Γ-W1-T3: staged contour traces draw the curve their exponent defines

New pure curve_tessellate joins the overlay's node vertices through curveMap,
one sample per pixel column; the knot no longer floats off its own trace.

src/core/instrument/CLAUDE.md

@@ -337,6 +337,7 @@ anything for a trigger shape.
 - `spline_edit` — THE point-editing grammar, and the one place it is written down: left-click grabs a node and adds one in empty space, right-click deletes, control-click toggles hard/smooth. Both spline consumers — the velocity-curve popup and the spline EG overlay — route their mouse-down through `resolveSplineEdit`, so the two cannot drift into two grammars. The endpoint and point-count rules are NOT restated here: `deletePoint` and `addPoint` own them, and the caller applies the resolved action to the curve. Also home to `splineOverlayBox`, the contour's mapping box inside the waveform overlay — the FULL area, no inset, so the drawn contour stays 1:1 with the sample's time axis. Spline points are excluded from `param_taper`'s Shift/Ctrl modifier law like waveform markers are: a point is a normalized position with no displayed unit, and control-click there is already claimed by the hard/smooth toggle above.
 - `curve_popup` — pure curve-popup geometry + dismissal test (FB1): centered sheet over the Sample face — width/height clamps, title row, Close button rect, curve-box rect, outside-sheet dismissal test. Mirror of `overflow_menu`; no LICE or REAPER types.
 - `envelope_overlay` — pure staged-envelope→polyline geometry for the Sample-view overlay (read from `envelope_overlay.h`): maps a `StageEnvelope` to a polyline inside a rect under whichever of TWO layout policies its `EnvKind` selects — an AHDSR draws a bounded param-domain schematic with its release RIGHT-ANCHORED to the canvas edge, an AHD draws 1:1 over the waveform's own time axis — plus a round mid-segment knot on every sloped stage that has a duration. Every vertex clamped in-canvas. Shares the `EnvNode`/`StageEnvelope`/`timeToX`/`levelToY` vocabulary with `envelope_edit` so the drawn handle and its grab region agree pixel-for-pixel. No VST3/REAPER/LICE types at the boundary.
+- `curve_tessellate` — the staged envelope's TRACE, split from `envelope_overlay` on the axis those two already have: that module decides where a node LANDS, this strokes the span BETWEEN two of them. Joins the non-knot vertices with the curve each stage's exponent defines, sampled one point per pixel column, at `start + (end - start) * curveMap(phi)` — the composition `envelopes.h`'s four evaluators use, so a drawn stage and the sound it makes cannot diverge. Node vertices keep their exact integer coordinates (the handles are drawn on them); only the interior samples are sub-pixel. A neutral exponent or a zero level span emits the two endpoints and nothing between, which is the straight stroke drawn before curves existed, vertex for vertex.
 - `envelope_edit` — pure node hit-test + pixel-delta→clamped-param inverse map for the draggable envelope nodes and their curve knots (read from `envelope_edit.h`): `nodeAtPoint` resolves a grab to the nearest node within a pick radius (Chebyshev distance, draw-order tie-break, knots appended last so a coincident endpoint handle wins); `resolveNodeDrag` maps a pixel delta since grab to a new `StageEnvelope` under the same caller-supplied per-param clamp bounds the knobs use — a drag can never produce a param a knob couldn't. Mirror of `card_drag`/`waveform_view`; the inverse of `envelope_overlay`'s params→polyline forward map, so node-drag, knot-drag and knob-edit read/write one shared model and can never diverge.
 
 ## Gotchas

src/core/instrument/ui/CMakeLists.txt

@@ -104,3 +104,12 @@ reasampler_pure_library(param_taper SOURCES param_taper.cpp LINK PUBLIC curve_la
 # is judged against the envelope node drag at the editor's own floor width (the sharper of the
 # taper's two consumers), read from the allocator/overlay rather than copied as a number.
 reasampler_test(param_taper LINK param_taper envelope_overlay sample_bands)
+
+# The staged trace, split from envelope_overlay's vertex model. stroke_aa is the trace-point
+# vocabulary, filled in place so the shell's scratch buffer is reused rather than a fresh
+# vector returned per paint; curve_law arrives through envelope_overlay but is named here
+# because this module evaluates the law rather than merely carrying its exponents.
+reasampler_pure_library(curve_tessellate
+    SOURCES curve_tessellate.cpp
+    LINK PUBLIC envelope_overlay stroke_aa curve_law)
+reasampler_test(curve_tessellate LINK curve_tessellate)

src/core/instrument/ui/curve_tessellate.cpp

@@ -0,0 +1,65 @@
+// curve_tessellate.cpp — see curve_tessellate.h. Pure geometry; no host types.
+
+#include "core/instrument/ui/curve_tessellate.h"
+
+#include <algorithm>
+#include <cstdlib>
+
+#include "core/util/curve_law.h"
+
+namespace reasampler::instrument::ui {
+
+using StrokePoint = reasampler::ui::StrokePoint;
+
+namespace {
+
+StrokePoint pt(double x, double y) {
+    return StrokePoint{static_cast<float>(x), static_cast<float>(y)};
+}
+
+// The samples strictly BETWEEN two nodes. The endpoints are the caller's, so a shared node is
+// emitted once and the polyline carries no zero-length joint.
+void appendInterior(int x0, int y0, int x1, int y1, double exponent,
+                    std::vector<StrokePoint>& out) {
+    const int span = std::abs(x1 - x0);
+    if (span < 2 || y1 == y0 || exponent == util::kCurveNeutral) return;
+    const double dx = static_cast<double>(x1 - x0);
+    const double dy = static_cast<double>(y1 - y0);
+    for (int i = 1; i < span; ++i) {
+        // phi is exact at every column, so x lands on the integer column and the last interior
+        // sample is one column short of the end node.
+        const double phi = static_cast<double>(i) / static_cast<double>(span);
+        out.push_back(pt(static_cast<double>(x0) + dx * phi,
+                         static_cast<double>(y0) + dy * util::curveMap(phi, exponent)));
+    }
+}
+
+}  // namespace
+
+double segmentCurve(const StageEnvelope& env, EnvNode endNode) {
+    switch (endNode) {
+        case EnvNode::AttackEnd:  return env.attackCurve;
+        case EnvNode::DecayEnd:   return env.decayCurve;
+        case EnvNode::ReleaseEnd: return env.releaseCurve;
+        default:                  return util::kCurveNeutral;
+    }
+}
+
+void buildEnvelopeTrace(const std::vector<EnvVertex>& poly, const StageEnvelope& env, int xLo,
+                        int xHi, std::vector<StrokePoint>& out) {
+    out.clear();
+    bool started = false;
+    int px = 0;
+    int py = 0;
+    for (const EnvVertex& v : poly) {
+        if (v.knot) continue;
+        const int x = std::max(xLo, std::min(xHi, v.x));
+        if (started) appendInterior(px, py, x, v.y, segmentCurve(env, v.node), out);
+        out.push_back(pt(x, v.y));
+        started = true;
+        px = x;
+        py = v.y;
+    }
+}
+
+}  // namespace reasampler::instrument::ui

src/core/instrument/ui/curve_tessellate.h

@@ -0,0 +1,34 @@
+// curve_tessellate.h — the staged envelope's TRACE: envelope_overlay's node vertices joined by
+// the curve each stage's exponent defines. Split from that module on the axis the two already
+// have — envelope_overlay decides where a node LANDS, this strokes the span BETWEEN two of
+// them over phi, so a re-scaled time axis changes nothing here.
+
+#pragma once
+
+#include <vector>
+
+#include "core/instrument/ui/envelope_overlay.h"
+#include "core/ui/stroke_aa.h"  // StrokePoint — the stroker's own vertex type
+
+namespace reasampler::instrument::ui {
+
+// The exponent governing the segment that ENDS at `node`: attack, decay and release are the
+// three sloped stages. Every other node ends a plateau, whose straightness comes from its own
+// zero level span rather than from an exponent, so neutral is returned and no caller needs a
+// second rule to recognize one.
+double segmentCurve(const StageEnvelope& env, EnvNode endNode);
+
+// Replaces `out` with the polyline the shell strokes. Knot vertices are handles, not line
+// vertices, and are skipped; node vertices keep their exact INTEGER coordinates (clamped to
+// [xLo, xHi]) because those are the positions their draggable handles are drawn at. Only the
+// interior samples are sub-pixel, one per pixel column, which is what makes the density follow
+// the canvas width instead of a fixed count.
+//
+// A segment's level runs start + (end - start) * curveMap(phi, exponent) — the composition
+// envelopes.h's four evaluators use, so the trace cannot diverge from the sound. A neutral
+// exponent or a zero level span emits the two endpoints and nothing between: the straight
+// stroke, vertex for vertex.
+void buildEnvelopeTrace(const std::vector<EnvVertex>& poly, const StageEnvelope& env, int xLo,
+                        int xHi, std::vector<reasampler::ui::StrokePoint>& out);
+
+}  // namespace reasampler::instrument::ui

src/shell/instrument/CMakeLists.txt

@@ -91,6 +91,7 @@ if(WIN32 AND EXISTS "${VST3_SDK}/public.sdk/source/main/pluginfactory.cpp")
         knob_deck deck_groups deck_values curve_popup spline_edit master_gain sample_usage
         bake_hold
         file_bytes curve_law stroke_aa
+        curve_tessellate
         bake_plan bake_render bake_reset bake_wire wav_codec)
     # SDK_INC gives the REAPER VST3 interfaces + API header for the bridge; WDL_INC gives
     # LICE for the editor. The VST3 SDK headers arrive via vst3_sdk PUBLIC.

src/shell/instrument/editor_paint_waveform.cpp

@@ -13,6 +13,7 @@
 #include <vector>
 
 #include "core/audio/peaks.h"                   // computeEnvelope (waveform binning)
+#include "core/instrument/ui/curve_tessellate.h"  // buildEnvelopeTrace (the staged trace)
 #include "core/instrument/ui/spline_edit.h"     // splineOverlayBox (the contour's mapping box)
 #include "core/instrument/ui/waveform_view.h"   // waveformSurface / laneEnvelope / frameToX
 #include "shell/instrument/editor_internal.h"   // kit adapters
@@ -212,17 +213,9 @@ void ReaSamplerEditor::paintEnvelopeOverlay(LICE_IBitmap* bmp, const OverlayArea
     const StageEnvelope env = packEnvelope(overlayEnv_, params_.play, frames, startFrame);
     const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, waveArea, totalSeconds);
 
-    // Clip x to the wave rect. Knots are handles, not line vertices. Vertices stay INTEGER here
-    // — unlike the spline traces above — because they are the same positions the draggable
-    // handles are drawn at, and a sub-pixel trace would sit off its own handles.
     const LICE_pixel line = toLice(roleColor(Role::OverlayTrace));
     std::vector<ui::StrokePoint>& trace = scratchPoints();
-    trace.clear();
-    for (const EnvVertex& v : poly) {
-        if (v.knot) continue;
-        const int vx = (std::max)(area.x, (std::min)(area.right() - 1, v.x));
-        trace.push_back(ui::StrokePoint{static_cast<float>(vx), static_cast<float>(v.y)});
-    }
+    buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
     // A degenerate envelope (every stage collapsed to zero span) can reduce this to ONE vertex.
     // strokePolylineAA's round-cap zero-length case then draws a dot at it, marking the sole
     // point rather than drawing nothing — kept deliberately as more legible than a blank trace.

tests/test_curve_tessellate.cpp

@@ -0,0 +1,395 @@
+// Standalone tests for reasampler::instrument::ui::curve_tessellate — no VST3, no REAPER, no
+// framework. Same fast assert loop as the sibling pure tests.
+//
+// Every assertion is expressed RELATIVE to the vertices buildEnvelopePolyline returns, never
+// against an absolute pixel literal, so a re-scaled overlay axis leaves this file untouched.
+// Covers: segmentCurve's node->exponent rule; the neutral exponent emitting today's straight
+// vertex list unchanged; knots excluded and node vertices preserved exactly; THE GATE — the
+// knot's centre within 1 px of the trace at every exponent, on all three sloped stages of both
+// layout policies; the mid-segment level matching curve_law's own curveMidLevel; curvature
+// direction; no overshoot past a segment's own endpoint levels; per-pixel-column density that
+// scales with the canvas; the x clamp; and the degenerate/empty cases.
+//
+// Both layout policies here ARE all three envelopes and both play modes: the editor's
+// packEnvelope collapses amp/filter/pitch x Gate/Trigger onto exactly these two EnvKinds, and
+// paintEnvelopeOverlay is the single paint path over them.
+
+#include "../src/core/instrument/ui/curve_tessellate.h"
+
+#include <cmath>
+#include <cstdio>
+#include <vector>
+
+#include "../src/core/util/curve_law.h"
+
+using namespace reasampler;
+using namespace reasampler::instrument::ui;
+using reasampler::ui::StrokePoint;
+
+static int g_fail = 0;
+#define CHECK(cond) do { if(!(cond)) { \
+    std::printf("FAIL line %d: %s\n", __LINE__, #cond); ++g_fail; } } while(0)
+
+static OverlayArea overlayOf(const Rect& r) { return OverlayArea{r}; }
+
+// Offset so left/top != 0 (catches origin bugs). Tall enough that a 1 px tolerance is a small
+// fraction of the level span, which is what makes the level assertions discriminating.
+static Rect wideArea() { return Rect::ltrb(20, 10, 1020, 210); }  // width 1000, height 200
+
+static StageEnvelope ahdsr(double a, double h, double d, double sus, double r) {
+    StageEnvelope e;
+    e.kind = EnvKind::Ahdsr;
+    e.attackSeconds = a;
+    e.holdSeconds = h;
+    e.decaySeconds = d;
+    e.sustainLevel = sus;
+    e.releaseSeconds = r;
+    return e;
+}
+
+static StageEnvelope ahd(double a, double d, double frac, double span) {
+    StageEnvelope e;
+    e.kind = EnvKind::Ahd;
+    e.attackSeconds = a;
+    e.decaySeconds = d;
+    e.holdFraction = frac;
+    e.originSeconds = 0.0;
+    e.spanSeconds = span;
+    return e;
+}
+
+static bool findNode(const std::vector<EnvVertex>& poly, EnvNode node, EnvVertex& out) {
+    for (const EnvVertex& v : poly) {
+        if (v.node == node) { out = v; return true; }
+    }
+    return false;
+}
+
+// The polyline's y where it crosses `x` — the trace as STROKED, not merely its samples, so a
+// knot between two samples is still measured against the line the user sees.
+static bool traceYAtX(const std::vector<StrokePoint>& t, double x, double& y) {
+    for (std::size_t i = 1; i < t.size(); ++i) {
+        const double x0 = t[i - 1].x, x1 = t[i].x;
+        if (x1 == x0) {
+            if (x == x0) { y = t[i].y; return true; }
+            continue;
+        }
+        const double lo = x0 < x1 ? x0 : x1, hi = x0 < x1 ? x1 : x0;
+        if (x < lo || x > hi) continue;
+        const double u = (x - x0) / (x1 - x0);
+        y = t[i - 1].y + (t[i].y - t[i - 1].y) * u;
+        return true;
+    }
+    return false;
+}
+
+// The three sloped stages, each named by the knot that rides it and the two nodes it runs
+// between — the same pairing gatePolyline/ahdPolyline place the knot from.
+struct Stage {
+    EnvNode knot;
+    EnvNode from;
+    EnvNode to;
+};
+static const Stage kStages[3] = {
+    {EnvNode::AttackCurve,  EnvNode::Origin,       EnvNode::AttackEnd},
+    {EnvNode::DecayCurve,   EnvNode::HoldEnd,      EnvNode::DecayEnd},
+    {EnvNode::ReleaseCurve, EnvNode::ReleaseStart, EnvNode::ReleaseEnd},
+};
+
+static const double kExponents[7] = {util::kCurveMin, 0.25, 0.5, util::kCurveNeutral,
+                                     2.0, 4.0, util::kCurveMax};
+
+// ---------------------------------------------------------------------------------------
+
+static void testSegmentCurve() {
+    StageEnvelope e = ahdsr(1.0, 0.0, 1.0, 0.5, 1.0);
+    e.attackCurve = 0.3;
+    e.decayCurve = 3.0;
+    e.releaseCurve = 7.0;
+    CHECK(segmentCurve(e, EnvNode::AttackEnd) == e.attackCurve);
+    CHECK(segmentCurve(e, EnvNode::DecayEnd) == e.decayCurve);
+    CHECK(segmentCurve(e, EnvNode::ReleaseEnd) == e.releaseCurve);
+    // The plateau-ending nodes carry no exponent of their own.
+    CHECK(segmentCurve(e, EnvNode::HoldEnd) == util::kCurveNeutral);
+    CHECK(segmentCurve(e, EnvNode::ReleaseStart) == util::kCurveNeutral);
+    CHECK(segmentCurve(e, EnvNode::Origin) == util::kCurveNeutral);
+}
+
+// The regression guard: at the neutral exponent the trace IS the non-knot vertex list, one
+// point per vertex, at the same integer coordinates — the straight stroke drawn before curves.
+static void testNeutralIsTodaysStraightLine() {
+    const Rect area = wideArea();
+    const StageEnvelope envs[2] = {ahdsr(2.0, 0.0, 2.0, 0.4, 2.0), ahd(1.2, 1.6, 0.5, 4.0)};
+    for (const StageEnvelope& env : envs) {
+        const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+        std::vector<StrokePoint> trace;
+        buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+        std::size_t nodes = 0;
+        for (const EnvVertex& v : poly) if (!v.knot) ++nodes;
+        CHECK(trace.size() == nodes);
+        std::size_t i = 0;
+        for (const EnvVertex& v : poly) {
+            if (v.knot) continue;
+            CHECK(trace[i].x == static_cast<float>(v.x));
+            CHECK(trace[i].y == static_cast<float>(v.y));
+            ++i;
+        }
+    }
+}
+
+// Knots are handles, not line vertices. A knot sits mid-canvas but is appended AFTER the last
+// node, so admitting one would break the trace's x ordering — which is what this catches.
+static void testKnotsExcludedAndNodesPreserved() {
+    const Rect area = wideArea();
+    StageEnvelope env = ahdsr(2.0, 0.0, 2.0, 0.4, 2.0);
+    env.attackCurve = 0.3;
+    env.decayCurve = 4.0;
+    env.releaseCurve = 0.4;
+    const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+    std::size_t knots = 0;
+    for (const EnvVertex& v : poly) if (v.knot) ++knots;
+    CHECK(knots == 3);
+
+    std::vector<StrokePoint> trace;
+    buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+    for (std::size_t i = 1; i < trace.size(); ++i) CHECK(trace[i].x >= trace[i - 1].x);
+
+    // Every node vertex still appears at its exact integer position: the handles are drawn
+    // there, and a trace that missed one would sit off its own handle.
+    for (const EnvVertex& v : poly) {
+        if (v.knot) continue;
+        bool found = false;
+        for (const StrokePoint& p : trace) {
+            if (p.x == static_cast<float>(v.x) && p.y == static_cast<float>(v.y)) found = true;
+        }
+        CHECK(found);
+    }
+}
+
+// THE GATE (plan acceptance criterion 1): at every exponent the knot's centre lies on the
+// trace within 1 px. Swept over all three sloped stages of the AHDSR schematic.
+static void testKnotLiesOnTraceAhdsr() {
+    const Rect area = wideArea();
+    for (const Stage& st : kStages) {
+        for (double pw : kExponents) {
+            StageEnvelope env = ahdsr(2.0, 0.0, 2.0, 0.4, 2.0);
+            if (st.knot == EnvNode::AttackCurve) env.attackCurve = pw;
+            else if (st.knot == EnvNode::DecayCurve) env.decayCurve = pw;
+            else env.releaseCurve = pw;
+
+            const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+            EnvVertex knot;
+            CHECK(findNode(poly, st.knot, knot));
+            std::vector<StrokePoint> trace;
+            buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+            double y = 0.0;
+            CHECK(traceYAtX(trace, static_cast<double>(knot.x), y));
+            CHECK(std::fabs(y - static_cast<double>(knot.y)) <= 1.0);
+        }
+    }
+}
+
+// The same gate on the AHD policy — its two sloped stages, its own 1:1 time axis.
+static void testKnotLiesOnTraceAhd() {
+    const Rect area = wideArea();
+    for (int stage = 0; stage < 2; ++stage) {
+        for (double pw : kExponents) {
+            StageEnvelope env = ahd(1.2, 1.6, 0.5, 4.0);
+            if (stage == 0) env.attackCurve = pw; else env.decayCurve = pw;
+            const EnvNode knotNode = stage == 0 ? EnvNode::AttackCurve : EnvNode::DecayCurve;
+
+            const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+            EnvVertex knot;
+            CHECK(findNode(poly, knotNode, knot));
+            std::vector<StrokePoint> trace;
+            buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+            double y = 0.0;
+            CHECK(traceYAtX(trace, static_cast<double>(knot.x), y));
+            CHECK(std::fabs(y - static_cast<double>(knot.y)) <= 1.0);
+        }
+    }
+}
+
+// The trace is the SAME law the audio evaluates: at a segment's midpoint its level is
+// curve_law's curveMidLevel of that stage's exponent, composed onto the endpoints the trace
+// itself returned.
+static void testMidSegmentLevelMatchesTheLaw() {
+    const Rect area = wideArea();
+    for (const Stage& st : kStages) {
+        for (double pw : kExponents) {
+            StageEnvelope env = ahdsr(2.0, 0.0, 2.0, 0.4, 2.0);
+            if (st.knot == EnvNode::AttackCurve) env.attackCurve = pw;
+            else if (st.knot == EnvNode::DecayCurve) env.decayCurve = pw;
+            else env.releaseCurve = pw;
+
+            const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+            EnvVertex a, b;
+            CHECK(findNode(poly, st.from, a));
+            CHECK(findNode(poly, st.to, b));
+            std::vector<StrokePoint> trace;
+            buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+
+            const double xm = 0.5 * (static_cast<double>(a.x) + static_cast<double>(b.x));
+            double y = 0.0;
+            CHECK(traceYAtX(trace, xm, y));
+            const double want = static_cast<double>(a.y) +
+                                (static_cast<double>(b.y) - static_cast<double>(a.y)) *
+                                    util::curveMidLevel(pw);
+            CHECK(std::fabs(y - want) <= 1.0);
+        }
+    }
+}
+
+// A curve must bend, and in the direction the exponent names: phi^p with p > 1 holds the level
+// LOW for longer, p < 1 lifts it early. Stated against the chord between the two endpoints the
+// trace returned, so it holds whichever way the segment slopes.
+static void testCurvatureDirection() {
+    const Rect area = wideArea();
+    for (const Stage& st : kStages) {
+        for (double pw : {0.25, 4.0}) {
+            StageEnvelope env = ahdsr(2.0, 0.0, 2.0, 0.4, 2.0);
+            if (st.knot == EnvNode::AttackCurve) env.attackCurve = pw;
+            else if (st.knot == EnvNode::DecayCurve) env.decayCurve = pw;
+            else env.releaseCurve = pw;
+
+            const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+            EnvVertex a, b;
+            CHECK(findNode(poly, st.from, a));
+            CHECK(findNode(poly, st.to, b));
+            std::vector<StrokePoint> trace;
+            buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+
+            const double xm = 0.5 * (static_cast<double>(a.x) + static_cast<double>(b.x));
+            double y = 0.0;
+            CHECK(traceYAtX(trace, xm, y));
+            const double chord = 0.5 * (static_cast<double>(a.y) + static_cast<double>(b.y));
+            // Normalized level at the midpoint, 0 at the start node, 1 at the end node.
+            const double dy = static_cast<double>(b.y) - static_cast<double>(a.y);
+            const double u = (y - static_cast<double>(a.y)) / dy;
+            CHECK(std::fabs(y - chord) > 1.0);          // it actually left the straight line
+            if (pw > util::kCurveNeutral) CHECK(u < 0.5);
+            else CHECK(u > 0.5);
+        }
+    }
+}
+
+// curveMap maps 0->0 and 1->1 at every positive exponent, so no sample may pass either of its
+// own segment's endpoint levels.
+static void testNoOvershoot() {
+    const Rect area = wideArea();
+    for (const Stage& st : kStages) {
+        for (double pw : kExponents) {
+            StageEnvelope env = ahdsr(2.0, 0.0, 2.0, 0.4, 2.0);
+            if (st.knot == EnvNode::AttackCurve) env.attackCurve = pw;
+            else if (st.knot == EnvNode::DecayCurve) env.decayCurve = pw;
+            else env.releaseCurve = pw;
+
+            const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+            EnvVertex a, b;
+            CHECK(findNode(poly, st.from, a));
+            CHECK(findNode(poly, st.to, b));
+            std::vector<StrokePoint> trace;
+            buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+            const double lo = a.y < b.y ? a.y : b.y;
+            const double hi = a.y < b.y ? b.y : a.y;
+            for (const StrokePoint& p : trace) {
+                if (p.x < static_cast<float>(a.x) || p.x > static_cast<float>(b.x)) continue;
+                CHECK(p.y >= static_cast<float>(lo) - 0.001f);
+                CHECK(p.y <= static_cast<float>(hi) + 0.001f);
+            }
+        }
+    }
+}
+
+// Density follows the canvas: one sample per pixel column, so a wider canvas gets proportionally
+// more of them. A fixed count would fail the second half. Uses the AHD policy, whose x axis is
+// the waveform's own and so is independent of the AHDSR schematic's scale.
+static void testDensityFollowsWidth() {
+    std::size_t counts[2] = {0, 0};
+    const int widths[2] = {1000, 4000};
+    for (int w = 0; w < 2; ++w) {
+        const Rect area = Rect::ltrb(20, 10, 20 + widths[w], 210);
+        StageEnvelope env = ahd(1.2, 1.6, 0.5, 4.0);
+        env.attackCurve = 4.0;
+        const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+        EnvVertex a, b;
+        CHECK(findNode(poly, EnvNode::Origin, a));
+        CHECK(findNode(poly, EnvNode::AttackEnd, b));
+        std::vector<StrokePoint> trace;
+        buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+
+        std::size_t n = 0;
+        float prevX = 0.0f;
+        for (const StrokePoint& p : trace) {
+            if (p.x < static_cast<float>(a.x) || p.x > static_cast<float>(b.x)) continue;
+            if (n > 0) CHECK(p.x - prevX <= 1.0f);  // no gap wider than one column
+            prevX = p.x;
+            ++n;
+        }
+        CHECK(n > 1);
+        counts[w] = n;
+    }
+    // 4x the canvas, ~4x the samples across the same stage.
+    CHECK(counts[1] > 3 * counts[0]);
+}
+
+// A plateau is straight because its two endpoints share a level, so a stray exponent on the
+// node that ends it must not curve it.
+static void testFlatSegmentEmitsNoInterior() {
+    const Rect area = wideArea();
+    StageEnvelope env = ahdsr(2.0, 0.0, 0.0, 1.0, 2.0);  // sustain == 1: the decay span is flat
+    env.attackCurve = util::kCurveNeutral;
+    env.decayCurve = 5.0;
+    env.releaseCurve = util::kCurveNeutral;
+    const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+    std::vector<StrokePoint> trace;
+    buildEnvelopeTrace(poly, env, area.x, area.right() - 1, trace);
+    std::size_t nodes = 0;
+    for (const EnvVertex& v : poly) if (!v.knot) ++nodes;
+    CHECK(trace.size() == nodes);
+}
+
+static void testClampAndDegenerate() {
+    const Rect area = wideArea();
+    StageEnvelope env = ahdsr(2.0, 0.0, 2.0, 0.4, 2.0);
+    env.attackCurve = 0.25;
+    env.decayCurve = 4.0;
+    const std::vector<EnvVertex> poly = buildEnvelopePolyline(env, overlayOf(area), 4.0);
+
+    // A narrower clamp than the vertices were built for: nothing escapes it.
+    std::vector<StrokePoint> trace;
+    const int lo = area.x + 100, hi = area.right() - 200;
+    buildEnvelopeTrace(poly, env, lo, hi, trace);
+    CHECK(!trace.empty());
+    for (const StrokePoint& p : trace) {
+        CHECK(p.x >= static_cast<float>(lo));
+        CHECK(p.x <= static_cast<float>(hi));
+    }
+
+    // The out vector is REPLACED, not appended to — a stale trace from the previous paint
+    // would otherwise stroke a line across the canvas.
+    buildEnvelopeTrace({}, env, area.x, area.right() - 1, trace);
+    CHECK(trace.empty());
+
+    // A degenerate surface still yields the flat baseline the painter needs.
+    const Rect flat = Rect::ltrb(20, 10, 20, 10);
+    const std::vector<EnvVertex> degen = buildEnvelopePolyline(env, overlayOf(flat), 0.0);
+    buildEnvelopeTrace(degen, env, flat.x, flat.x, trace);
+    CHECK(trace.size() == degen.size());
+}
+
+int main() {
+    testSegmentCurve();
+    testNeutralIsTodaysStraightLine();
+    testKnotsExcludedAndNodesPreserved();
+    testKnotLiesOnTraceAhdsr();
+    testKnotLiesOnTraceAhd();
+    testMidSegmentLevelMatchesTheLaw();
+    testCurvatureDirection();
+    testNoOvershoot();
+    testDensityFollowsWidth();
+    testFlatSegmentEmitsNoInterior();
+    testClampAndDegenerate();
+    if (g_fail == 0) std::printf("curve_tessellate: all tests passed\n");
+    return g_fail == 0 ? 0 : 1;
+}