projection, half moulding

docs/chapters/projections/project.js

@@ -0,0 +1,116 @@
+let curve;
+
+setup() {
+  curve = new Bezier(this, [
+    {x:248,y:188},
+    {x:218,y:294},
+    {x:45,y:290},
+    {x:12,y:236},
+    {x:14,y:82},
+    {x:186,y:177},
+    {x:221,y:90},
+    {x:18,y:156},
+    {x:34,y:57},
+    {x:198,y:18}
+  ]);
+
+  this.cursor.x = 280;
+  this.cursor.y = 265
+
+  setMovable(curve.points);
+}
+
+draw() {
+  clear();
+  curve.drawSkeleton(`lightblue`);
+  curve.drawCurve();
+  curve.drawPoints();
+
+  if (this.currentPoint) return;
+
+  const x = this.cursor.x,
+        y = this.cursor.y,
+        LUT = curve.getLUT(20),
+        i = this.findClosest(x, y, LUT);
+
+  this.showCandidateInterval(x, y, LUT, i);
+  this.drawProjection(x, y, LUT, i);
+}
+
+findClosest(x, y, LUT, distance = Number.MAX_SAFE_INTEGER) {
+  let i = 0;
+  LUT.forEach((p, index) => {
+    p.t = index/(LUT.length-1);
+    p.distance = dist(x, y, p.x, p.y);
+    if (p.distance < distance) {
+      distance = p.distance;
+      i = index;
+    }
+  });
+  return i;
+}
+
+showCandidateInterval(x, y, LUT, i) {
+  let c = LUT[i];
+  setColor(`rgba(100,255,100)`);
+  circle(c.x, c.y, 3);
+  line(c.x, c.y, x, y);
+  if (i>0) { c = LUT[i-1]; circle(c.x, c.y, 3); line(c.x, c.y, x, y); }
+  if (i<LUT.length-1) { c = LUT[i+1]; circle(c.x, c.y, 3); line(c.x, c.y, x, y); }
+  c = LUT[i];
+}
+
+drawProjection(x, y, LUT, i) {
+  let B = this.refineBinary(x, y, LUT, i);
+  setColor(`rgba(100,100,255)`);
+  circle(B.x, B.y, 3);
+  line(B.x, B.y, x, y);
+}
+
+/*
+  We already know that LUT[i1] and LUT[i2] are *not* good distances,
+  so we know that a better distance will be somewhere between them.
+  We generate three new points between those two, so we end up with
+  five points, and then check which three of those five are a new,
+  better, interval to check within.
+*/
+refineBinary(x, y, LUT, i) {
+  let q, count=1, distance = Number.MAX_SAFE_INTEGER;
+
+  do {
+    let i1 = i === 0 ? 0 : i-1,
+        i2 = i === LUT.length - 1 ? LUT.length -1 : i+1,
+        t1 = LUT[i1].t,
+        t2 = LUT[i2].t,
+        lut = [],
+        step = (t2 - t1)/5;
+
+    if (step < 0.001) break;
+
+    lut.push(LUT[i1]);
+    for(let j=1; j<=3; j++) {
+      let n = curve.get(t1 + j *step);
+      n.distance = dist(n.x, n.y, x, y);
+      if (n.distance < distance) {
+        distance = n.distance;
+        q = n;
+        i = j;
+      }
+      lut.push(n);
+    }
+    lut.push(LUT[i2]);
+
+    // update the LUT to be our new five point LUT, and run again.
+    LUT = lut;
+
+    // The "count" test is mostly a safety measure: it will
+    // never kick in, but something that _will_ terminate is
+    // always better than while(true). Never use while(true)
+  } while (count++ < 25);
+
+  return q;
+}
+
+onMouseMove() {
+  redraw();
+}