offsetting

2025-09-09 16:10:42 +02:00 · 2020-09-04 22:01:35 -07:00
parent 83dcab57cb
commit 7e5c6e2eba
38 changed files with 15520 additions and 412 deletions
--- a/docs/chapters/offsetting/offsetting.js
+++ b/docs/chapters/offsetting/offsetting.js
@@ -0,0 +1,118 @@
+let curve;
+
+setup() {
+  const type  = this.parameters.type ?? `quadratic`;
+  if (type === `quadratic`) {
+    curve = Bezier.defaultQuadratic(this);
+  } else {
+    curve = Bezier.defaultCubic(this);
+  }
+  setMovable(curve.points);
+  setSlider(`.slide-control`, `distance`, 20);
+}
+
+draw() {
+  clear();
+  noFill();
+
+  curve.drawSkeleton();
+
+  var reduced = this.reduce(curve);
+  reduced.forEach(c => {
+    setStroke( randomColor() );
+    this.drawCurve(c);
+    circle(c.points[0].x, c.points[0].y, 2);
+  });
+  var last = reduced.slice(-1)[0];
+  let p = last.points[3] ?? last.points[2];
+  circle(p.x, p.y, 3);
+
+  setStroke(`#FF000050`);
+  var offset = curve.offset(this.distance);
+  offset.forEach(c => {
+    circle(c.points[0].x, c.points[0].y, 2);
+    this.drawCurve(c);
+  });
+
+  last = offset.slice(-1)[0];
+  p = last.points[3] ?? last.points[2];
+  circle(p.x, p.y, 3);
+
+  setStroke(`#0000FF50`);
+  var offset = curve.offset(-this.distance);
+  offset.forEach(c => {
+    circle(c.points[0].x, c.points[0].y, 2);
+    this.drawCurve(c);
+  });
+
+  last = offset.slice(-1)[0];
+  p = last.points[3] ?? last.points[2];
+  circle(p.x, p.y, 3);
+
+  curve.drawPoints();
+}
+
+drawCurve(c) {
+  start()
+  c.getLUT(16).forEach(p => vertex(p.x, p.y));
+  end();
+}
+
+reduce(curve) {
+  let i,
+    t1 = 0,
+    t2 = 0,
+    step = 0.01,
+    segment,
+    pass1 = [],
+    pass2 = [];
+
+  // first pass: split on extrema
+  let extrema = curve.extrema().values;
+  if (extrema.indexOf(0) === -1) {
+    extrema = [0].concat(extrema);
+  }
+  if (extrema.indexOf(1) === -1) {
+    extrema.push(1);
+  }
+  for (t1 = extrema[0], i = 1; i < extrema.length; i++) {
+    t2 = extrema[i];
+    segment = curve.split(t1, t2);
+    segment._t1 = t1;
+    segment._t2 = t2;
+    pass1.push(segment);
+    t1 = t2;
+  }
+
+  // second pass: further reduce these segments to simple segments
+  pass1.forEach(p1 => {
+    t1 = 0;
+    t2 = 0;
+    while (t2 <= 1) {
+      for (t2 = t1 + step; t2 <= 1 + step; t2 += step) {
+        segment = p1.split(t1, t2);
+        if (!segment.simple()) {
+          t2 -= step;
+          if ( abs(t1 - t2) < step) {
+            // we can never form a reduction
+            return [];
+          }
+          segment = p1.split(t1, t2);
+          segment._t1 = map(t1, 0, 1, p1._t1, p1._t2);
+          segment._t2 = map(t2, 0, 1, p1._t1, p1._t2);
+          pass2.push(segment);
+          t1 = t2;
+          break;
+        }
+      }
+    }
+    if (t1 < 1) {
+      segment = p1.split(t1, 1);
+      segment._t1 = map(t1, 0, 1, p1._t1, p1._t2);
+      segment._t2 = p1._t2;
+      pass2.push(segment);
+    }
+  });
+
+  return pass2;
+}