fix(plot): a crosshair readout quotes a sample, never a value between two

The readout's y was a linear interpolation between the two samples adjacent to
the pointer, which answers "what is the signal at this instant" -- a number the
series does not contain. On a source whose samples are already averaged or
decimated at ingest that is a value nothing measured, and at a zoom past the
sample spacing it is visibly not the datum under the pointer.

`crosshair_span()`'s `t` becomes a selector rather than a blend factor: the
nearer end wins, a tie reading the earlier sample (the bias the span already
takes for a degenerate pair). `t` is measured on the samples' own x through
`neighbours()`/`x_at()`, so "nearer" is exact on a non-uniform clock too, and
the lookup still reads level 0, so the value is a stored sample and never an
LOD bucket's aggregate. `crosshair_interpolate()` had no other caller and is
gone.

`CrosshairRow::marker` is placed from the same y, so the dot follows the
reported sample: past the sample spacing it sits beside the polyline rather
than on it, deliberately -- one y feeding both keeps the mark and the number
from ever disagreeing.

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

README.md

@@ -47,7 +47,7 @@ run touched a GPU, so read it as an upper bound and a record of the software pat
 - cursors in both orientations — vertical markers and horizontal rulers;
 - draggable regions and measurement bands with exact interval statistics;
 - a signal legend anchored to an axes corner;
-- a hover crosshair with a per-signal, interpolated readout;
+- a hover crosshair with a per-signal readout of the nearest sample's value;
 - a multi-plot `Figure` of stacked rows sharing one synchronised x axis;
 - live follow (`XFollow::Live`) with relative (multiplicative) zoom and mouse panning;
 - XY series for irregularly sampled data (`plot/data/xy_series.hpp`): sorted-ascending x

docs/data-and-performance.md

@@ -166,10 +166,10 @@ 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.
 
-## Exact versus interpolated
+## One sample or a statistic of many
 
-The library deliberately holds two conventions next to each other, and they do **not**
+Every number the library reports is one the samples actually hold. What differs between
-agree:
+these two is *how many* samples answer the question:
 
 - **`Series::reduce` / `sum` / `sumsq` are exact over a sample range.** They answer "what
   are the samples' extremes / sum / sum of squares over `[begin, end)`". Each is
@@ -179,15 +179,18 @@ agree:
   and no query allocates. `Measure::evaluate` and `Plot::region_stats` are built on these,
   never on the `*_buckets` forms, which would silently report wrong extremes for an
   unaligned interval.
-- **The crosshair readout is interpolated, and says so.** `crosshair_span(series, x)`
+- **The crosshair readout is a single sample — the nearest one.** `crosshair_span(series,
-  returns the two samples `x` lies between (`begin`, `end`, `t`), and
+  x)` returns the two samples `x` lies between (`begin`, `end`, `t`), and the readout takes
-  `crosshair_interpolate(y_begin, y_end, t)` does a linear interpolation: it answers "what
+  whichever of the two is nearer: `t <= 0.5` the earlier, otherwise the later. It answers
-  is the signal *at* this instant", which is generally between two samples — a different
+  "which datum is under the pointer", not "what is the signal *at* this instant" — a
-  question from an interval statistic. The lookup is O(1) (one division and a floor) and
+  linearly interpolated y is a number the series does not contain, and on a source whose
-  allocation-free; `Plot::crosshair_value(trace, x, out_y)` exposes the same number to a
+  samples are already averaged or decimated at ingest it is a claim about a signal nobody
-  host. A row whose trace has no sample at the crosshair's x shows `kCrosshairNoValue`
+  measured. The lookup is O(1) and allocation-free, and it reads level 0, so the value is a
-  (an em dash, `"—"`), and an x outside the series window yields no value rather than the
+  stored sample and never an LOD bucket's aggregate; `Plot::crosshair_value(trace, x,
-  nearest sample's.
+  out_y)` exposes the same number to a host, and `CrosshairRow::marker` is placed from that
+  same y, so the dot and the number cannot disagree. A row whose trace has no sample at the
+  crosshair's x shows `kCrosshairNoValue` (an em dash, `"—"`), and an x outside the series
+  window yields no value rather than clamping to the first or last sample.
 
 `Measurement` (from `Plot::measurement()`) documents `integral` as a **left-Riemann sum**,
 `sum(begin, end) * dx` — the samples taken as the value at the left edge of each step. That

docs/interaction.md

@@ -113,9 +113,10 @@ across the figure, and `Figure::set_crosshair(x, hovered_row, y_in_row, active)`
 horizontal line **only in the row the pointer is in** — a figure's rows share x and not y, so
 a figure-wide horizontal line would be a value that means something different in each row.
 
-Readout values are **interpolated**, not interval statistics (see
+Readout values are the **nearest sample's**, neither interpolated between two samples nor an
-[data-and-performance.md](data-and-performance.md)); a row whose trace has no sample at the
+interval statistic (see [data-and-performance.md](data-and-performance.md)); a row whose trace
-crosshair's x is listed with the em dash `"—"` and no marker, rather than a fabricated value.
+has no sample at the crosshair's x is listed with the em dash `"—"` and no marker, rather than a
+fabricated value.
 
 ## The gesture table (exactly as implemented)
 

include/plot/data/series.hpp

@@ -97,7 +97,7 @@ class Series {
   /// lands exactly on a sample). False when x lies outside the series' x
   /// bounds; `i0`/`i1` are then untouched. The crosshair and measurement
   /// paths read coordinates only through this and `x_at()`, so a series with
-  /// its own x array interpolates exactly.
+  /// its own x array brackets exactly.
   virtual bool neighbours(f64 x, u64& i0, u64& i1) const;
 
   /// Index of the sample nearest data-space `x`, clamped to `[0, size()-1]`;

include/plot/plot/crosshair.hpp

@@ -44,10 +44,11 @@ struct CrosshairStyle {
 /// drawn -- the single-coordinate `Plot::set_crosshair()` leaves the vertical one only,
 /// and a `Figure` is always vertical-only because its rows share x and not y.
 ///
-/// **The readout's values are interpolated, and deliberately so.** The y a row reports for
+/// **The readout's values are samples.** The y a row reports for a trace is the y of
-/// a trace is *linear interpolation between the two samples adjacent to `x`*, not a sample
+/// whichever of the two samples adjacent to `x` is **nearer** to it -- not a value
-/// and not an interval statistic -- see `crosshair_span()` for the rule stated in full, and
+/// interpolated between them, and not an interval statistic. See `crosshair_span()` for the
-/// for why it is the opposite convention from `Series::reduce()`/`sum()`/`sumsq()`.
+/// rule stated in full, and for how it differs from
+/// `Series::reduce()`/`sum()`/`sumsq()`.
 struct Crosshair {
   /// Whether the crosshair is drawn at all. Set by `Plot::set_crosshair()`; cleared by
   /// `Plot::clear_crosshair()`, which `input::Controller` calls when the pointer leaves the
@@ -58,7 +59,7 @@ struct Crosshair {
   /// Draw the horizontal line (the row of `y`). On for the two-coordinate overload only:
   /// a crosshair placed at one coordinate has no second value to mark a row with.
   bool horizontal = true;
-  /// List the visible traces and their interpolated values in a panel beside the pointer.
+  /// List the visible traces and their values in a panel beside the pointer.
   /// On by default, and free to leave on: a plot with no visible trace has no rows to
   /// measure and the panel is then not placed at all.
   bool show_readout = true;
@@ -84,14 +85,19 @@ struct Crosshair {
 /// arithmetic, which is O(1) in the series' length. The crosshair runs on every pointer
 /// move, so that is a requirement rather than a nicety.
 ///
-/// **Interpolated, not exact.** The value a caller builds from this span by
+/// **`t` chooses between the two samples; it does not blend them.** The value a caller
-/// `crosshair_interpolate()` between the two samples is the signal *at* `x`, which is
+/// builds from this span is the y of whichever end `t` is nearer to (`Plot::crosshair_value()`
-/// generally between two samples -- the opposite convention from `Series::reduce()`,
+/// takes `t <= 0.5` as `begin`), so a readout quotes a sample the series actually holds. It
-/// `sum()` and `sumsq()`, which are **exact over a sample range**. The two conventions sit
+/// used to be a linear interpolation between the two, which reads as "the signal at this
-/// next to each other in this library on purpose and they do not agree: `reduce()` answers
+/// instant" -- a number that is *between* the data and therefore in no row of it. On a
-/// "what are the samples' extremes over this interval", this answers "what is the signal at
+/// decimated or averaged source that is a value nothing measured, and at a zoom past the
-/// this instant". A readout that pretended to be exact would be quoting an extreme or a
+/// sample spacing it is visibly not the datum the pointer is over.
-/// mean of a window as if it were the value under the pointer.
+///
+/// So `t` is a *selector*, and this remains a different convention from
+/// `Series::reduce()`, `sum()` and `sumsq()`, which are **exact over a sample range**: those
+/// answer "what are the samples' extremes/total over this interval", this answers "which
+/// sample is under the pointer, and what is its value". Both now quote the data; what differs
+/// is whether the answer is one sample or a statistic of many.
 ///
 /// `valid` is false -- and every field left at its default -- for an **empty series**, a
 /// non-positive `dx()`, a non-finite `x`, and an `x` strictly outside the series' window
@@ -104,13 +110,14 @@ struct CrosshairSpan {
   /// Index of the first sample whose x is at or after the query: `begin` when the query
   /// lands on a sample, `begin + 1` between two of them.
   u64 end = 0;
-  /// The query's position between the two samples, in `[0, 1]`.
+  /// The query's position between the two samples, in `[0, 1]`. A *selector*, not a blend
+  /// factor -- see the struct comment.
   f64 t = 0.0;
   bool valid = false;
 };
 
 /// The sample span `x` falls in, on `series`; see `CrosshairSpan` for the rule, for the
-/// interpolation convention it is half of, and for the cases that yield `valid == false`.
+/// convention it is half of, and for the cases that yield `valid == false`.
 ///
 /// O(1) and allocation-free: a subtraction, a division and a truncation. The series' own sample
 /// fetch is the caller's -- `Plot::crosshair_value()` reads the span through
@@ -118,13 +125,6 @@ struct CrosshairSpan {
 /// allocates.
 CrosshairSpan crosshair_span(const data::Series& series, f64 x) noexcept;
 
-/// The interpolated y at `t` between two samples: `y_begin` at `t == 0`, `y_end` at
-/// `t == 1`. The one place the interpolation's arithmetic lives, so the lookup's rule and
-/// its documentation cannot drift apart.
-inline f64 crosshair_interpolate(f64 y_begin, f64 y_end, f64 t) noexcept {
-  return y_begin + (y_end - y_begin) * t;
-}
-
 /// One trace's line of the readout: which trace it is about, the value under the pointer
 /// and the boxes the renderer stages.
 ///
@@ -150,7 +150,7 @@ struct CrosshairRow {
   /// entries -- so a row that is not listed is still a listed *trace*, with a marker, just
   /// not a line in a panel that has no room for it.
   bool listed = false;
-  /// The trace's interpolated y at the crosshair's x, on the trace's own y axis. Only
+  /// The y of the trace's sample nearest the crosshair's x, on the trace's own y axis. Only
   /// meaningful when `valid`.
   f64 y = 0.0;
   /// The trace's name, or the positional placeholder of an unnamed one.
@@ -161,9 +161,12 @@ struct CrosshairRow {
   /// `kCrosshairNoValue`, the em dash. The absence is therefore *legible* -- a blank cell reads as
   /// "still loading" rather than as "nothing here" -- and nothing numeric is fabricated for it.
   std::string value;
-  /// The trace's intersection with the crosshair, in framebuffer pixels: the pen the
+  /// Where the renderer draws the marker, in framebuffer pixels: the pen for `y`, placed
-  /// renderer draws the marker at. Placed through the *trace's own* axis pair, so the
+  /// through the *trace's own* axis pair, so a trace on a secondary y axis is marked on the
-  /// marker is where that trace is actually drawn. Meaningless when `!valid`.
+  /// scale it is drawn against. It is the nearest **sample**, so at a zoom past the sample
+  /// spacing the marker sits beside the polyline rather than on it -- deliberately: it marks
+  /// the datum the row reports, and one y feeding both keeps the dot and the number from ever
+  /// disagreeing. Meaningless when `!valid`.
   Vec2 marker{};
   /// The swatch's box, `Legend::swatch_w` x `Legend::swatch_h` centred in the row. Empty
   /// when `!listed`.

include/plot/plot/plot.hpp

@@ -101,8 +101,8 @@ struct PlotLayout {
   /// where a pointer can grab it cannot drift apart.
   std::vector<RegionLayout> regions;
   /// The crosshair's geometry, when one is active: the two lines' stroke boxes, the
-  /// readout panel and one row per visible trace with the interpolated value the pointer
+  /// readout panel and one row per visible trace with the value of the sample nearest the
-  /// is over. Placed here rather than derived by the renderer, exactly as the legend and
+  /// pointer. Placed here rather than derived by the renderer, exactly as the legend and
   /// the regions are -- and, like them, entirely inside `axes`: the panel is flipped and
   /// clamped against the rect it was measured for, so nothing of the readout can be drawn
   /// over a label strip or into a figure's neighbouring row.
@@ -693,10 +693,13 @@ class Plot {
   /// coordinates it holds and the geometry `layout()` places from them cannot disagree.
   const Crosshair& crosshair() const noexcept { return crosshair_; }
 
-  /// The **interpolated** value of `trace`'s series at a data `x`: `crosshair_span()`
+  /// The value of `trace`'s **nearest sample** to a data `x`: `crosshair_span()` brackets
-  /// between the two adjacent samples, then `crosshair_interpolate()` -- the same lookup
+  /// `x`, and the nearer of the two samples is the answer (`t <= 0.5` takes the earlier) --
-  /// the readout's rows are built from, exposed for a host that wants the number for
+  /// the same lookup the readout's rows are built from, exposed for a host that wants the
-  /// itself (a status line, a tooltip of its own).
+  /// number for itself (a status line, a tooltip of its own).
+  ///
+  /// Never a value interpolated between two samples: see `CrosshairSpan` for why a readout
+  /// quotes the data rather than the signal it implies.
   ///
   /// False, leaving `out_y` untouched, for an id that names no trace, a trace with no
   /// series, and an `x` the series has no sample at -- the cases `CrosshairSpan::valid`
@@ -816,7 +819,7 @@ class Plot {
   /// never names a trace.
   void build_legend();
   /// Measures the crosshair into `layout_.crosshair`: the two lines' stroke boxes, one row
-  /// per visible trace with its interpolated value and marker, and the readout panel --
+  /// per visible trace with its nearest sample's value and marker, and the readout panel --
   /// placed beside the crosshair, flipped where it would cross an edge and clamped, so
   /// every rect it produces is inside `axes`. A plot with no visible trace still gets its
   /// lines: the rows are the readout's, not the crosshair's.

src/plot/plot.cpp

@@ -1082,7 +1082,7 @@ const PlotLayout& Plot::layout() {
   build_regions();
   build_legend();
   // The crosshair last: its panel is fitted into `axes` and its lines are held inside it, and
-  // its rows are the interpolated values at a data x -- so it wants the transforms the
+  // its rows are the sample values nearest a data x -- so it wants the transforms the
   // settled layout pins, exactly as the legend and the regions do.
   build_crosshair();
   return layout_;
@@ -1352,13 +1352,13 @@ void Plot::build_regions() {
 CrosshairSpan crosshair_span(const data::Series& series, f64 x) noexcept {
   CrosshairSpan span;
   const u64 n = series.size();
-  // No samples and no finite query: nothing to interpolate between.
+  // No samples and no finite query: nothing to bracket.
   if (n == 0u || !std::isfinite(x)) return span;
 
   // The bracketing samples, straight from the series (`neighbours()`/`x_at()`):
   // the window is closed at both ends -- the oldest and the newest sample are
-  // samples too -- and a query outside it has no neighbours to interpolate
+  // samples too -- and a query outside it has no neighbours at all. Answering
-  // between. Answering with the nearest sample's value instead is the clamped lie
+  // with the nearest sample's value instead is the clamped lie
   // this refuses: the readout would report a number as if it were under the
   // pointer when the series does not reach that far. The series owns where its
   // samples are, so an XY series is bracketed by its own x array exactly, where
@@ -1371,8 +1371,8 @@ CrosshairSpan crosshair_span(const data::Series& series, f64 x) noexcept {
   // A query that landed **on** a sample is a span of one, whichever side the
   // series' bracket reported: a sample at the query is the answer, and the two
   // ends of the window are samples too -- a bracket of (0, 1) at a query sitting
-  // on sample 0 would read as an interpolation with no width. Decided on the
+  // on sample 0 would read as a span with a width it does not have. Decided on
-  // samples' own coordinates, so it holds for any `neighbours()` implementation.
+  // the samples' own coordinates, so it holds for any `neighbours()` impl.
   if (series.x_at(i0) == x) {
     span.begin = span.end = i0;
     span.t = 0.0;
@@ -1387,16 +1387,16 @@ CrosshairSpan crosshair_span(const data::Series& series, f64 x) noexcept {
   }
 
   if (i0 == i1) {
-    // The series bracketed a single sample for a query that is not on it: nothing
+    // The series bracketed a single sample for a query that is not on it: there
-    // to interpolate with, and the sample is the honest answer.
+    // is no second sample to choose between, and this one is the honest answer.
     span.begin = span.end = i0;
     span.t = 0.0;
   } else {
     span.begin = i0;
     span.end = i1;
-    // `t` from the samples' own x coordinates, so the interpolation is exact on
+    // `t` from the samples' own x coordinates, so "which is nearer" is exact on
     // any grid, uniform or not. A degenerate pair (two samples sharing an x)
-    // interpolates nothing and reads the earlier sample.
+    // reads the earlier sample.
     const f64 xa = series.x_at(i0);
     const f64 xb = series.x_at(i1);
     span.t = xb > xa ? (x - xa) / (xb - xa) : 0.0;
@@ -1455,7 +1455,12 @@ bool Plot::crosshair_value(u32 trace, f64 x, f64& out_y) const {
   if (crosshair_scratch_.size() != 2u * pairs) return false;  // a series that produced nothing
   const f64 y_begin = static_cast<f64>(crosshair_scratch_[1u]);
   const f64 y_end = static_cast<f64>(crosshair_scratch_[2u * pairs - 1u]);
-  out_y = crosshair_interpolate(y_begin, y_end, span.t);
+  // **The nearer sample, never a value between two of them.** A readout quotes the data: a
+  // number the series does not contain is a claim about a signal between its samples, which
+  // is the caller's to make and not a plot's to put in a panel. `span.t` is measured on the
+  // samples' own x, 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.
+  out_y = span.t <= 0.5 ? y_begin : y_end;
   return true;
 }
 
@@ -1530,7 +1535,7 @@ void Plot::build_crosshair() {
     row.label_box = Rect{};
     row.value_box = Rect{};
     row.label.assign(trace.name.empty() ? crosshair_unnamed_label(i) : trace.name);
-    // The value: the interpolated number where the trace has a sample at this x, and the em dash
+    // The value: the nearest sample's number where the trace has one at this x, and the em dash
     // where it does not. The row is listed either way, so the absence has to be *said* -- a blank
     // value cell reads as a value that has not arrived -- and the dash is measured into the panel's
     // width like any other value, so the row's boxes are placed by one rule.

tests/test_figure.cpp

@@ -877,8 +877,8 @@ namespace {
 
 /// The figure the crosshair cases hover: three rows at deliberately *different* sample rates on
 /// the one shared x, plus a fourth whose data does not reach the hovered x at all. Rows that
-/// sample at different rates are the point -- one x, three different interpolations -- and the
+/// sample at different rates are the point -- one x, and each row reporting a sample off its own
-/// last row is the case a readout must not invent a value for.
+/// grid -- and the last row is the case a readout must not invent a value for.
 plot::Figure crosshair_figure() {
   plot::Figure figure(4u);
   figure.set_viewport(whole_figure());
@@ -906,7 +906,7 @@ plot::Figure crosshair_figure() {
 
 /// Spec §15, the sync: `Figure::set_crosshair()` applies **one** data x to every row, so one
 /// hover is one instant and N readouts rather than N independent ones. Rows at different sample
-/// rates therefore report *their own* interpolations of the same x -- the shared axis is x, and
+/// rates therefore report *their own* nearest sample to the same x -- the shared axis is x, and
 /// each row's series is read on its own grid -- while a row whose series does not reach that x
 /// reports no value at all instead of a fabricated one.
 PLOT_TEST(figure_crosshair_applies_one_x_to_every_row) {
@@ -930,14 +930,15 @@ PLOT_TEST(figure_crosshair_applies_one_x_to_every_row) {
   PLOT_CHECK(first.rows[0].label == "fast");
   PLOT_CHECK_NEAR(first.rows[0].y, 30.0, 1e-9);
 
-  // Row 1 samples every *two* units: x = 3 is halfway between sample 1 (y = 100) and sample 2
+  // Row 1 samples every *two* units: x = 3 is halfway between sample 1 (x = 2, y = 100) and
-  // (y = 200), so it reports 150 -- a different number for the same x, which is what makes this
+  // sample 2 (x = 4, y = 200), which is the tie, so it reports sample 1's 100 -- a different
-  // case about the rows rather than about one series read four times.
+  // number for the same x, which is what makes this case about the rows rather than about one
+  // series read four times. Not 150: a readout quotes a sample, and this row has none at x = 3.
   const plot::CrosshairLayout& second = figure.plot(1u).layout().crosshair;
   PLOT_CHECK(second.rows.size() == 1u);
   PLOT_CHECK(second.rows[0].valid);
   PLOT_CHECK(second.rows[0].label == "slow");
-  PLOT_CHECK_NEAR(second.rows[0].y, 150.0, 1e-9);
+  PLOT_CHECK_NEAR(second.rows[0].y, 100.0, 1e-9);
   PLOT_CHECK(second.rows[0].value != first.rows[0].value);
 
   // Row 2's trace has no series yet: no row at all -- it is not a signal under the pointer.
@@ -972,7 +973,9 @@ PLOT_TEST(figure_crosshair_applies_one_x_to_every_row) {
     PLOT_CHECK_NEAR(figure.plot(row).crosshair().x, 1.0, 1e-12);
   }
   PLOT_CHECK_NEAR(figure.plot(0u).layout().crosshair.rows[0].y, 10.0, 1e-9);
-  PLOT_CHECK_NEAR(figure.plot(1u).layout().crosshair.rows[0].y, 50.0, 1e-9);  // 0 + 100 * 0.5
+  // Not 50: x = 1 is the tie between this row's samples at x = 0 (y = 0) and x = 2 (y = 100),
+  // and a readout quotes one of them.
+  PLOT_CHECK_NEAR(figure.plot(1u).layout().crosshair.rows[0].y, 0.0, 1e-9);
   PLOT_CHECK(!figure.plot(3u).layout().crosshair.rows[0].valid);
 
   // On *every* row at once, and only the rows free it.

tests/test_plot.cpp

@@ -1965,20 +1965,21 @@ class CountingSeries final : public plot::data::Series {
 
 }  // namespace
 
-/// Spec §15, the lookup: a readout's y is **linear interpolation between the two samples
+/// Spec §15, the lookup: a readout's y is **the nearer of the two samples adjacent to the
-/// adjacent to the crosshair's x**, and hand-computed here rather than checked against the
+/// crosshair's x**, never a value between them. Every y asserted here is therefore one of the
-/// implementation's own arithmetic. The four corners of the rule are all asserted: a query
+/// series' own `tens` values -- a number *between* two of them, 15 or 22.5, is precisely what
-/// between two samples, the two exact-sample ends of the window (where the span collapses onto
+/// this refuses, and what it used to return. The corners of the rule are all covered: a query
-/// one sample), and a one-sample series, whose window is that sample alone.
+/// either side of the midpoint, a query exactly on it (the tie), the two exact-sample ends of
-PLOT_TEST(crosshair_value_is_interpolated_between_neighbours) {
+/// the window (where the span collapses onto one sample), and a one-sample series.
+PLOT_TEST(crosshair_value_is_the_nearest_sample) {
   CrosshairScene scene;
   const u32 trace = scene.plot.add_trace(
       {&scene.series, plot::Color::hex(0x40C0FF), 1.5f, scene.ax, scene.ay});
 
   // The span itself, for a query halfway between sample 1 (x = 1, y = 10) and sample 2
-  // (x = 2, y = 20): the two neighbours, and the fraction between them. Asserting the span and
+  // (x = 2, y = 20): the two neighbours, and the fraction between them. The span still reports
-  // not only the value is what pins the convention -- a nearest-sample lookup would report the
+  // both and the fraction between them -- `t` is a *selector* now, not a blend factor, so the
-  // span's `t` as 0 or 1, and an average of a *range* would not report a span at all.
+  // bracketing is unchanged and only what is built from it differs.
   const plot::CrosshairSpan half = plot::crosshair_span(scene.series, 1.5);
   PLOT_CHECK(half.valid);
   PLOT_CHECK(half.begin == 1u);
@@ -1986,14 +1987,25 @@ PLOT_TEST(crosshair_value_is_interpolated_between_neighbours) {
   PLOT_CHECK_NEAR(half.t, 0.5, 1e-12);
 
   f64 y = 0.0;
+  // Either side of the midpoint reads the sample it is nearer to, and *is* that sample: 10 and
+  // 20 are `tens` values, where an interpolation would have answered 11 and 19.
+  PLOT_CHECK(scene.plot.crosshair_value(trace, 1.1, y));
+  PLOT_CHECK_NEAR(y, 10.0, 1e-9);
+  PLOT_CHECK(scene.plot.crosshair_value(trace, 1.9, y));
+  PLOT_CHECK_NEAR(y, 20.0, 1e-9);
+  // Exactly halfway is the tie, and it reads the *earlier* sample -- the bias
+  // `crosshair_span()` already takes for a degenerate pair. 15.0 is the old answer.
   PLOT_CHECK(scene.plot.crosshair_value(trace, 1.5, y));
-  PLOT_CHECK_NEAR(y, 15.0, 1e-9);
+  PLOT_CHECK_NEAR(y, 10.0, 1e-9);
-  // A quarter of the way through another pair: 20 + (30 - 20) * 0.25.
+  // A quarter of the way through another pair: sample 2, not 22.5.
   PLOT_CHECK(scene.plot.crosshair_value(trace, 2.25, y));
-  PLOT_CHECK_NEAR(y, 22.5, 1e-9);
+  PLOT_CHECK_NEAR(y, 20.0, 1e-9);
+  // Just short of the next sample is that sample, so the readout steps rather than ramps.
+  PLOT_CHECK(scene.plot.crosshair_value(trace, 2.99, y));
+  PLOT_CHECK_NEAR(y, 30.0, 1e-9);
 
   // The ends of the window are samples too, so a query exactly on one reads that sample --
-  // and reads it *as* a span of one, with nothing to its left or right to interpolate with.
+  // and reads it *as* a span of one, with no neighbour on the far side.
   const plot::CrosshairSpan first = plot::crosshair_span(scene.series, 0.0);
   PLOT_CHECK(first.valid);
   PLOT_CHECK(first.begin == 0u);
@@ -2008,9 +2020,10 @@ PLOT_TEST(crosshair_value_is_interpolated_between_neighbours) {
   PLOT_CHECK(scene.plot.crosshair_value(trace, 3.0, y));
   PLOT_CHECK_NEAR(y, 30.0, 1e-9);
 
-  // Outside the window there is no value at all -- not the nearest sample's, not the end of
+  // Outside the window there is no value at all. The nearest-sample rule is a rule for an x the
-  // the window's, which are the clamped lies the header refuses -- and a series with no
+  // series *brackets*; extending it past the ends would answer with the first or last sample for
-  // samples has no span at any x.
+  // any x whatever, which is the clamped lie the header refuses. A series with no samples has no
+  // span at any x.
   PLOT_CHECK(!plot::crosshair_span(scene.series, -1e-9).valid);
   PLOT_CHECK(!plot::crosshair_span(scene.series, 3.0 + 1e-9).valid);
   PLOT_CHECK(!scene.plot.crosshair_value(trace, 4.0, y));
@@ -2023,7 +2036,7 @@ PLOT_TEST(crosshair_value_is_interpolated_between_neighbours) {
   PLOT_CHECK(!scene.plot.crosshair_value(/*trace=*/99u, 1.0, y));  // an id that names nothing
 
   // A one-sample series: the sample itself is the only query it answers, and it answers it
-  // without a neighbour to interpolate against.
+  // with no second sample to be nearer to.
   plot::data::ArraySeries single(std::vector<f32>{7.0f}, 5.0, 1.0);
   plot::Plot one;
   one.add_x_axis({"t", {0.0, 10.0}, false, plot::AxisPlace::Bottom, false});
@@ -2039,7 +2052,9 @@ PLOT_TEST(crosshair_value_is_interpolated_between_neighbours) {
   PLOT_CHECK(!one.crosshair_value(single_trace, 5.5, y));
 
   // The readout's row is the same lookup: the number a user reads off the panel is the value
-  // this test computed by hand, not a second derivation of it.
+  // this test computed by hand, not a second derivation of it. x = 1.5 is the tie, so the row
+  // reads sample 1 -- and the formatted cell is `"10"`, where the interpolating readout showed
+  // `"15"`, a number the series does not contain.
   scene.plot.set_crosshair(1.5, true);
   const plot::CrosshairLayout& crosshair = scene.plot.layout().crosshair;
   PLOT_CHECK(crosshair.active);
@@ -2049,8 +2064,8 @@ PLOT_TEST(crosshair_value_is_interpolated_between_neighbours) {
   // the figure's case pins).
   PLOT_CHECK(crosshair.rows.size() == 1u);
   PLOT_CHECK(crosshair.rows[0].valid);
-  PLOT_CHECK_NEAR(crosshair.rows[0].y, 15.0, 1e-9);
+  PLOT_CHECK_NEAR(crosshair.rows[0].y, 10.0, 1e-9);
-  PLOT_CHECK(crosshair.rows[0].value == "15");
+  PLOT_CHECK(crosshair.rows[0].value == "10");
 }
 
 /// Spec §15, the readout's membership: **every visible trace gets a row, whether or not it is
@@ -2080,14 +2095,16 @@ PLOT_TEST(crosshair_readout_lists_every_visible_trace_including_unnamed_ones) {
   PLOT_CHECK(crosshair.rows[1].label == plot::crosshair_unnamed_label(1u));
   PLOT_CHECK(crosshair.rows[1].label == "#1");
 
-  // Both are listed with the value their own series has at x = 1.5, the swatch, the label's box
+  // Both are listed with the value their own series has nearest x = 1.5, the swatch, the label's
-  // and the value's box -- all placed by the plot, all inside the panel it measured.
+  // box and the value's box -- all placed by the plot, all inside the panel it measured. x = 1.5
+  // is the tie between samples 1 and 2, which reads the earlier one: 10, not the 15 an
+  // interpolating readout showed.
   PLOT_CHECK(crosshair.panel.w > 0.0f && crosshair.panel.h > 0.0f);
   for (const plot::CrosshairRow& row : crosshair.rows) {
     PLOT_CHECK(row.valid);
     PLOT_CHECK(row.listed);
-    PLOT_CHECK_NEAR(row.y, 15.0, 1e-9);
+    PLOT_CHECK_NEAR(row.y, 10.0, 1e-9);
-    PLOT_CHECK(row.value == "15");
+    PLOT_CHECK(row.value == "10");
     PLOT_CHECK(row.swatch.x >= crosshair.panel.x);
     PLOT_CHECK(row.swatch.right() <= crosshair.panel.right());
     PLOT_CHECK(row.swatch.y >= crosshair.panel.y);
@@ -2148,7 +2165,7 @@ PLOT_TEST(crosshair_readout_lists_every_visible_trace_including_unnamed_ones) {
   PLOT_CHECK(on.rows[0].listed);
   PLOT_CHECK(on.rows[1].listed);
   PLOT_CHECK(on.panel.w > 0.0f && on.panel.h > 0.0f);
-  PLOT_CHECK(on.rows[0].value == "15");
+  PLOT_CHECK(on.rows[0].value == "10");
 }
 
 /// Spec §15, the panel's placement: near the pointer, flipped over it where it would otherwise
@@ -2253,11 +2270,14 @@ PLOT_TEST(crosshair_lookup_does_not_scan) {
   p.add_y_axis({"v", {0.0, 99.0}, false, plot::AxisPlace::Left, false});
   const u32 trace = p.add_trace({&series, plot::Color::hex(0x40C0FF), 1.5f, 0u, 0u});
 
-  // A query between two samples: 1234 % 100 = 34, the next is 35, halfway between them.
+  // A query between two samples: 1234 % 100 = 34, the next is 35, and 1234.5 is the tie, which
+  // reads the earlier -- 34, where the interpolating readout answered 34.5. Both samples are
+  // still read: the bound below is on how much data the lookup touches, not on which end it
+  // then reports.
   f64 y = 0.0;
   const u64 before_reads = series.samples_read();
   PLOT_CHECK(p.crosshair_value(trace, 1234.5, y));
-  PLOT_CHECK_NEAR(y, 34.5, 1e-9);
+  PLOT_CHECK_NEAR(y, 34.0, 1e-9);
   PLOT_CHECK(series.samples_read() - before_reads <= 2u);
   PLOT_CHECK(series.gather_calls() <= 1u);
 
@@ -2288,7 +2308,7 @@ PLOT_TEST(crosshair_lookup_does_not_scan) {
   const plot::CrosshairLayout& crosshair = p.layout().crosshair;
   PLOT_CHECK(crosshair.rows.size() == 1u);
   PLOT_CHECK(crosshair.rows[0].valid);
-  PLOT_CHECK_NEAR(crosshair.rows[0].y, 34.5, 1e-9);
+  PLOT_CHECK_NEAR(crosshair.rows[0].y, 34.0, 1e-9);
   PLOT_CHECK(series.samples_read() - reads <= 2u);
   PLOT_CHECK(series.gather_calls() - calls <= 1u);
   // And the readout is not vacuous: the series it read two samples of really does hold a
@@ -2511,9 +2531,12 @@ PLOT_TEST(scrolled_back_live_window_keeps_its_decades) {
 }
 
 /// The XY routing, crosshair half: the span brackets the samples the *array*
-/// names, and the interpolation fraction is measured on the samples' own positions
+/// names, and `t` is measured on the samples' own positions -- (5-1)/(10-1) over the
-/// -- (5-1)/(10-1) over the wide gap, where a uniform-grid guess would have read
+/// wide gap, where a uniform-grid guess would have read samples that do not exist at
-/// samples that do not exist at the positions it assumed.
+/// the positions it assumed. The gap is what makes the value worth asserting too:
+/// x = 5 sits 4 from sample 1 and 5 from sample 2, so the nearest-sample rule has a
+/// real choice to get right, and it only has that choice because `t` came from the
+/// array.
 PLOT_TEST(xy_series_crosshair_brackets_its_own_samples) {
   XyScene scene;
   const u32 trace = scene.plot.add_trace(
@@ -2526,7 +2549,11 @@ PLOT_TEST(xy_series_crosshair_brackets_its_own_samples) {
   PLOT_CHECK_NEAR(span.t, 4.0 / 9.0, 1e-12);
   f64 y = 0.0;
   PLOT_CHECK(scene.plot.crosshair_value(trace, 5.0, y));
-  PLOT_CHECK_NEAR(y, 10.0 + 10.0 * (4.0 / 9.0), 1e-9);
+  PLOT_CHECK_NEAR(y, 10.0, 1e-9);  // sample 1, the nearer end of the gap
+  // And past the gap's midpoint it is the other sample, so the choice is `t`'s and not a
+  // fixed preference for one end.
+  PLOT_CHECK(scene.plot.crosshair_value(trace, 6.0, y));
+  PLOT_CHECK_NEAR(y, 20.0, 1e-9);
 
   // On a sample, at both ends of the array's window, and outside it: the same
   // closed-window rule a uniform series follows, on the array's own coordinates.

tests/test_xy_series.cpp

@@ -72,9 +72,9 @@ PLOT_TEST(xy_series_reports_its_own_grid) {
 }
 
 PLOT_TEST(xy_series_neighbour_lookups_crosshair_style) {
-  // The crosshair asks neighbours() at an arbitrary x and interpolates between
+  // The crosshair asks neighbours() at an arbitrary x and reports whichever of
-  // the two samples it gets back. On a non-uniform grid that needs real
+  // the two samples it gets back is nearer. On a non-uniform grid that needs
-  // searches: a uniform-grid formula would land megabytes off here.
+  // real searches: a uniform-grid formula would land megabytes off here.
   auto x = spread_x(1000);
   const std::vector<f64> xs = x;
   plot::data::XYSeries s(std::move(x), saw_y(1000));