1 files changed, 50 insertions, 16 deletions

diff --git a/tools/mq_editor/utils.js b/tools/mq_editor/utils.js
index 96d807c..7ab274e 100644
--- a/tools/mq_editor/utils.js
+++ b/tools/mq_editor/utils.js
@@ -1,31 +1,52 @@
 // Shared utilities for mq_editor
 
-// Evaluate cubic bezier curve at time t (robust: handles dt<=0)
+// Evaluate interpolating curve at time t via Lagrange interpolation.
+// The curve passes through all 4 control points at their stored time positions.
+// Knot positions: u_k = (t_k - t0) / (t3 - t0), k=0..3.
+// TODO: support arbitrary number of inner control points
 function evalBezier(curve, t) {
   const dt = curve.t3 - curve.t0;
   if (dt <= 0) return curve.v0;
   let u = (t - curve.t0) / dt;
-  u = Math.max(0, Math.min(1, u));
-  const u1 = 1.0 - u;
-  return u1*u1*u1 * curve.v0 +
-         3*u1*u1*u * curve.v1 +
-         3*u1*u*u  * curve.v2 +
-         u*u*u     * curve.v3;
+  u = clamp(u, 0, 1);
+  const u1 = (curve.t1 - curve.t0) / dt;
+  const u2 = (curve.t2 - curve.t0) / dt;
+  const d0 = (-u1) * (-u2) * (-1);
+  const d1 = u1 * (u1 - u2) * (u1 - 1);
+  const d2 = u2 * (u2 - u1) * (u2 - 1);
+  const d3 = (1 - u1) * (1 - u2);
+  if (Math.abs(d0) < 1e-9 || Math.abs(d1) < 1e-9 || Math.abs(d2) < 1e-9 || Math.abs(d3) < 1e-9)
+    return curve.v0 + (curve.v3 - curve.v0) * u;
+  const l0 = (u - u1) * (u - u2) * (u - 1) / d0;
+  const l1 = u * (u - u2) * (u - 1) / d1;
+  const l2 = u * (u - u1) * (u - 1) / d2;
+  const l3 = u * (u - u1) * (u - u2) / d3;
+  return l0 * curve.v0 + l1 * curve.v1 + l2 * curve.v2 + l3 * curve.v3;
 }
 
-// Evaluate amplitude component of unified bezier curve at time t
+// Evaluate amplitude component of interpolating curve at time t
 function evalBezierAmp(curve, t) {
   const dt = curve.t3 - curve.t0;
   if (dt <= 0) return curve.a0;
   let u = (t - curve.t0) / dt;
-  u = Math.max(0, Math.min(1, u));
-  const u1 = 1.0 - u;
-  return u1*u1*u1 * curve.a0 +
-         3*u1*u1*u * curve.a1 +
-         3*u1*u*u  * curve.a2 +
-         u*u*u     * curve.a3;
+  u = clamp(u, 0, 1);
+  const u1 = (curve.t1 - curve.t0) / dt;
+  const u2 = (curve.t2 - curve.t0) / dt;
+  const d0 = (-u1) * (-u2) * (-1);
+  const d1 = u1 * (u1 - u2) * (u1 - 1);
+  const d2 = u2 * (u2 - u1) * (u2 - 1);
+  const d3 = (1 - u1) * (1 - u2);
+  if (Math.abs(d0) < 1e-9 || Math.abs(d1) < 1e-9 || Math.abs(d2) < 1e-9 || Math.abs(d3) < 1e-9)
+    return curve.a0 + (curve.a3 - curve.a0) * u;
+  const l0 = (u - u1) * (u - u2) * (u - 1) / d0;
+  const l1 = u * (u - u2) * (u - 1) / d1;
+  const l2 = u * (u - u1) * (u - 1) / d2;
+  const l3 = u * (u - u1) * (u - u2) / d3;
+  return l0 * curve.a0 + l1 * curve.a1 + l2 * curve.a2 + l3 * curve.a3;
 }
 
+function clamp(v, lo, hi) { return v < lo ? lo : v > hi ? hi : v; }
+
 // Get canvas-relative {x, y} from a mouse event
 function getCanvasCoords(e, canvas) {
   const rect = canvas.getBoundingClientRect();
@@ -34,16 +55,29 @@ function getCanvasCoords(e, canvas) {
 
 // Build upper/lower band point arrays for a frequency curve.
 // factorAbove/factorBelow are fractional offsets (e.g. 0.02 = ±2%).
+// freqMult: optional frequency scaling for harmonics (default 1.0).
 // Returns { upper: [[x,y],...], lower: [[x,y],...] }
-function buildBandPoints(viewer, curve, factorAbove, factorBelow) {
+function buildBandPoints(viewer, curve, factorAbove, factorBelow, freqMult = 1.0) {
   const STEPS = 60;
   const upper = [], lower = [];
   for (let i = 0; i <= STEPS; ++i) {
     const t = curve.t0 + (curve.t3 - curve.t0) * i / STEPS;
     if (t < viewer.t_view_min - 0.01 || t > viewer.t_view_max + 0.01) continue;
-    const f = evalBezier(curve, t);
+    const f = evalBezier(curve, t) * freqMult;
     upper.push([viewer.timeToX(t), viewer.freqToY(f * (1 + factorAbove))]);
     lower.push([viewer.timeToX(t), viewer.freqToY(f * (1 - factorBelow))]);
   }
   return { upper, lower };
 }
+
+// Build center line points at freq * freqMult along the curve.
+function buildCenterPoints(viewer, curve, freqMult = 1.0) {
+  const STEPS = 60;
+  const pts = [];
+  for (let i = 0; i <= STEPS; ++i) {
+    const t = curve.t0 + (curve.t3 - curve.t0) * i / STEPS;
+    if (t < viewer.t_view_min - 0.01 || t > viewer.t_view_max + 0.01) continue;
+    pts.push([viewer.timeToX(t), viewer.freqToY(evalBezier(curve, t) * freqMult)]);
+  }
+  return pts;
+}