feat(render): a reduced column can be graded by dwell, not drawn as one flat band

A pixel column reduced from a dense envelope is honest about where the signal
went and silent about how long it was there: its min and max are identical
whether its samples fill the span or pile at its two ends, so a ramp and a pulse
are one band. Style::intensity_grading grades it instead -- bright where the
signal sits, faint where it only passes through -- by asking the gather for a
level finer than the pixel grid and reading the distribution from those
sub-buckets. Off by default: a change of look, not a correction of one.

The measure is dwell per row, each segment depositing one unit spread over the
rows it spans; counting +1 per row instead grades a sine's fast middle as
brightly as its rails, which is the pattern inverted. The accumulator is one
column wide (a full w*h density image is 33 MB at 4K) with each span written as
two delta writes, and normalisation is against the column's own peak -- a
frame-wide scale fades the trace out exactly where it moves fastest. Alpha is
quantised into tiers, one LineBatch and one draw call each, because the line
pipeline's colour is a uniform and a per-segment alpha is inexpressible.

The finer ask is floored at level 1 whenever the flat path would have used the
pyramid: level_for() answers 0 -- raw samples -- as soon as a sub-column falls
under one bucket, so an unfloored ask turns a moderately dense frame into an
O(visible) gather (measured at 172 samples a pixel: raw=1154 lod=0 and 6.4 ms a
frame against raw=710 lod=453 and 2.3 ms). Grading is a way of drawing a
reduction and may not undo it.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

README.md

@@ -37,6 +37,18 @@ 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;
 - 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`,

docs/data-and-performance.md

@@ -166,6 +166,116 @@ 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. 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.
+
 ## One sample or a statistic of many
 
 Every number the library reports is one the samples actually hold. What differs between

include/plot/data/array_series.hpp

@@ -33,7 +33,7 @@ class ArraySeries final : public Series {
   Range x_bounds() const override;
   Range y_bounds() const override;
   const MinMaxPyramid& pyramid() const override;
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
               GatherMode mode = GatherMode::Envelope) const override;
 
  protected:

include/plot/data/series.hpp

@@ -59,12 +59,20 @@ class Series {
 
   /// Appends interleaved (x, y) pairs for level `level`.
   ///
-  /// **x is relative to `x0()`**: the emitted value is `x_at(i) - x0()` as
-  /// f32, never the absolute coordinate. A consumer reconstructs the absolute
-  /// x in f64 (`x0() + emitted`) before mapping it to the screen; staging an
-  /// absolute epoch-time x as f32 would quantise it to a grid coarser than
-  /// the pixel (f32 carries 24 bits -- 1 s at 1.7e9), while the relative
-  /// value `i*dx` is small and exact. y is unchanged.
+  /// **x is relative to `x_origin`**: the emitted value is `x_at(i) - x_origin` as f32, never
+  /// the absolute coordinate. A consumer reconstructs the absolute x in f64
+  /// (`x_origin + emitted`) before mapping it to the screen; staging an absolute epoch-time x
+  /// as f32 would quantise it to a grid coarser than the pixel (f32 carries 24 bits -- 1 s at
+  /// 1.7e9). y is unchanged.
+  ///
+  /// **The caller names the origin because only the caller knows the span the f32 has to be
+  /// exact against.** The origin was `x0()` -- the start of the series' *retained window* --
+  /// and a relative value's ULP is then a fraction of the whole window however little of it is
+  /// on screen: 1.9 us over 20 s of retained data, which at a view 10 us wide is more than a
+  /// hundred pixels between where a sample is *drawn* and the x a readout quotes for the same
+  /// sample (`x_at()`, exact f64). Passing the visible range's minimum instead makes the error
+  /// 2^-24 of the *visible span* -- a fixed 4e-5 of a pixel over a 700 px axis -- at every
+  /// zoom. A caller with no view in mind may pass `x0()` and get the old behaviour.
   ///
   /// Level 0 emits the raw samples of [begin, end). Level >= 1 emits one
   /// geometry element per *complete* level bucket wholly inside the retained
@@ -85,7 +93,7 @@ class Series {
   /// level_for() picks), and never reaches outside the retained window -- nor
   /// outside [begin, end). Pairs are appended to out_xy, which is never
   /// cleared.
-  virtual void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  virtual void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                       GatherMode mode = GatherMode::Envelope) const = 0;
 
   /// Absolute x of sample `i` (`x0() + i*dx()` on a uniform-grid series).
@@ -121,7 +129,7 @@ class Series {
 
   /// The shared body of the concrete gather() overrides: raw samples at level 0,
   /// bucket geometry above it (per `mode`).
-  void gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  void gather_impl(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                    GatherMode mode) const;
 
  private:
@@ -143,7 +151,7 @@ class Series {
   /// 0 is entirely this, and a level >= 1 gather uses it for the two partial edge
   /// buckets a pyramid of complete buckets cannot answer for. Precondition:
   /// begin < end, end <= size().
-  void gather_raw(u64 begin, u64 end, std::vector<f32>& out_xy) const;
+  void gather_raw(u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy) const;
 };
 
 }  // namespace plot::data

include/plot/data/stream_series.hpp

@@ -92,7 +92,7 @@ class StreamSeries final : public Series {
   Range x_bounds() const override;
   Range y_bounds() const override;
   const MinMaxPyramid& pyramid() const override;
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
               GatherMode mode = GatherMode::Envelope) const override;
   /// Always true: this series' `x_bounds()` is the retained ring window, which
   /// slides with every `acquire()` -- the property `XFollow::Live` follows.

include/plot/data/xy_series.hpp

@@ -53,8 +53,8 @@ class XYSeries final : public Series {
   Range x_bounds() const override;
   Range y_bounds() const override;
   const MinMaxPyramid& pyramid() const override;
-  /// Same contract as `Series::gather`, with x emitted relative to `x0()`.
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  /// Same contract as `Series::gather`, with x emitted relative to `x_origin`.
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
               GatherMode mode = GatherMode::Envelope) const override;
 
   /// The sample's own x.

include/plot/plot/figure.hpp

@@ -138,6 +138,16 @@ class Figure {
   }
   f32 min_y_gutter() const noexcept { return min_y_gutter_; }
 
+  /// The empty band every row keeps to the right of its `axes`, in device pixels (0.0
+  /// by default, so `axes` reaches the viewport's right edge). It is set here rather
+  /// than row by row for the left gutter's reason: the rows' axes have to line up, and
+  /// they end on a common column only if they are told one width. See
+  /// `Plot::set_right_gutter()` for what it is for. Negative values are clamped to 0.
+  void set_right_gutter(f32 device_px) noexcept {
+    right_gutter_ = device_px > 0.0f ? device_px : 0.0f;
+  }
+  f32 right_gutter() const noexcept { return right_gutter_; }
+
   /// Whether the shared x axis is the figure's: every row reserves no x label strip
   /// and one shared axis is drawn under the last row (the default), or every row
   /// draws its own labels and the figure draws nothing extra.
@@ -326,6 +336,7 @@ class Figure {
   FigureLayout layout_{};
   f32 row_gap_ = 0.0f;
   f32 min_y_gutter_ = 0.0f;
+  f32 right_gutter_ = 0.0f;
   bool labels_bottom_only_ = true;
 };
 

include/plot/plot/plot.hpp

@@ -88,6 +88,11 @@ struct PlotLayout {
   /// no text backend there is no title to lay out at all and both stay 0.0f.
   f32 y_title_width = 0.0f;
   f32 x_title_height = 0.0f;
+  /// The empty band kept between `axes`' right edge and the viewport's, 0.0f unless a
+  /// caller asked for one (see `Plot::set_right_gutter()`). Reported because it is
+  /// clamped by the same cap as the strips above, so what was asked for and what was
+  /// reserved are not always the same number.
+  f32 right_gutter = 0.0f;
   /// The measured legend: inside `axes`, never reserving any part of it, and empty
   /// when there is nothing to draw. It is measured with the same text backend the
   /// strips above are, and against the same `axes` rect the caller reads back, so
@@ -640,6 +645,20 @@ class Plot {
   }
   f32 min_y_gutter() const noexcept { return min_y_gutter_; }
 
+  /// An empty band reserved between `axes`' right edge and the viewport's, in device
+  /// pixels. 0.0 -- the default -- is what the layout has always done: `axes` reaches
+  /// the viewport's right edge, which leaves the rightmost x tick label, *centred* on
+  /// that edge, half of it to be drawn in and nothing to draw it in -- and puts the
+  /// newest sample's ink on the frame. It is the mirror of the left gutter in purpose
+  /// and not in kind: nothing is drawn here, so there is nothing to measure and the
+  /// value is the caller's to choose. Reserved inside the same cap as the label and
+  /// title strips, so it can no more squeeze `axes` below the half-viewport floor than
+  /// they can. Negative values are clamped to 0.
+  void set_right_gutter(f32 device_px) noexcept {
+    right_gutter_ = device_px > 0.0f ? device_px : 0.0f;
+  }
+  f32 right_gutter() const noexcept { return right_gutter_; }
+
   /// Grid segments for the primary axis pair (x axis 0, y axis 0), in data space.
   const Grid& grid() const noexcept { return grid_; }
 
@@ -867,6 +886,9 @@ class Plot {
   /// The floor a figure imposes on the left gutter; see set_min_y_gutter(). 0.0 means
   /// none, which is what a plot standing on its own keeps.
   f32 min_y_gutter_ = 0.0f;
+  /// The empty band kept to the right of `axes`; see set_right_gutter(). 0.0 means none,
+  /// which is what the layout did before the setter existed.
+  f32 right_gutter_ = 0.0f;
   /// Which handles a pointer is on, published by the input layer (see HotHandles).
   HotHandles hot_{};
 

include/plot/render/renderer.hpp

@@ -29,6 +29,15 @@ 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;
   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
@@ -404,6 +413,13 @@ 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.
@@ -445,11 +461,12 @@ class Renderer {
   /// `origin_x` back in, in f64, before the single f32 narrowing (B1), so a
   /// large-magnitude x -- an epoch axis -- never loses sub-pixel precision.
   void stage_segment(f64 origin_x, f64 x0, f64 y0, f64 x1, f64 y1, bool log_x, bool log_y);
-  /// Stages `n` interleaved `x,y` points of a gathered window (see
-  /// `Series::gather`): x **relative to the series' `x0()`**, y absolute. The
-  /// absolute data x is reconstructed in f64 (`series_x0 + rel`) and staged as
+  /// Stages `n` interleaved `x,y` points of a gathered window (see `Series::gather`): x
+  /// **relative to `origin_x`**, which the caller asked the gather for, y absolute. On linear
+  /// axes that is already what the batch wants and the buffer is handed over as it is; a log
+  /// axis reconstructs the absolute x in f64 per segment and stages
   /// `to_space(x_abs) - to_space(origin_x)` -- O(visible pixels), not O(epoch).
-  void stage_xy(const f32* xy, u32 n, f64 series_x0, f64 origin_x, bool log_x, bool log_y);
+  void stage_xy(const f32* xy, u32 n, f64 origin_x, bool log_x, bool log_y);
   /// Lays one run of text out at a framebuffer position and stages it into
   /// `batch`, shifting it into viewport space and tinting it `color` (the
   /// per-instance `a_colour`). Returns the pen past the run.
@@ -499,6 +516,29 @@ 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 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
@@ -610,7 +650,25 @@ 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/style.hpp

@@ -177,6 +177,82 @@ 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.
+  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/array_series.cpp

@@ -75,9 +75,9 @@ Range ArraySeries::y_bounds() const { return y_bounds_; }
 
 const MinMaxPyramid& ArraySeries::pyramid() const { return pyramid_; }
 
-void ArraySeries::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+void ArraySeries::gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                          GatherMode mode) const {
-  gather_impl(level, begin, end, out_xy, mode);
+  gather_impl(level, begin, end, x_origin, out_xy, mode);
 }
 
 void ArraySeries::copy_raw(u64 begin, u64 end, f32* out) const {

src/data/series.cpp

@@ -176,21 +176,24 @@ u64 Series::snap_index(f64 x) const {
   return static_cast<u64>(k);
 }
 
-void Series::gather_raw(u64 begin, u64 end, std::vector<f32>& out_xy) const {
+void Series::gather_raw(u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy) const {
   const f64 step = dx();
+  // Sample i sits at `x0() + i*step`, so this is `x_at(i) - x_origin` with the subtraction done
+  // once in f64 rather than per sample: see gather() for why the caller owns the origin.
+  const f64 shift = x0() - x_origin;
   f32 raw[kGatherChunk];
   for (u64 i = begin; i < end;) {
     const u64 take = std::min<u64>(kGatherChunk, end - i);
     copy_raw(i, i + take, raw);
     for (u64 k = 0; k < take; ++k) {
-      out_xy.push_back(f32(f64(i + k) * step));   // x relative to x0(): see gather()
+      out_xy.push_back(f32(shift + f64(i + k) * step));   // x relative to x_origin: see gather()
       out_xy.push_back(raw[k]);
     }
     i += take;
   }
 }
 
-void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+void Series::gather_impl(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                          GatherMode mode) const {
   const u64 n = size();
   const u64 b = std::min(begin, n);
@@ -198,7 +201,7 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
   if (b >= e) return;
 
   if (level == 0) {
-    gather_raw(b, e, out_xy);
+    gather_raw(b, e, x_origin, out_xy);
     return;
   }
   // Public levels clamp to the deepest representable one (R3): past
@@ -226,6 +229,7 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
   // picks, so the envelope path stays O(buckets) and the geometry still spans
   // the requested range exactly, for every mode.
   const f64 step = dx();
+  const f64 shift = x0() - x_origin;   // as in gather_raw(): x_at(i) - x_origin = shift + i*step
   const u64 span = u64{kBucket} << level;
   const u64 origin = pyramid().window_base();
   const u64 lbase = pyramid().level_base(level);
@@ -235,11 +239,11 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
   if (first >= last) {
     // No complete bucket of this level is inside the range -- a window squeezed
     // into one bucket -- so the raw samples are the only exact geometry there is.
-    gather_raw(b, e, out_xy);
+    gather_raw(b, e, x_origin, out_xy);
     return;
   }
   const u64 lead = first * span - origin;   // window index the first emitted bucket starts at
-  if (b < lead) gather_raw(b, std::min(lead, e), out_xy);
+  if (b < lead) gather_raw(b, std::min(lead, e), x_origin, out_xy);
 
   switch (mode) {
     case GatherMode::Envelope: {
@@ -252,9 +256,9 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
         const MinMax m = pyramid().bucket(level, bi);
         const u64 first_sample = bi * span - origin;   // >= 0: stored buckets start inside the window
         const u64 last_sample = std::min((bi + 1) * span, origin + e) - 1 - origin;
-        out_xy.push_back(f32(f64(first_sample) * step));   // x relative to x0()
+        out_xy.push_back(f32(shift + f64(first_sample) * step));   // x relative to x_origin
         out_xy.push_back(m.min);
-        out_xy.push_back(f32(f64(last_sample) * step));
+        out_xy.push_back(f32(shift + f64(last_sample) * step));
         out_xy.push_back(m.max);
       }
       break;
@@ -269,7 +273,7 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
         const u64 centre = bi * span + span / 2 - origin;   // inside [b, e): the bucket is wholly inside
         f32 v = 0.0f;
         copy_raw(centre, centre + 1, &v);
-        out_xy.push_back(f32(f64(centre) * step));   // x relative to x0()
+        out_xy.push_back(f32(shift + f64(centre) * step));   // x relative to x_origin
         out_xy.push_back(v);
       }
       break;
@@ -283,7 +287,7 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
         const u32 count = pyramid().bucket_count(level, bi);
         if (count == 0) continue;
         const u64 centre = bi * span + span / 2 - origin;
-        out_xy.push_back(f32(f64(centre) * step));   // x relative to x0()
+        out_xy.push_back(f32(shift + f64(centre) * step));   // x relative to x_origin
         out_xy.push_back(f32(pyramid().bucket_sum(level, bi) / f64(count)));
       }
       break;
@@ -291,7 +295,7 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
   }
 
   const u64 trail = last * span - origin;   // one past the last emitted bucket's span
-  if (trail < e) gather_raw(trail, e, out_xy);
+  if (trail < e) gather_raw(trail, e, x_origin, out_xy);
 }
 
 }  // namespace plot::data

src/data/stream_series.cpp

@@ -87,9 +87,9 @@ Range StreamSeries::y_bounds() const { return y_bounds_; }
 
 const MinMaxPyramid& StreamSeries::pyramid() const { return pyramid_; }
 
-void StreamSeries::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+void StreamSeries::gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                           GatherMode mode) const {
-  gather_impl(level, begin, end, out_xy, mode);
+  gather_impl(level, begin, end, x_origin, out_xy, mode);
 }
 
 void StreamSeries::copy_raw(u64 begin, u64 end, f32* out) const {

src/data/xy_series.cpp

@@ -100,16 +100,16 @@ u64 XYSeries::snap_index(f64 x) const {
              : hi;                      // ties go to the lower index
 }
 
-void XYSeries::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+void XYSeries::gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                       GatherMode mode) const {
   const u64 n = size();
   const u64 b = std::min(begin, n);
   const u64 e = std::min(std::max(end, b), n);
   if (b >= e) return;
 
-  // x emitted relative to x0(): see Series::gather(). The x array is f64, so
+  // x emitted relative to the caller's origin: see Series::gather(). The x array is f64, so
   // the subtraction happens wide and only the small, exact offset narrows.
-  const f64 origin = x0();
+  const f64 origin = x_origin;
 
   if (level == 0) {
     for (u64 i = b; i < e; ++i) {
@@ -127,7 +127,7 @@ void XYSeries::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
   // `begin`, `last` one past the last bucket wholly before `end`, and the two
   // edge spans around them are read from the raw arrays -- so no emitted
   // geometry comes from outside [begin, end), and the emitted x values are the
-  // array's own coordinates relative to x0().
+  // array's own coordinates relative to the caller's origin.
   const u64 span = u64{kBucket} << level;
   const u64 lend = pyramid().level_size(level);
   const u64 first = std::min(ceil_div(b, span), lend);

src/plot/figure.cpp

@@ -451,6 +451,10 @@ const FigureLayout& Figure::layout() {
     // not drawn once per row. A figure told to label every row keeps them everywhere,
     // and then there is no shared axis to speak of: each row has its own.
     p.set_x_strip_mode(labels_bottom_only_ && row != bottom_row ? XStrip::None : XStrip::Both);
+    // Before either pass below, and the same value for every row: nothing is measured on
+    // the right, so unlike the left gutter this needs no measurement pass -- the rows 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

src/plot/plot.cpp

@@ -1039,12 +1039,21 @@ const PlotLayout& Plot::layout() {
     x_height = std::min(x_height, x_budget);
     const f32 y_title_width = std::min(y_title_w, y_budget - y_width);
     const f32 x_title_height = std::min(x_title_h, x_budget - x_height);
+    // The right-hand band, out of what is left of the same allowance the two left
+    // strips were served from -- so the three together cannot take more than
+    // `1 - kMinAxesShare` of the width however much each asks for. Nothing is drawn
+    // in it, so unlike the strips above it is a want and never a measurement, and it
+    // cannot feed the fixed point below: the y labels are chosen from the row's range
+    // and height, so a narrower `axes` does not change what they need.
+    const f32 right_gutter =
+        std::min(right_gutter_, y_budget - (y_width + y_title_width));
     layout_.y_axis_width = y_width;
     layout_.x_axis_height = x_height;
     layout_.y_title_width = y_title_width;
     layout_.x_title_height = x_title_height;
+    layout_.right_gutter = right_gutter;
     layout_.axes = Rect{viewport_.x + y_width + y_title_width, viewport_.y,
-                        vw - (y_width + y_title_width),
+                        vw - (y_width + y_title_width + right_gutter),
                         vh - (x_height + x_title_height)};
     layout_.y_title_area = Rect{viewport_.x, layout_.axes.y, y_title_width, layout_.axes.h};
     layout_.y_label_area =
@@ -1464,7 +1473,10 @@ bool Plot::crosshair_point(u32 trace, f64 x, f64& out_x, f64& out_y) const {
   // when it fell between them. The scratch is cleared and refilled rather than reallocated,
   // and sized for two pairs from construction, so the pointer path allocates nothing.
   crosshair_scratch_.clear();
-  series->gather(0u, span.begin, span.end + 1u, crosshair_scratch_);
+  // The origin is the query itself: only y is read out of the pairs below -- the x comes back
+  // through `x_at()` -- so this names the one origin that cannot lose precision for a caller
+  // that might.
+  series->gather(0u, span.begin, span.end + 1u, x, crosshair_scratch_);
   const usize pairs = static_cast<usize>(span.end - span.begin + 1u);
   if (crosshair_scratch_.size() != 2u * pairs) return false;  // a series that produced nothing
   const f64 y_begin = static_cast<f64>(crosshair_scratch_[1u]);
@@ -1480,9 +1492,9 @@ bool Plot::crosshair_point(u32 trace, f64 x, f64& out_x, f64& out_y) const {
   // `NearestSample`: the nearer of the two, and **its own x with it**. `span.t` is measured on
   // the samples' own coordinates, so "nearer" is exact on any grid; a tie reads the earlier
   // sample, which is the bias `crosshair_span()` already takes for a degenerate pair. The x
-  // comes back through `x_at()` rather than from the gathered pairs, which are relative to
-  // `x0()` by the `Series::gather()` contract -- adding it back here would be a second
-  // reconstruction of a coordinate the series will hand over directly.
+  // comes back through `x_at()` rather than from the gathered pairs, which are relative to a
+  // caller-named origin by the `Series::gather()` contract -- adding it back here would be a
+  // second reconstruction of a coordinate the series will hand over directly.
   const bool take_begin = span.t <= 0.5;
   out_x = series->x_at(take_begin ? span.begin : span.end);
   out_y = take_begin ? y_begin : y_end;

src/plot/ticks.cpp

@@ -98,7 +98,10 @@ void format_time(f64 seconds, char* buf, usize n) {
   const char* const sign = seconds < 0.0 ? "-" : "";
   const f64 t = std::fabs(seconds);
 
-  if (t < 1.0) {
+  // `0.9995` and not `1.0`: three significant figures of 0.9999 s are `1e+03ms`, so a value
+  // that *rounds* to a second belongs to the whole-second branch below, which writes it `1s`.
+  // The same spill one rung down is handled inside the ladder.
+  if (t < 0.9995) {
     // Sub-second: the prefix that keeps the mantissa in [1, 1000) -- the same rule the SI
     // formatter uses on a y axis, and the reading a zoomed-in window needs. A fixed
     // millisecond unit printed `0.005ms` where `5us` is what the axis is showing, and
@@ -119,8 +122,12 @@ void format_time(f64 seconds, char* buf, usize n) {
         {1.0e-9, "ns"},
         {1.0e-12, "ps"},
     };
+    // The rung is picked by the *rounded* mantissa, which is what `format_si`'s own 999.5
+    // check buys there: 0.9999 ms is `999.9µs` before rounding and `1e+03µs` after, so it is
+    // the millisecond rung's value and reads `1ms`. Testing the raw `t < u.scale` let the
+    // mantissa reach 1000 at every rung boundary.
     for (const auto& u : kUnits) {
-      if (t < u.scale) continue;
+      if (t < u.scale * 0.9995) continue;
       std::snprintf(buf, n, "%s%.3g%s", sign, t / u.scale, u.unit);
       return;
     }

src/render/renderer.cpp

@@ -616,9 +616,14 @@ 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 +648,7 @@ 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 {
@@ -736,24 +741,16 @@ void Renderer::stage_segment(f64 origin_x, f64 x0, f64 y0, f64 x1, f64 y1, bool
                           static_cast<f32>(space(y1, log_y))});
 }
 
-void Renderer::stage_xy(const f32* xy, u32 n, f64 series_x0, f64 origin_x, bool log_x,
-                        bool log_y) {
+void Renderer::stage_xy(const f32* xy, u32 n, f64 origin_x, bool log_x, bool log_y) {
   if (!log_x && !log_y) {
-    // The common case: reconstruct the absolute data x in f64 (`x0 + rel` --
-    // the gather contract's own reconstruction), stage it relative to the
-    // draw's origin, and the f32 is O(visible pixels), not O(epoch).
-    staged_.clear();
-    staged_.reserve(usize(n) * 2u);
-    const f64 origin_s = space(origin_x, log_x);
-    for (u32 i = 0; i < n; ++i) {
-      staged_.push_back(static_cast<f32>(xy[2u * i] + series_x0 - origin_s));
-      staged_.push_back(xy[2u * i + 1u]);
-    }
-    lines_.add_polyline_xy(staged_.data(), n);
+    // The common case costs nothing at all: the gather emitted x relative to this very origin
+    // (`draw_traces` asks it for `x_range.min`, which is the draw's origin too) and a linear y
+    // needs no mapping, so the gathered buffer *is* the staged one.
+    lines_.add_polyline_xy(xy, n);
     return;
   }
   for (u32 i = 0; i + 1u < n; ++i) {
-    stage_segment(origin_x, xy[2u * i] + series_x0, xy[2u * i + 1u], xy[2u * i + 2u] + series_x0,
+    stage_segment(origin_x, xy[2u * i] + origin_x, xy[2u * i + 1u], xy[2u * i + 2u] + origin_x,
                   xy[2u * i + 3u], log_x, log_y);
   }
 }
@@ -980,6 +977,304 @@ 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;
+
+  // 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. The deposits are fractions, so this cannot be an
+    // integer test: it is a share of the column's own peak, small enough to keep a row a
+    // single thin segment grazed and large enough not to light a row on rounding alone.
+    const f32 lit_floor = 0.01f * peak;
+    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;
+    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);
+        column_rows_[r0] += w;
+        column_rows_[r1 + 1u] -= w;
+      }
+    }
+    px = sx;
+    py = sy;
+    have_prev = true;
+  }
+  if (open) emit_column();
+  return staged;
+}
+
 void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
   // 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
@@ -1021,12 +1316,38 @@ 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
+    // carry (`Style::intensity_grading`), so the gather is asked for the level a
+    // 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();
-    series.gather(level, first, last, gather_, trace.mode);
+    // The visible range's minimum is the gather origin: the emitted f32 is then O(the span on
+    // screen), so its ULP is a fixed 2^-24 of the axis at every zoom. `series.x0()` -- the origin
+    // before -- is the start of the *retained window*, so the quantisation was a fraction of data
+    // the view need not even hold, and a deep zoom drew a sample visibly off the x a readout
+    // quotes for it. See `Series::gather()`.
+    series.gather(level, first, last, x_range.min, gather_, trace.mode);
     if (gather_.size() < 4u) continue;  // fewer than two points is no segment
 
     stats_.visible_samples += visible;
@@ -1041,7 +1362,7 @@ void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
       const auto& yt = plot.y_transform(trace.axis_y);
       const f32 half = 0.5f * style_.device(style_.marker_px);
       for (u32 k = 0; k + 1 < gather_.size(); k += 2) {
-        const f64 x_abs = series.x0() + static_cast<f64>(gather_[k]);
+        const f64 x_abs = x_range.min + static_cast<f64>(gather_[k]);
         const f64 y_abs = static_cast<f64>(gather_[k + 1]);
         if (!std::isfinite(x_abs) || !std::isfinite(y_abs)) continue;
         const f32 sx = static_cast<f32>(xt.to_screen_x(x_abs));
@@ -1059,11 +1380,11 @@ void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
       ++stats_.lod_traces;
     }
 
-    // Gathered x is relative to `series.x0()` (the gather contract); the staging
-    // reconstructs the absolute data x in f64 and emits `to_space(x_abs) -
-    // to_space(origin)` -- the visible x range's minimum is the natural origin
-    // for a trace -- so the f32 is O(visible pixels), not O(epoch) (B1). The
-    // mapping folds the origin back into the offset uniform, in f64.
+    // Gathered x is relative to `x_range.min` (the gather contract, with the origin this
+    // function asked for); the staging reconstructs the absolute data x in f64 and emits
+    // `to_space(x_abs) - to_space(origin)` about that same origin, so the f32 is O(visible
+    // pixels), not O(epoch) (B1). The mapping folds the origin back into the offset uniform,
+    // in f64.
     const bool log_x = plot.x_axis(trace.axis_x).log;
     const bool log_y = plot.y_axis(trace.axis_y).log;
     const Mapping map = mapping(plot, trace.axis_x, trace.axis_y, x_range.min);
@@ -1087,7 +1408,7 @@ void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
       f64 next = std::numeric_limits<f64>::infinity();
       for (usize k = count; k > 0; --k) {
         const usize p = k - 1u;  // the point index; `i` above is the trace's
-        const f64 x = static_cast<f64>(gather_[2u * p]) + series.x0();
+        const f64 x = static_cast<f64>(gather_[2u * p]) + x_range.min;
         if (!(x < next)) continue;  // out of order with what follows: unreadable, and a NaN too
         next = x;
         gather_[2u * (count - 1u - kept)] = gather_[2u * p];
@@ -1114,9 +1435,73 @@ 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, series.x0(), x_range.min, log_x, log_y);
+      // A window denser than two gathered points per pixel column is drawn as *columns*
+      // 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 {
+        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
     // (so their size is device pixels whatever the data scale is). The stride is
@@ -1132,7 +1517,7 @@ void Renderer::draw_traces(const Plot& plot, const PlotLayout& layout) {
       const f64 origin_s = space(x_range.min, log_x);
       u32 staged = 0;
       for (u32 p = 0; p < points; p += stride) {
-        const f64 x_abs = static_cast<f64>(gather_[2u * p]) + series.x0();
+        const f64 x_abs = static_cast<f64>(gather_[2u * p]) + x_range.min;
         const f32 rx = static_cast<f32>(space(x_abs, log_x) - origin_s);
         const f32 ry = static_cast<f32>(space(gather_[2u * p + 1u], log_y));
         const Vec2 centre{rx * map.scale.x + map.offset.x, ry * map.scale.y + map.offset.y};

tests/test_figure.cpp

@@ -425,6 +425,52 @@ PLOT_TEST(figure_gutter_never_squeezes_the_axes_below_the_floor) {
   }
 }
 
+/// The other side of the same band. `axes` reached the viewport's right edge, which left
+/// the rightmost x tick label -- centred on it -- half outside the plot, so a figure can
+/// ask for an empty band there. One value for every row, like the left gutter, because
+/// the rows' axes have to end on a common column as well as start on one.
+PLOT_TEST(figure_rows_share_one_right_gutter) {
+  plot::Figure figure = different_magnitude_figure();
+  figure.layout();
+  const plot::f32 flush = figure.plot(0u).layout().axes.right();
+  PLOT_CHECK_NEAR(static_cast<plot::f64>(figure.right_gutter()), 0.0, 1e-12);
+  // The default is the layout as it always was: nothing between the data and the frame.
+  PLOT_CHECK_NEAR(static_cast<plot::f64>(flush), static_cast<plot::f64>(kW), 1e-4);
+
+  figure.set_right_gutter(30.0f);
+  figure.layout();
+  const plot::Rect first = figure.plot(0u).layout().axes;
+  for (plot::u32 row = 0; row < 3u; ++row) {
+    const plot::PlotLayout& rl = figure.plot(row).layout();
+    PLOT_CHECK_NEAR(static_cast<plot::f64>(rl.right_gutter), 30.0, 1e-4);
+    PLOT_CHECK_NEAR(static_cast<plot::f64>(rl.axes.right()), static_cast<plot::f64>(kW) - 30.0,
+                    1e-4);
+    // The band comes off the right alone: the left gutter the rows agreed on is untouched,
+    // so a host can balance the two sides without the one moving when it sets the other.
+    PLOT_CHECK_NEAR(static_cast<plot::f64>(rl.axes.x), static_cast<plot::f64>(first.x), 1e-4);
+    PLOT_CHECK_NEAR(static_cast<plot::f64>(rl.axes.w), static_cast<plot::f64>(first.w), 1e-4);
+    // ... and the x strip follows the data area rather than the viewport, or the shared
+    // axis would be labelled over a band that holds no data.
+    PLOT_CHECK_NEAR(static_cast<plot::f64>(rl.x_label_area.w), static_cast<plot::f64>(rl.axes.w),
+                    1e-4);
+  }
+  // Clamped by the same cap as the strips: a band wider than the whole figure cannot
+  // squeeze `axes` below the floor `Plot::layout()` guarantees.
+  figure.set_right_gutter(10.0f * kW);
+  figure.layout();
+  for (plot::u32 row = 0; row < 3u; ++row) {
+    const plot::Rect& axes = figure.plot(row).layout().axes;
+    PLOT_CHECK(axes.w >= 0.5f * kW - 1e-3f);
+  }
+  // Negative means "none", like the gutter and the row gap, and the data area goes back
+  // to the viewport's edge.
+  figure.set_right_gutter(-5.0f);
+  PLOT_CHECK_NEAR(static_cast<plot::f64>(figure.right_gutter()), 0.0, 1e-12);
+  figure.layout();
+  PLOT_CHECK_NEAR(static_cast<plot::f64>(figure.plot(0u).layout().axes.right()),
+                  static_cast<plot::f64>(flush), 1e-4);
+}
+
 /// The degenerate neighbour: a figure of one row imposes exactly what that row
 /// measured, so it lays out as the plot would on its own -- the gutter cannot move a
 /// row that has no sibling to line up with.

tests/test_plot.cpp

@@ -1939,11 +1939,11 @@ class CountingSeries final : public plot::data::Series {
   }
   plot::Range y_bounds() const override { return {0.0, 99.0}; }
   const plot::data::MinMaxPyramid& pyramid() const override { return pyramid_; }
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out,
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out,
               plot::data::GatherMode mode = plot::data::GatherMode::Envelope) const override {
     ++gather_calls_;
     samples_read_ += end - begin;
-    gather_impl(level, begin, end, out, mode);
+    gather_impl(level, begin, end, x_origin, out, mode);
   }
 
   u64 gather_calls() const noexcept { return gather_calls_; }
@@ -2471,9 +2471,9 @@ class XyFixture final : public plot::data::Series {
   }
   plot::Range y_bounds() const override { return {0.0, 20.0}; }
   const plot::data::MinMaxPyramid& pyramid() const override { return pyramid_; }
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out,
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out,
               plot::data::GatherMode mode = plot::data::GatherMode::Envelope) const override {
-    gather_impl(level, begin, end, out, mode);
+    gather_impl(level, begin, end, x_origin, out, mode);
   }
 
   f64 x_at(u64 i) const override { return x_[static_cast<std::size_t>(i)]; }

tests/test_render_smoke.cpp

@@ -38,6 +38,23 @@ constexpr plot::u32 kH = 360;
 /// 1M-wide window holds ~16 of them (the dense envelope spans the full height in
 /// every column) while a 640-wide one is a nearly flat line (the sparse path's
 /// polyline crosses every column exactly once).
+/// A sine of **one period per pixel column** for the window
+/// `a_dense_trace_can_be_graded_by_dwell` draws (60 000 x-units over a 572 px axis, so
+/// 104.9 samples a column). That is the one density at which a column *has* a dwell
+/// structure to grade: its envelope spans the full amplitude, so the band is tall, and
+/// the sub-buckets inside it are a fraction of a period each, so the ones at the sine's
+/// turning points are short and the ones crossing its middle are long. A period of many
+/// columns leaves every band a thin ribbon with nothing to distinguish, and a period of a
+/// fraction of a column fills every sub-bucket to the full amplitude -- also nothing.
+std::vector<plot::f32> fast_sine_samples() {
+  std::vector<plot::f32> y(1'000'000);
+  const double w = 2.0 * 3.14159265358979323846 / 104.9;
+  for (plot::u64 i = 0; i < y.size(); ++i) {
+    y[i] = static_cast<plot::f32>(std::sin(static_cast<double>(i) * w));
+  }
+  return y;
+}
+
 std::vector<plot::f32> sine_samples() {
   std::vector<plot::f32> y(1'000'000);
   for (plot::u64 i = 0; i < y.size(); ++i) {
@@ -723,11 +740,11 @@ class LyingGridSeries final : public plot::data::Series {
     if (x_at(i0) != x && i0 + 1u < kN) i1 = i0 + 1u;
     return true;
   }
-  void gather(u32, u64 begin, u64 end, std::vector<f32>& out,
+  void gather(u32, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out,
               plot::data::GatherMode) const override {
     ++gather_calls_;
     for (u64 i = begin; i < end; ++i) {
-      out.push_back(static_cast<f32>(x_at(i) - x0()));
+      out.push_back(static_cast<f32>(x_at(i) - x_origin));
       out.push_back(kY);
     }
   }
@@ -868,6 +885,260 @@ PLOT_TEST(dense_and_sparse_paths_agree_on_extent) {
   ctx.destroy();
 }
 
+/// A window denser than the pixel grid inks **whole columns**, which is what kills the moire.
+///
+/// Reported as "strong moire patterns due to a large number of vertical lines" on a high rate,
+/// a high frequency or a noisy signal. The polyline at this density is a stack of near-vertical
+/// hairlines at *fractional* x -- one to two envelope buckets per column, each a min->max
+/// hairline plus a connector -- so a column's brightness is a non-linear function of those
+/// sub-pixel phases, and the phases repeat at the beat between the bucket pitch and the pixel
+/// pitch. That beat is the pattern, and panning sweeps it, so it crawls.
+///
+/// The observable is the beat's own cause, measured: how many **distinct coverage levels** the
+/// trace's ink takes. One segment per column puts every column's ink at one sub-pixel phase, so
+/// the AA ramp is evaluated at the same few distances everywhere and the ink lands on **4**
+/// levels; the polyline's hairlines sit at arbitrary phases and its ink spreads over **126** of
+/// them. That spread *is* the texture, and it is what beats against the pixel pitch.
+///
+/// A count of partially covered pixels is *not* the reading, which is worth knowing before
+/// adding one: both renderings put about the same amount of ink in the fringe (577 against 652
+/// here, of 1400-odd inked pixels), because a 1.5 px stroke with a 1 px fringe always spills
+/// into its neighbour. The fix is not that the fringe is gone, it is that it is the *same*
+/// fringe in every column.
+///
+/// The window is one period of the sine over 107 samples per pixel: dense enough for the
+/// reduction and slow enough that the band is a *thin ribbon*, which is where the beat shows.
+/// A window whose buckets each span several periods paints a solid block and hides it.
+PLOT_TEST(a_dense_trace_is_drawn_as_whole_pixel_columns) {
+  plottest::HeadlessContext ctx(kW, kH);
+  plot::Status st;
+  PLOT_CHECK(ctx.create(&st));
+  PLOT_CHECK(plot::gl::load(nullptr));
+  plot::Renderer r;
+  PLOT_CHECK(r.init(&st));
+
+  plot::data::ArraySeries s(sine_samples(), 0.0, 1.0);
+  plot::Plot p;
+  p.set_viewport({0, 0, static_cast<plot::f32>(kW), static_cast<plot::f32>(kH)});
+  const plot::u32 ax = p.add_x_axis({"t", {0.0, 60'000.0}, false, plot::AxisPlace::Bottom, false});
+  const plot::u32 ay = p.add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+  p.add_trace({&s, plot::Color::hex(0x40C0FF), 1.5f, ax, ay});
+
+  r.begin_frame(kW, kH, {0, 0, static_cast<plot::f32>(kW), static_cast<plot::f32>(kH)});
+  r.draw(p);
+  r.end_frame();
+  dump_if_requested(r, "columns.ppm");
+
+  const plot::Rect a = p.layout().axes;
+  // Blue over the background minus red is the trace's coverage, linearly: 8 at no coverage
+  // and 199 at full (0x40C0FF over 0x101418). Nothing else in this frame is blue-dominant --
+  // the grid and the axis line are grey -- so the two bands below are the trace's own ink,
+  // split at three quarters covered.
+  plot::u32 inked = 0;
+  plot::u32 histogram[256] = {};
+  for (plot::u32 row = 0; row < static_cast<plot::u32>(a.h); ++row) {
+    for (plot::u32 col = 0; col < static_cast<plot::u32>(a.w); ++col) {
+      plot::u8 px[4] = {};
+      const plot::u32 x = static_cast<plot::u32>(a.x) + col;
+      PLOT_CHECK(ctx.read_pixel(x, ctx.height - 1u - (static_cast<plot::u32>(a.y) + row), px));
+      const int cover = static_cast<int>(px[2]) - static_cast<int>(px[0]);
+      if (cover > 40) {   // the trace's ink, at a quarter covered or better
+        ++inked;
+        ++histogram[cover];
+      }
+    }
+  }
+  // How many *distinct* coverages the ink takes is the beat, measured. A column's ink is
+  // placed at one sub-pixel phase, so the AA ramp is evaluated at the same few distances in
+  // every column and the ink lands on a handful of levels; a polyline's hairlines sit at
+  // arbitrary phases, so its ink spreads over the whole range of them. The floor of 4 pixels
+  // per level ignores the stragglers at the ribbon's turning points.
+  plot::u32 levels = 0;
+  for (plot::u32 c = 0; c < 256u; ++c) {
+    if (histogram[c] >= 4u) ++levels;
+  }
+  std::printf("[columns] axes=[%.1f %.1f %.1f %.1f] raw=%u lod=%u columns=%u segments=%u "
+              "visible=%llu inked=%u levels=%u\n",
+              a.x, a.y, a.w, a.h, r.stats().raw_traces, r.stats().lod_traces,
+              r.stats().column_traces, r.stats().staged_segments,
+              static_cast<unsigned long long>(r.stats().visible_samples), inked, levels);
+
+  // The reduction ran, and on the *raw* path: the gate is the gathered density, not the level.
+  PLOT_CHECK(r.stats().column_traces == 1);
+  PLOT_CHECK(r.stats().visible_samples > 50'000u);
+  // One segment per column, so the frame's whole geometry -- grid and axis lines included --
+  // is bounded by the axis' width: 627 against the polyline's 60 054.
+  PLOT_CHECK(r.stats().staged_segments < static_cast<plot::u32>(a.w) + 64u);
+  // The ribbon is there, and its ink sits on a handful of coverage levels (4) rather than on a
+  // continuum of them (126).
+  PLOT_CHECK(inked > static_cast<plot::u32>(a.w));
+  PLOT_CHECK(levels <= 8u);
+
+  PLOT_CHECK(!r.last_frame_had_gl_error());
+  ctx.destroy();
+}
+
+/// `Style::intensity_grading`: a reduced column is drawn **graded by dwell** -- bright
+/// where the signal sits, faint where it only passes through -- which is the second half
+/// of the moire answer. The columns alone removed the beat; this is what puts back the
+/// information a flat band throws away, the way a phosphor display does.
+///
+/// The observable is the thing the feature claims and nothing weaker: within one column,
+/// the rows at the **edges** of the band are brighter than the rows in its **middle**.
+/// For a sine of one period per column that is exactly right -- it dwells at its turning
+/// points and crosses its middle at full speed -- and it is a property of the *rendering*
+/// rather than of the waveform, because the same frame drawn ungraded puts the band's
+/// edge and its middle at the same coverage. Both frames are measured here, so what is
+/// asserted is the difference between them.
+///
+/// It also pins what grading may *not* cost. The reduction still runs (`column_traces`),
+/// so the beat is still gone; the geometry is still bounded by the axis' width times a
+/// small factor, because a run is a stretch of equal tier and not a row; and the draw
+/// calls are bounded by the steps, since the line pipeline's colour is a uniform.
+PLOT_TEST(a_dense_trace_can_be_graded_by_dwell) {
+  plottest::HeadlessContext ctx(kW, kH);
+  plot::Status st;
+  PLOT_CHECK(ctx.create(&st));
+  PLOT_CHECK(plot::gl::load(nullptr));
+  plot::Renderer r;
+  PLOT_CHECK(r.init(&st));
+
+  plot::data::ArraySeries s(fast_sine_samples(), 0.0, 1.0);
+  plot::Plot p;
+  p.set_viewport({0, 0, static_cast<plot::f32>(kW), static_cast<plot::f32>(kH)});
+  const plot::u32 ax = p.add_x_axis({"t", {0.0, 60'000.0}, false, plot::AxisPlace::Bottom, false});
+  const plot::u32 ay = p.add_y_axis({"v", {-1.0, 1.0}, false, plot::AxisPlace::Left, false});
+  p.add_trace({&s, plot::Color::hex(0x40C0FF), 1.5f, ax, ay});
+
+  // The band's edges against its middle, averaged over columns across the axis. The
+  // shares are of the band's own height, so the reading does not depend on where the
+  // band happens to sit or on how tall it is: the outer fifth at each end against the
+  // middle fifth.
+  struct Profile {
+    plot::u32 edge = 0;     ///< mean peak coverage over the band's two outer fifths
+    plot::u32 middle = 0;   ///< mean peak coverage over its middle fifth
+    plot::u32 columns = 0;  ///< columns that held a band at all
+  };
+  auto profile = [&](const plot::Rect& a) -> Profile {
+    const plot::u32 rows = static_cast<plot::u32>(a.h);
+    std::vector<int> cover(rows, 0);
+    plot::u64 edge_sum = 0;
+    plot::u64 middle_sum = 0;
+    Profile out;
+    for (plot::u32 col = 8; col + 8 < static_cast<plot::u32>(a.w); col += 16) {
+      plot::u32 lo = rows;
+      plot::u32 hi = 0;
+      for (plot::u32 row = 0; row < rows; ++row) {
+        plot::u8 px[4] = {};
+        const plot::u32 x = static_cast<plot::u32>(a.x) + col;
+        PLOT_CHECK(ctx.read_pixel(x, ctx.height - 1u - (static_cast<plot::u32>(a.y) + row), px));
+        cover[row] = static_cast<int>(px[2]) - static_cast<int>(px[0]);
+        if (cover[row] > 20) {   // the faintest step is 0.3 of 191, so this is under it
+          if (row < lo) lo = row;
+          hi = row;
+        }
+      }
+      // A band of fewer than 15 rows has no middle fifth to speak of; at this density
+      // there is none, but the reading would be meaningless if there were.
+      if (lo >= hi || hi - lo < 15u) continue;
+      const plot::u32 h = hi - lo + 1u;
+      const plot::u32 fifth = h / 5u;
+      int edge = 0;
+      int middle = 0;
+      for (plot::u32 row = lo; row <= hi; ++row) {
+        const plot::u32 d = row - lo;
+        if (d < fifth || d >= h - fifth) {
+          if (cover[row] > edge) edge = cover[row];
+        } else if (d >= 2u * fifth && d < 3u * fifth) {
+          if (cover[row] > middle) middle = cover[row];
+        }
+      }
+      edge_sum += static_cast<plot::u64>(edge);
+      middle_sum += static_cast<plot::u64>(middle);
+      ++out.columns;
+    }
+    if (out.columns != 0) {
+      out.edge = static_cast<plot::u32>(edge_sum / out.columns);
+      out.middle = static_cast<plot::u32>(middle_sum / out.columns);
+    }
+    return out;
+  };
+
+  // Ungraded first: the reference the grading is read against.
+  r.begin_frame(kW, kH, {0, 0, static_cast<plot::f32>(kW), static_cast<plot::f32>(kH)});
+  r.draw(p);
+  r.end_frame();
+  dump_if_requested(r, "ungraded.ppm");
+  const plot::Rect a = p.layout().axes;
+  const Profile flat = profile(a);
+  const plot::u32 flat_segments = r.stats().staged_segments;
+  const plot::u32 flat_draws = r.stats().draw_calls;
+  PLOT_CHECK(r.stats().column_traces == 1 && r.stats().graded_traces == 0);
+  PLOT_CHECK(!r.last_frame_had_gl_error());
+
+  r.style().intensity_grading = true;
+  r.begin_frame(kW, kH, {0, 0, static_cast<plot::f32>(kW), static_cast<plot::f32>(kH)});
+  r.draw(p);
+  r.end_frame();
+  dump_if_requested(r, "graded.ppm");
+  const Profile lit = profile(a);
+
+  std::printf("[graded] axes=[%.1f %.1f %.1f %.1f] flat edge=%u middle=%u cols=%u seg=%u "
+              "draws=%u | graded edge=%u middle=%u cols=%u seg=%u draws=%u columns=%u "
+              "graded_traces=%u\n",
+              a.x, a.y, a.w, a.h, flat.edge, flat.middle, flat.columns, flat_segments,
+              flat_draws, lit.edge, lit.middle, lit.columns, r.stats().staged_segments,
+              r.stats().draw_calls, r.stats().column_traces, r.stats().graded_traces);
+
+  // Both frames measured a band in most of the columns they sampled, or the two
+  // profiles are not comparable and everything below is vacuous.
+  PLOT_CHECK(flat.columns > 20u && lit.columns == flat.columns);
+  // The flat band is flat: its edge and its middle are one ink (191 and 191).
+  PLOT_CHECK(flat.middle > 0u && flat.edge * 100u < flat.middle * 115u);
+  // The graded one is not, and in the direction a sine dwells in: 191 against 131, a
+  // middle at 0.69 of the edge. The figure is a *tier* ratio and not the dwell ratio --
+  // the per-row dwell at the rails is several times the crossing's, and
+  // `intensity_gamma` (0.45) and `intensity_floor` (0.3) are there to compress exactly
+  // that into a range an eye reads as shading rather than as a gap. So the threshold is
+  // what the quantised ink does, with room for a step either way.
+  PLOT_CHECK(lit.middle > 0u && lit.middle * 100u < lit.edge * 80u);
+  // The reduction still ran, so the beat the columns removed is still gone.
+  PLOT_CHECK(r.stats().column_traces == 1 && r.stats().graded_traces == 1);
+  // A run is a stretch of equal tier, not a row: the geometry stays bounded by the
+  // axis' width times a small factor, nothing like `w * h`. Measured 8303 over a 572 px
+  // axis, 14.5 runs a column -- the dwell profile's own structure (four tiers from the
+  // dim middle out to each rail) plus the quantiser's dither at each boundary. The flat
+  // path's 627 is the other end of the scale, and 572 * 156 rows is what this is not.
+  PLOT_CHECK(r.stats().staged_segments < 24u * static_cast<plot::u32>(a.w));
+  // And the draw calls by the steps: one per tier that staged anything, over the flat
+  // frame's single trace draw.
+  PLOT_CHECK(r.stats().draw_calls <= flat_draws + r.style().intensity_steps);
+
+  // And the level floor, which the window above cannot see: at 105 samples a pixel the
+  // flat path is already on raw samples, so grading asks for nothing finer. A wider
+  // window puts the flat path on the pyramid, and there a sub-column is `spp / 8` -- which
+  // falls under one bucket long before the column does, so an unfloored ask answers level
+  // 0 and gathers the whole visible window. That is a real cost and it was measured: at
+  // 1.3 MS/s over a 2 s window udpscope's own frame report went from `raw=710 lod=453` to
+  // `raw=1154 lod=0` and 2.3 -> 6.4 ms a frame. The floor is one bucket level, so the
+  // reading is simply that a graded frame stays on the pyramid.
+  p.set_x_range(ax, {0.0, 200'000.0});
+  r.begin_frame(kW, kH, {0, 0, static_cast<plot::f32>(kW), static_cast<plot::f32>(kH)});
+  r.draw(p);
+  r.end_frame();
+  std::printf("[graded] wide: raw=%u lod=%u columns=%u graded=%u seg=%u visible=%llu\n",
+              r.stats().raw_traces, r.stats().lod_traces, r.stats().column_traces,
+              r.stats().graded_traces, r.stats().staged_segments,
+              static_cast<unsigned long long>(r.stats().visible_samples));
+  PLOT_CHECK(r.stats().visible_samples > 100'000u);
+  PLOT_CHECK(r.stats().lod_traces == 1 && r.stats().raw_traces == 0);
+  PLOT_CHECK(r.stats().column_traces == 1 && r.stats().graded_traces == 1);
+  PLOT_CHECK(r.stats().staged_segments < 24u * static_cast<plot::u32>(a.w));
+
+  PLOT_CHECK(!r.last_frame_had_gl_error());
+  ctx.destroy();
+}
+
 // Resolution #1 of the brief: the renderer draws into whatever framebuffer is
 // bound and clears only its viewport, so a host that embeds the plot in a
 // sub-rect (Qt/GTK/ImGui) keeps the rest of its surface. Coordinates are given
@@ -1512,9 +1783,10 @@ PLOT_TEST(a_clamped_front_does_not_draw_a_segment_across_the_panel) {
       if (x_at(k) != x && k + 1u < 8u) i1 = k + 1u;
       return true;
     }
-    void gather(u32, u64 begin, u64 end, std::vector<f32>& out, plot::data::GatherMode) const override {
+    void gather(u32, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out,
+                plot::data::GatherMode) const override {
       for (u64 i = begin; i < end; ++i) {
-        out.push_back(static_cast<f32>(x_at(i) - x0()));
+        out.push_back(static_cast<f32>(x_at(i) - x_origin));
         out.push_back(i < 2u ? -1.0f : 1.0f);
       }
     }

tests/test_series.cpp

@@ -24,7 +24,7 @@ PLOT_TEST(array_series_bounds_and_gather) {
   PLOT_CHECK_NEAR(s.x_bounds().max, 11.5, 1e-9);
   PLOT_CHECK_NEAR(s.y_bounds().min, -2.0, 1e-6);
   std::vector<f32> out;
-  s.gather(0, 0, 4, out);
+  s.gather(0, 0, 4, s.x0(), out);
   PLOT_CHECK(out.size() == 8);             // interleaved x,y
   // x is relative to x0(): sample 0 emits 0, not 10 (the relative-x contract).
   PLOT_CHECK_NEAR(out[0], 0.0, 1e-6);
@@ -104,7 +104,7 @@ PLOT_TEST(stream_series_exact_queries_survive_ring_wrap) {
   PLOT_CHECK_NEAR(s.sumsq(0, n), sumsq, 1e-1);
 
   std::vector<f32> out;
-  s.gather(0, 0, n, out);                               // level 0: raw samples
+  s.gather(0, 0, n, s.x0(), out);                               // level 0: raw samples
   PLOT_CHECK(out.size() == 2 * n);
   // x is relative to x0(): the oldest retained sample emits 0, the newest
   // (n - 1) * dx, never the absolute data coordinates (relative-x contract).
@@ -157,7 +157,7 @@ PLOT_TEST(stream_series_push_and_read_are_race_free) {
       (void)s.sum(0, n);
       (void)s.sumsq(0, n);
       std::vector<f32> out;
-      s.gather(0, 0, n, out);                           // reads the oldest edge
+      s.gather(0, 0, n, s.x0(), out);                           // reads the oldest edge
       if (out.size() != 2 * n) sizes_ok = false;
     }
     ++reads;
@@ -258,7 +258,7 @@ PLOT_TEST(stream_series_sliding_window_queries_match_bruteforce) {
   // wholly at or after window index 0, `last` one past the last wholly inside
   // the window -- so every emitted bucket's samples lie inside the window.
   std::vector<f32> out;
-  s.gather(1, 0, n, out);
+  s.gather(1, 0, n, s.x0(), out);
   const u64 first =
       std::max(base / span + (base % span == 0 ? u64{0} : u64{1}), lbase);   // ceil, then clamp
   const u64 last = std::min((base + n) / span, lbase + lsize);
@@ -374,7 +374,7 @@ PLOT_TEST(gather_at_a_lod_level_reaches_both_ends_of_the_window) {
 
   const auto check_ends = [&](u32 level) {
     std::vector<f32> out;
-    s.gather(level, 0, n, out);
+    s.gather(level, 0, n, s.x0(), out);
     PLOT_CHECK(out.size() >= 8u);
     // Oldest: the first emitted pair is the retained sample at index 0, not the
     // first whole bucket (which starts `lead` samples later). x is relative to
@@ -403,7 +403,7 @@ PLOT_TEST(gather_at_a_lod_level_reaches_both_ends_of_the_window) {
   PLOT_CHECK((ny % 256u) != 0u);   // 5000 = 19 * 256 + 136 at level 2
   plot::data::ArraySeries a(y, 0.0, 1e-6);
   std::vector<f32> out;
-  a.gather(2, 0, ny, out);
+  a.gather(2, 0, ny, a.x0(), out);
   PLOT_CHECK(out.size() >= 8u);
   PLOT_CHECK_NEAR(out[0], 0.0, 1e-9);                       // level 2 starts on the grid
   PLOT_CHECK_NEAR(out[out.size() - 2], f32(f64(ny - 1) * 1e-6), 1e-9);
@@ -469,7 +469,7 @@ PLOT_TEST(gather_envelope_stays_inside_an_unaligned_range) {
 
   const auto check_range = [&](u32 level) {
     std::vector<f32> out;
-    s.gather(level, b, e, out);
+    s.gather(level, b, e, s.x0(), out);
     PLOT_CHECK(out.size() >= 4u);
     for (plot::usize i = 0; i + 1 < out.size(); i += 2) {
       PLOT_CHECK(f64(out[i]) >= f64(b));    // emitted x inside [begin, end)
@@ -499,7 +499,7 @@ PLOT_TEST(gather_envelope_stays_inside_an_unaligned_range) {
   const u64 buckets = last - first;
   PLOT_CHECK(lead > b && last * span < e);   // both edge spans really are partial
   std::vector<f32> out;
-  s.gather(level, b, e, out);
+  s.gather(level, b, e, s.x0(), out);
   PLOT_CHECK(out.size() == 2 * ((lead - b) + 2 * buckets + (e - last * span)));
   plot::usize o = 0;
   for (u64 i = b; i < lead; ++i, o += 2) {   // the partial leading bucket, raw
@@ -544,7 +544,7 @@ PLOT_TEST(stream_gather_envelope_stays_inside_an_unaligned_range) {
   const plot::Range exact = s.reduce(b, e);
   PLOT_CHECK(exact.max < 1.0 && exact.min > -1.0);
   std::vector<f32> out;
-  s.gather(1, b, e, out);
+  s.gather(1, b, e, s.x0(), out);
   PLOT_CHECK(out.size() >= 4u);
   for (plot::usize i = 0; i + 1 < out.size(); i += 2) {
     PLOT_CHECK(f64(out[i]) >= f64(b));              // relative x inside [begin, end)
@@ -614,11 +614,11 @@ PLOT_TEST(gather_level_beyond_the_pyramid_clamps) {
   for (u64 i = 0; i < y.size(); ++i) y[i] = f32(i % 13) - 6.0f;
   plot::data::ArraySeries s(std::move(y), 0.0, 1.0);
   std::vector<f32> deepest;
-  s.gather(plot::data::kMaxPyramidLevel, 0, s.size(), deepest);
+  s.gather(plot::data::kMaxPyramidLevel, 0, s.size(), s.x0(), deepest);
   PLOT_CHECK(!deepest.empty());
   for (const u32 level : {u32{58}, u32{200}, u32{1000}, ~u32{0}}) {
     std::vector<f32> out;
-    s.gather(level, 0, s.size(), out);
+    s.gather(level, 0, s.size(), s.x0(), out);
     PLOT_CHECK(out == deepest);   // clamped to the same deepest geometry
   }
   // The cap is where the span shift still fits: level 57 spans exactly 2^63.
@@ -657,9 +657,9 @@ PLOT_TEST(gather_modes_envelope_nearest_mean) {
   PLOT_CHECK(buckets == 16);
 
   std::vector<f32> env, near, mean;
-  s.gather(level, 0, kN, env, plot::data::GatherMode::Envelope);
-  s.gather(level, 0, kN, near, plot::data::GatherMode::Nearest);
-  s.gather(level, 0, kN, mean, plot::data::GatherMode::Mean);
+  s.gather(level, 0, kN, s.x0(), env, plot::data::GatherMode::Envelope);
+  s.gather(level, 0, kN, s.x0(), near, plot::data::GatherMode::Nearest);
+  s.gather(level, 0, kN, s.x0(), mean, plot::data::GatherMode::Mean);
 
   // Envelope: two points per bucket, min at the bucket's first sample, max at
   // its last (this sawtooth's per-bucket min is its first sample's value and
@@ -692,7 +692,7 @@ PLOT_TEST(gather_modes_envelope_nearest_mean) {
 
   // Level 0 and sub-bucket ranges are the raw samples for every mode.
   std::vector<f32> raw;
-  s.gather(0, 5, 300, raw, plot::data::GatherMode::Mean);
+  s.gather(0, 5, 300, s.x0(), raw, plot::data::GatherMode::Mean);
   PLOT_CHECK(raw.size() == 2 * (300 - 5));
   PLOT_CHECK_NEAR(raw[0], 5.0, 1e-9);
 }
@@ -712,17 +712,17 @@ PLOT_TEST(gather_skips_all_nan_buckets) {
 
   // first = 0, last = 256/128 = 2: buckets 0 and 1, no lead/trail raw spans.
   std::vector<f32> env, mean, near;
-  s.gather(1, 0, 256, env, plot::data::GatherMode::Envelope);
+  s.gather(1, 0, 256, s.x0(), env, plot::data::GatherMode::Envelope);
   PLOT_CHECK(env.size() == 4);              // bucket 0's two pairs only
   PLOT_CHECK_NEAR(env[0], 0.0, 1e-9);
   PLOT_CHECK_NEAR(env[1], 1.0, 1e-9);
   PLOT_CHECK_NEAR(env[2], 127.0, 1e-9);
   PLOT_CHECK_NEAR(env[3], 1.0, 1e-9);
-  s.gather(1, 0, 256, mean, plot::data::GatherMode::Mean);
+  s.gather(1, 0, 256, s.x0(), mean, plot::data::GatherMode::Mean);
   PLOT_CHECK(mean.size() == 2);             // bucket 1 has no finite mean: skipped
   PLOT_CHECK_NEAR(mean[0], 64.0, 1e-9);
   PLOT_CHECK_NEAR(mean[1], 1.0, 1e-9);
-  s.gather(1, 0, 256, near, plot::data::GatherMode::Nearest);
+  s.gather(1, 0, 256, s.x0(), near, plot::data::GatherMode::Nearest);
   PLOT_CHECK(near.size() == 4);             // every bucket still has a centre sample
   PLOT_CHECK_NEAR(near[0], 64.0, 1e-9);
   PLOT_CHECK_NEAR(near[1], 1.0, 1e-9);
@@ -739,7 +739,7 @@ PLOT_TEST(stream_series_freeze_copies_the_last_acquire_window) {
   const u64 n = s.size();
   const plot::Range bounds = s.y_bounds();
   std::vector<f32> gathered;
-  s.gather(1, 0, n, gathered);
+  s.gather(1, 0, n, s.x0(), gathered);
   const plot::Range reduced = s.reduce(0, n);
 
   // Freeze now, while the ring still holds exactly the published window.
@@ -754,7 +754,7 @@ PLOT_TEST(stream_series_freeze_copies_the_last_acquire_window) {
   PLOT_CHECK_NEAR(fr.max, reduced.max, 1e-6);
   PLOT_CHECK_NEAR(frozen.sum(0, n), s.sum(0, n), 1e-3);
   std::vector<f32> frozen_gathered;
-  frozen.gather(1, 0, n, frozen_gathered);
+  frozen.gather(1, 0, n, frozen.x0(), frozen_gathered);
   PLOT_CHECK(frozen_gathered == gathered);   // same geometry, byte for byte
 
   // The producer now laps the ring (700 more pushes overwrite the oldest
@@ -769,6 +769,46 @@ PLOT_TEST(stream_series_freeze_copies_the_last_acquire_window) {
   PLOT_CHECK(frozen.reduce(0, n).max == reduced.max);
 }
 
+// --- The gather origin: f32 precision against the view, not the window -------
+
+PLOT_TEST(a_gather_origin_at_the_view_keeps_a_deep_zoom_on_the_sample_it_quotes) {
+  // 20 s of retained data at 1 kS/s examined through a 10 us window -- the shape of
+  // a scope zoomed in on a long ring. gather() stages x as f32, so what the origin
+  // decides is the span that f32 has to resolve: the whole retained window (which
+  // is what `x0()`, the old implicit origin, names) or the part of it on screen. A
+  // readout quotes `x_at()` in exact f64, so the difference between the two is the
+  // distance between where a sample is *drawn* and the x reported for it.
+  constexpr u64 kN = 20001;
+  std::vector<f32> y(static_cast<plot::usize>(kN));
+  for (u64 i = 0; i < kN; ++i) y[static_cast<plot::usize>(i)] = f32(i % 71);
+  const plot::data::ArraySeries s(std::move(y), /*x0=*/0.0, /*dx=*/1e-3);
+  PLOT_CHECK_NEAR(s.x_bounds().max, 20.0, 1e-9);
+
+  const f64 centre = s.x_at(kN - 2u);                      // 19.999 s, near the far end
+  const plot::Range view{centre - 5e-6, centre + 5e-6};    // 10 us across
+  const f64 px_per_x = 700.0 / (view.max - view.min);      // a typical axis width
+
+  const auto worst_error_px = [&](f64 origin) {
+    std::vector<f32> out;
+    s.gather(0, kN - 3u, kN, origin, out);
+    PLOT_CHECK(out.size() == 6u);
+    f64 worst = 0.0;
+    for (u64 k = 0; k < 3u; ++k) {
+      // Exactly the renderer's reconstruction: the origin added back in f64.
+      const f64 drawn = origin + f64(out[static_cast<plot::usize>(2u * k)]);
+      worst = std::max(worst, std::abs(drawn - s.x_at(kN - 3u + k)) * px_per_x);
+    }
+    return worst;
+  };
+
+  // The visible range's minimum: the f32 resolves 2^-24 of what is on screen, so
+  // the error is a fixed fraction of a pixel at every zoom.
+  PLOT_CHECK(worst_error_px(view.min) < 0.05);
+  // The start of the retained window -- what every caller used to get -- resolves
+  // 2^-24 of 20 s instead, which at this zoom is most of the axis.
+  PLOT_CHECK(worst_error_px(s.x0()) > 10.0);
+}
+
 // --- Incremental append: ArraySeries::push() ----------------------------------
 
 PLOT_TEST(array_series_push_matches_commit) {

tests/test_ticks.cpp

@@ -263,6 +263,18 @@ PLOT_TEST(format_time_never_lets_a_field_reach_its_radix) {
   plot::format_time(86399.5, b, sizeof b);  PLOT_CHECK(std::string(b) == "1d");
   plot::format_time(86400.0, b, sizeof b);  PLOT_CHECK(std::string(b) == "1d");
 
+  // A mantissa may not reach its own radix either: three significant figures of a value a
+  // hair under a rung's top round up to 1000, and `%.3g` writes that `1e+03`. A one-second
+  // tick computed as 0.9999999 s read `1e+03ms` on a live axis, which is where this was seen.
+  plot::format_time(0.9999999, b, sizeof b);  PLOT_CHECK(std::string(b) == "1s");
+  plot::format_time(0.9995, b, sizeof b);     PLOT_CHECK(std::string(b) == "1s");
+  plot::format_time(0.9994, b, sizeof b);     PLOT_CHECK(std::string(b) == "999ms");
+  plot::format_time(0.9999999e-3, b, sizeof b); PLOT_CHECK(std::string(b) == "1ms");
+  plot::format_time(0.9994e-3, b, sizeof b);  PLOT_CHECK(std::string(b) == "999\u00b5s");
+  plot::format_time(0.9999999e-6, b, sizeof b); PLOT_CHECK(std::string(b) == "1\u00b5s");
+  plot::format_time(0.9999999e-9, b, sizeof b); PLOT_CHECK(std::string(b) == "1ns");
+  plot::format_time(-0.9999999, b, sizeof b); PLOT_CHECK(std::string(b) == "-1s");
+
   // Sweep the boundary neighbourhoods and check every emitted field.
   const double values[] = {0.4, 0.9995, 1.0, 59.4, 59.4999, 59.5, 59.9, 60.0, 90.0, 119.5, 3599.4,
                            3599.5, 3599.9, 86399.4, 86399.5, 86399.9, 86400.0, 172800.0, -119.5,

tests/test_xy_series.cpp

@@ -52,7 +52,8 @@ PLOT_TEST(xy_series_reports_its_own_grid) {
   PLOT_CHECK_NEAR(s.y_bounds().max, 48.0, 1e-6);
 
   // Epoch-style offset: the same shape shifted by 1.7e9 keeps exact bounds, and
-  // gather() emits x relative to x0() -- small numbers, not quantised epochs.
+  // gather() emits x relative to the origin the caller names -- x0() here, so
+  // small numbers, not quantised epochs.
   std::vector<f64> epoch = spread_x(500);
   const std::vector<f64> es = epoch;   // un-moved copy for the expectations
   for (auto& v : epoch) v += 1.7e9;
@@ -60,7 +61,7 @@ PLOT_TEST(xy_series_reports_its_own_grid) {
   PLOT_CHECK_NEAR(e.x_bounds().min, 1.7e9, 1e-3);
   PLOT_CHECK_NEAR(e.x_bounds().max, 1.7e9 + (xs.back() - xs.front()), 1e-3);
   std::vector<f32> out;
-  e.gather(0, 0, 500, out);
+  e.gather(0, 0, 500, e.x0(), out);
   PLOT_CHECK(out.size() == 1000);
   // x is relative to x0(): x_at(i) - x0(), the array's own offsets -- small
   // values even though the absolute epoch is 1.7e9. The expectations come from
@@ -186,7 +187,7 @@ PLOT_TEST(xy_series_gather_envelope_matches_exact_reduces) {
   const u64 span = u64{kBucket} << level;
   const u64 b = 500 + 33, e = 3500 - 57;   // unaligned on the bucket grid
   std::vector<f32> out;
-  s.gather(level, b, e, out, plot::data::GatherMode::Envelope);
+  s.gather(level, b, e, s.x0(), out, plot::data::GatherMode::Envelope);
   PLOT_CHECK(out.size() >= 8u);
   // Emitted x stays inside [x_at(begin), x_at(end)) and the geometry reaches
   // both the range's extremes (the lead/trail raw spans carry them).