of one pass *is* the width: one segment across the window, one cell per column.
+  const double width = static_cast<double>(f.plot.density_grid(0u).columns());
+  const double one = f.plot.density_grid(0u).ink();
+  PLOT_CHECK_NEAR(one, width, 1.0);
+
+  f.plot.accumulate_density();
+  const double two = f.plot.density_grid(0u).ink();
+  PLOT_CHECK_NEAR(two, width * 1.5, 2.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).peak(), 1.5f, 1e-3);
+
+  f.plot.accumulate_density();
+  const double three = f.plot.density_grid(0u).ink();
+  PLOT_CHECK_NEAR(three, width * 1.75, 2.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).peak(), 1.75f, 1e-3);
+
+  // The steady state of a stream that keeps sweeping: 1 + 1/2 + 1/4 + ... = 2 passes.
+  for (int i = 0; i < 40; ++i) f.plot.accumulate_density();
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).peak(), 2.0f, 1e-3);
+
+  // A factor of 0 is "only the newest acquisition is on screen": the grid is the last pass.
+  cfg.per_acquisition = 0.0f;
+  f.plot.set_density(cfg);
+  f.plot.accumulate_density();
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).ink(), width, 1.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).peak(), 1.0f, 1e-3);
+
+  std::printf("[density] per-acquisition ink: 1=%.0f 2=%.0f 3=%.0f peak_steady=%.3f\n", one, two,
+              three, 2.0);
+}
+
+/// The time constant is the other question: the image fades while you watch, by the frame's own
+/// `dt` against a constant stated in seconds, and it is the *caller* who advances it -- there is
+/// no clock in the library, which is what makes the reading reproducible.
+PLOT_TEST(a_density_fades_by_its_time_constant) {
+  DensityFixture f;
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  cfg.decay = plot::DensityDecay::TimeConstant;
+  cfg.time_constant_s = 2.0f;
+  f.plot.set_density(cfg);
+  f.plot.accumulate_density();
+  const double full = f.plot.density_grid(0u).ink();
+
+  // A frame that has not been measured yet (dt <= 0) does not wipe the grid, and neither does
+  // a frame under `PerAcquisition`, which fades in `accumulate_density()` instead.
+  f.plot.decay_density(0.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).ink(), full, 1e-6);
+  f.plot.decay_density(-1.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).ink(), full, 1e-6);
+
+  // Quarter of a time constant: exp(-0.25).
+  f.plot.decay_density(0.5);
+  const double quarter = full * std::exp(-0.25);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).ink(), quarter, quarter * 1e-4);
+
+  // Ten more constants and the display is gone to within a rounding: 4.5e-5 of the ink.
+  for (int i = 0; i < 10; ++i) f.plot.decay_density(2.0);
+  PLOT_CHECK(f.plot.density_grid(0u).ink() < quarter * 1e-3);
+  PLOT_CHECK(f.plot.density_grid(0u).peak() < 1e-3f);
+
+  // A non-positive constant freezes the grid rather than fading it.
+  cfg.time_constant_s = 0.0f;
+  f.plot.set_density(cfg);
+  f.plot.accumulate_density();
+  const double frozen = f.plot.density_grid(0u).ink();
+  f.plot.decay_density(100.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).ink(), frozen, 1e-6);
+
+  // And `PerAcquisition` fades in `accumulate_density()` alone: a frame that only passed
+  // changes nothing.
+  cfg.decay = plot::DensityDecay::PerAcquisition;
+  f.plot.set_density(cfg);
+  const double before = f.plot.density_grid(0u).ink();
+  f.plot.decay_density(1.0);
+  PLOT_CHECK_NEAR(f.plot.density_grid(0u).ink(), before, 1e-6);
+
+  std::printf("[density] time-constant ink: full=%.0f quarter=%.1f frozen=%.0f\n", full, quarter,
+              frozen);
+}
+
+/// Switching off drops the image at once -- not at the next acquisition, which a trigger that
+/// has stopped firing never sends -- and turning it back on starts from an empty grid.
+PLOT_TEST(switching_a_density_off_drops_the_image_at_once) {
+  DensityFixture f;
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  f.plot.set_density(cfg);
+  f.plot.accumulate_density();
+  PLOT_CHECK(f.plot.density_grid(0u).ink() > 0.0);
+
+  f.plot.clear_density();
+  PLOT_CHECK(f.plot.density_grid(0u).ink() == 0.0);
+  PLOT_CHECK(f.plot.density_grid(0u).peak() == 0.0f);
+  // The clear keeps the allocation -- the grid is still the screen's -- so the next
+  // accumulation does not have to reallocate it.
+  PLOT_CHECK(f.plot.density_grid(0u).cell_count() > 0u);
+
+  f.plot.accumulate_density();
+  PLOT_CHECK(f.plot.density_grid(0u).ink() > 0.0);
+
+  cfg.enabled = false;
+  f.plot.set_density(cfg);
+  PLOT_CHECK(f.plot.density_grid(0u).cell_count() == 0u);
+  PLOT_CHECK(f.plot.density_grid(0u).ink() == 0.0);
+
+  // ... and an accumulation while it is off deposits nothing (it is not a hidden build-up).
+  f.plot.accumulate_density();
+  PLOT_CHECK(f.plot.density_grid(0u).cell_count() == 0u);
+}
+
+/// What is deposited is where the *trace* is, and nowhere else: a trace off the visible y range
+/// leaves no ink rather than a band along the edge it left by, and a NaN sample is a gap that
+/// joins nothing.
+PLOT_TEST(a_density_deposits_only_where_the_trace_is) {
+  // y = 5 against a [-1, 1] axis: the segment's whole column span is above the axes.
+  DensityFixture off(std::vector<f32>{5.0f, 5.0f});
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  off.plot.set_density(cfg);
+  off.plot.accumulate_density();
+  PLOT_CHECK_NEAR(off.plot.density_grid(0u).ink(), 0.0, 1e-9);
+
+  // ... and the same series inside the axis deposits one cell per column, in two rows: the
+  // first half at y = -1 and the second at y = +1, joined by a diagonal.
+  DensityFixture split(std::vector<f32>{-1.0f, 1.0f});
+  split.plot.set_density(cfg);
+  split.plot.accumulate_density();
+  const plot::DensityGrid& grid = split.plot.density_grid(0u);
+  PLOT_CHECK(grid.ink() >= static_cast<double>(grid.columns()));
+  const plot::Transform ty = split.plot.y_transform(split.ay);
+  const plot::Rect axes = split.plot.layout().axes;
+  // The row a device y lands in is the grid's own mapping: the axis rect scaled by the grid's
+  // cells-per-pixel (1 while the rect is under `kDensityCellCap`, less past it).
+  const plot::f32 sy =
+      axes.h > 0.0f ? static_cast<plot::f32>(grid.rows()) / std::ceil(axes.h) : 1.0f;
+  // The deposit keeps one ULP of the bottom edge off its row, so `y = -1` -- which maps *onto*
+  // the bottom edge -- lands in the last row rather than one past the end.
+  const auto row_of = [&](plot::f64 y) {
+    return static_cast<plot::u32>(std::clamp(
+        static_cast<int>(std::floor((ty.to_screen_y(y) - axes.y) * sy)), 0,
+        static_cast<int>(grid.rows()) - 1));
+  };
+  PLOT_CHECK(grid.at(0u, row_of(-1.0)) > 0.0f);
+  PLOT_CHECK(grid.at(grid.columns() - 1u, row_of(1.0)) > 0.0f);
+  // Inverted on screen: y = +1 is the *lower* row index, which is the one y flip of the mapping.
+  PLOT_CHECK(row_of(1.0) < row_of(-1.0));
+
+  // A NaN in the middle is a gap: it joins nothing, so the trace is deposited as two runs and
+  // the columns where the gap is stay empty -- where the same series with the sample filled in
+  // lights every one of them. Five samples at x = 0, 0.25, 0.5, 0.75, 1.0.
+  const auto column_ink = [](const plot::DensityGrid& g, plot::u32 column) {
+    double sum = 0.0;
+    for (plot::u32 r = 0; r < g.rows(); ++r) sum += static_cast<double>(g.at(column, r));
+    return sum;
+  };
+  DensityFixture whole(std::vector<f32>{0.0f, 0.0f, 0.0f, 0.0f, 0.0f}, 0.25);
+  whole.plot.set_density(cfg);
+  whole.plot.accumulate_density();
+  DensityFixture gap(
+      std::vector<f32>{0.0f, 0.0f, std::numeric_limits<f32>::quiet_NaN(), 0.0f, 0.0f}, 0.25);
+  gap.plot.set_density(cfg);
+  gap.plot.accumulate_density();
+
+  const plot::DensityGrid& whole_grid = whole.plot.density_grid(0u);
+  const plot::DensityGrid& gap_grid = gap.plot.density_grid(0u);
+  const plot::Transform tx = gap.plot.x_transform(gap.ax);
+  const plot::Rect gap_axes = gap.plot.layout().axes;
+  const plot::f32 gsx = gap_axes.w > 0.0f
+                            ? static_cast<plot::f32>(gap_grid.columns()) / std::ceil(gap_axes.w)
+                            : 1.0f;
+  const plot::u32 column = static_cast<plot::u32>(std::clamp(
+      static_cast<int>(std::floor((tx.to_screen_x(0.5) - gap_axes.x) * gsx)), 0,
+      static_cast<int>(gap_grid.columns()) - 1));
+  PLOT_CHECK(column_ink(whole_grid, column) > 0.0);  // the sample is there: the column is lit
+  PLOT_CHECK(column_ink(gap_grid, column) == 0.0);   // the NaN is a gap: nothing joins across it
+  PLOT_CHECK(gap_grid.ink() < whole_grid.ink());
+
+  std::printf("[density] off-range ink=%.0f split ink=%.0f gap ink=%.0f whole ink=%.0f\n",
+              off.plot.density_grid(0u).ink(), grid.ink(), gap_grid.ink(), whole_grid.ink());
+}
+
+/// **One grid per trace.** A plot of two signals holds two images, each deposited from its own
+/// trace and drawn in its own colour (the colour is the renderer's, and here the *count* is what is
+/// read): the two traces at two levels leave ink in two different rows, so one grid holding one
+/// trace's ink and not the other's is the reading that says the images are not shared.
+PLOT_TEST(a_density_holds_one_grid_per_trace) {
+  plot::data::ArraySeries lo(std::vector<plot::f32>{-0.5f, -0.5f}, 0.0, 1.0);
+  plot::data::ArraySeries hi(std::vector<plot::f32>{0.5f, 0.5f}, 0.0, 1.0);
+  plot::Plot p;
+  p.set_viewport({0.0f, 0.0f, 640.0f, 480.0f});
+  const plot::u32 ax = p.add_x_axis({"t", {0.0, 1.0}, false, plot::AxisPlace::Bottom, false});
+  const plot::u32 ay = p.add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+  PLOT_CHECK(p.add_trace({&lo, plot::Color::hex(0x4FA3FF), 1.5f, ax, ay, "lo"}) == 0u);
+  PLOT_CHECK(p.add_trace({&hi, plot::Color::hex(0xFF8A4F), 1.5f, ax, ay, "hi"}) == 1u);
+  p.set_x_range(ax, {0.0, 1.0});
+  p.set_y_range(ay, {-1.0, 1.0});
+  p.layout();
+
+  plot::DensityConfig cfg;
+  cfg.enabled = true;
+  p.set_density(cfg);
+  p.accumulate_density();
+
+  PLOT_CHECK(p.trace_count() == 2u);
+  const plot::DensityGrid& g0 = p.density_grid(0u);
+  const plot::DensityGrid& g1 = p.density_grid(1u);
+  // Both are sized to the one axes rect, and each holds exactly its own trace's one pass: the ink
+  // is the width in each grid, so neither picked up the other trace's ink (two traces would be two
+  // widths in a shared grid).
+  PLOT_CHECK(g0.cell_count() > 0u);
+  PLOT_CHECK(g1.cell_count() == g0.cell_count());
+  PLOT_CHECK_NEAR(g0.ink(), static_cast<double>(g0.columns()), 1.0);
+  PLOT_CHECK_NEAR(g1.ink(), static_cast<double>(g1.columns()), 1.0);
+
+  const plot::Transform ty = p.y_transform(ay);
+  const plot::Rect axes = p.layout().axes;
+  const plot::f32 sy =
+      axes.h > 0.0f ? static_cast<plot::f32>(g0.rows()) / std::ceil(axes.h) : 1.0f;
+  const auto row_of = [&](plot::f64 y) {
+    return static_cast<plot::u32>(std::floor((ty.to_screen_y(y) - axes.y) * sy));
+  };
+  const plot::u32 lo_row = row_of(-0.5);
+  const plot::u32 hi_row = row_of(0.5);
+  PLOT_CHECK(lo_row != hi_row);
+  PLOT_CHECK(g0.at(0u, lo_row) > 0.0f);
+  PLOT_CHECK(g1.at(0u, hi_row) > 0.0f);
+  PLOT_CHECK(g0.at(0u, hi_row) == 0.0f);  // no trace but `lo` is in the lower grid
+  PLOT_CHECK(g1.at(0u, lo_row) == 0.0f);
+
+  // An out-of-range trace reads an empty image rather than anything borrowed.
+  PLOT_CHECK(p.density_grid(2u).cell_count() == 0u);
+  PLOT_CHECK(p.density_grid(9u).ink() == 0.0);
+
+  std::printf("[density] per-trace grids: cells=%zu each ink=%.0f/%.0f rows lo=%u hi=%u\n",
+              g0.cell_count(), g0.ink(), g1.ink(), lo_row, hi_row);
+}

tests/test_ring_buffer.cpp

@@ -21,6 +21,43 @@ PLOT_TEST(ring_clear_resets) {
   PLOT_CHECK_NEAR(r[0], 42.0);
 }
 
+PLOT_TEST(ring_clear_to_resumes_the_absolute_count) {
+  // A recompute: a derived ring is emptied and refilled from the absolute origin its source
+  // retains, so it has to come back numbered as the source is. `clear()` restarts at 0, which
+  // leaves a refilled ring reporting a produced() a whole window behind an identically fed one.
+  plot::data::RingBuffer<f32> src(8);
+  plot::data::RingBuffer<f32> derived(8);
+  for (int i = 0; i < 20; ++i) {
+    src.push(f32(i));
+    derived.push(f32(i) * 2.0f);
+  }
+  PLOT_CHECK(src.base() == 12);
+
+  derived.clear_to(src.base());
+  for (u64 i = 0; i < src.size(); ++i) derived.push(src[i] * 3.0f);
+
+  // Numbered as the source: same produced(), same base(), and the retained windows pair up.
+  PLOT_CHECK(derived.produced() == src.produced());
+  PLOT_CHECK(derived.base() == src.base());
+  PLOT_CHECK(derived.size() == src.size());
+  PLOT_CHECK_NEAR(derived[0], 36.0);    // 12 * 3
+  PLOT_CHECK_NEAR(derived[7], 57.0);    // 19 * 3
+  // And the absolute reader agrees with the windowed one, which is what a snapshot reads.
+  f32 at = 0.0f;
+  derived.copy_from(19, 1, &at);
+  PLOT_CHECK_NEAR(at, 57.0);
+}
+
+PLOT_TEST(ring_clear_to_zero_is_clear) {
+  plot::data::RingBuffer<f32> r(8);
+  for (int i = 0; i < 5; ++i) r.push(f32(i));
+  r.clear_to(0);
+  PLOT_CHECK(r.size() == 0);
+  PLOT_CHECK(r.produced() == 0);
+  r.push(42.0f);
+  PLOT_CHECK_NEAR(r[0], 42.0);
+}
+
 PLOT_TEST(ring_capacity_rounds_up_to_a_power_of_two) {
   // The capacity is rounded up so slot addressing stays a mask, and capacity()
   // reports the rounded value -- the one callers must size for (R4).
@@ -35,3 +72,27 @@ PLOT_TEST(ring_capacity_rounds_up_to_a_power_of_two) {
   PLOT_CHECK_NEAR(r[0], 872.0);           // oldest retained
   PLOT_CHECK_NEAR(r[127], 999.0);         // newest
 }
+
+PLOT_TEST(ring_amend_rewrites_a_retained_slot) {
+  // Backfill: a slot pushed as a placeholder is rewritten once the data that belongs there
+  // arrives. The index is absolute, because that is the only coordinate a late packet can
+  // compute -- a retained-window index would have moved by the time it got here.
+  plot::data::RingBuffer<f32> r(8);
+  for (int i = 0; i < 6; ++i) r.push(f32(i));
+  PLOT_CHECK(r.amend(3, 42.0f));
+  PLOT_CHECK_NEAR(r[3], 42.0);
+  PLOT_CHECK(r.produced() == 6);   // an amend is not a push
+}
+
+PLOT_TEST(ring_amend_refuses_an_index_the_ring_no_longer_holds) {
+  // The window slides on the producer, so a late amend may arrive after its slot was
+  // overwritten. Writing it anyway would corrupt whatever sample now owns that slot, so the
+  // bounds test is the whole safety of the operation and the caller reads the result.
+  plot::data::RingBuffer<f32> r(8);
+  for (int i = 0; i < 20; ++i) r.push(f32(i));
+  PLOT_CHECK(r.base() == 12);
+  PLOT_CHECK(!r.amend(3, 42.0f));     // aged out
+  PLOT_CHECK(!r.amend(20, 42.0f));    // never produced
+  PLOT_CHECK_NEAR(r[0], 12.0);        // and nothing moved
+  PLOT_CHECK_NEAR(r[7], 19.0);
+}