curvature

docs/chapters/curvature/curvature.js

@@ -0,0 +1,77 @@
+let q, c;
+
+setup() {
+  q = new Bezier(this, 60,55, 125,160, 365,165);
+  c = new Bezier(this, 385,165, 645,165, 645,70, 750,165);
+
+  setSlider(`.slide-control`, `position`, 0);
+  setMovable(q.points.concat(c.points));
+}
+
+draw() {
+  clear();
+
+  [q, c].forEach(curve => {
+    curve.drawSkeleton();
+    curve.drawCurve();
+    this.drawCurvature(curve);
+    curve.drawPoints();
+  });
+
+  if (this.parameters.omni) {
+    let t = this.position;
+    let curve = q;
+    if (t>1) { t -= 1; curve = c; }
+    this.drawIncidentCircle(curve, t)
+  }
+}
+
+drawCurvature(curve) {
+  let s, t, p, n, k, ox, oy;
+  for(s=0; s<256; s++) {
+    setStroke(`rgba(255,127,${s},0.6)`);
+    t = s/255;
+    p = curve.get(t);
+    n = curve.normal(t);
+    k = this.computeCurvature(curve, t) * 10000;
+
+    ox = k * n.x;
+    oy = k * n.y;
+    line(p.x, p.y, p.x + ox, p.y + oy);
+
+    // And if requested, also draw it along the anti-normal.
+    if (this.parameters.omni) {
+      setStroke(`rgba(${s},127,255,0.6)`);
+      line(p.x, p.y, p.x - ox, p.y - oy);
+    }
+  }
+}
+
+computeCurvature(curve, t) {
+  const d = curve.derivative(t),
+        dd = curve.dderivative(t),
+        num = d.x * dd.y - d.y * dd.x,
+        qdsum = d.x * d.x + d.y * d.y,
+        dnm = pow(qdsum, 3 / 2);
+
+  if (num === 0 || dnm === 0) return 0;
+
+  return num / dnm;
+}
+
+drawIncidentCircle(curve, t) {
+  let p = curve.get(t),
+      n = curve.normal(t),
+      k = this.computeCurvature(curve, t),
+      r = 1 / k,
+      rx = p.x + n.x * r,
+      ry = p.y + n.y * r;
+
+  setFill(`rgba(200,200,255,0.4)`);
+  setStroke(`red`);
+
+  line(p.x, p.y, rx, ry);
+  circle(p.x, p.y, 3);
+  circle(rx, ry, 3);
+  circle(rx, ry, abs(r));
+}