517 lines
12 KiB
HTML
517 lines
12 KiB
HTML
<!doctype html>
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<html lang="en">
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<head>
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<meta charset="utf-8" />
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<meta name="viewport" content="width=device-width,initial-scale=1" />
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<title>Delaunay (Bowyer–Watson) on Canvas</title>
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<style>
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html, body {
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height: 100%;
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margin: 0;
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background: #111;
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color: #ddd;
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font-family: system-ui, -apple-system, Segoe UI, Roboto, Arial, sans-serif;
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}
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#wrap {
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display: grid;
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grid-template-rows: auto 1fr;
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height: 100%;
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}
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#bar {
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display: flex;
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flex-wrap: wrap;
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gap: 10px;
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align-items: center;
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padding: 10px 12px;
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background: #1a1a1a;
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border-bottom: 1px solid #2a2a2a;
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}
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#bar > * { margin: 0; }
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label {
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display: inline-flex;
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align-items: center;
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gap: 6px;
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white-space: nowrap;
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}
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input[type="range"] { width: 220px; }
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button {
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background: #2a2a2a;
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color: #ddd;
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border: 1px solid #3a3a3a;
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padding: 7px 10px;
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border-radius: 6px;
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cursor: pointer;
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}
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button:hover { background: #333; }
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button:disabled { opacity: .5; cursor: default; }
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.small {
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font-size: 12px;
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opacity: .85;
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}
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#c {
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display: block;
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width: 100%;
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height: 100%;
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}
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</style>
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</head>
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<body>
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<div id="wrap">
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<div id="bar">
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<label>
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N
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<input id="n" type="range" min="10" max="600" value="120" />
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<span id="nVal">120</span>
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</label>
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<button id="regen">Regenerate points</button>
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<button id="solve">Solve (one go)</button>
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<label>
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<input id="animate" type="checkbox" checked />
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Animate
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</label>
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<label>
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Step ms
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<input id="stepMs" type="range" min="0" max="200" value="12" />
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<span id="stepMsVal">12</span>
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</label>
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<button id="run" title="Start/stop animation">Start</button>
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<span class="small" id="status"></span>
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</div>
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<canvas id="c"></canvas>
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</div>
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<script>
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(() => {
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"use strict";
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// ----------------------------
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// Canvas + UI
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// ----------------------------
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const canvas = document.getElementById("c");
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const ctx = canvas.getContext("2d", { alpha: false });
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const nSlider = document.getElementById("n");
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const nVal = document.getElementById("nVal");
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const regenBtn = document.getElementById("regen");
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const solveBtn = document.getElementById("solve");
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const animateChk = document.getElementById("animate");
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const stepMs = document.getElementById("stepMs");
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const stepMsVal = document.getElementById("stepMsVal");
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const runBtn = document.getElementById("run");
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const statusEl = document.getElementById("status");
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let W = 0, H = 0, DPR = 1;
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function resize() {
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const rect = canvas.getBoundingClientRect();
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DPR = Math.max(1, Math.floor(window.devicePixelRatio || 1));
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W = Math.max(1, Math.floor(rect.width));
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H = Math.max(1, Math.floor(rect.height));
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canvas.width = W * DPR;
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canvas.height = H * DPR;
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ctx.setTransform(DPR, 0, 0, DPR, 0, 0);
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draw();
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}
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window.addEventListener("resize", resize);
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nSlider.addEventListener("input", () => {
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nVal.textContent = nSlider.value;
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});
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stepMs.addEventListener("input", () => {
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stepMsVal.textContent = stepMs.value;
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});
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// ----------------------------
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// Geometry helpers
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// ----------------------------
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function orient2d(a, b, c) {
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// Positive if a->b->c is counter-clockwise
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return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
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}
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function circumcircleContains(a, b, c, p) {
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// Robust-enough incircle test for typical canvas demos:
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// Uses determinant form; assumes triangle (a,b,c) is CCW.
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const ax = a.x - p.x;
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const ay = a.y - p.y;
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const bx = b.x - p.x;
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const by = b.y - p.y;
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const cx = c.x - p.x;
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const cy = c.y - p.y;
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const a2 = ax * ax + ay * ay;
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const b2 = bx * bx + by * by;
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const c2 = cx * cx + cy * cy;
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const det =
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ax * (by * c2 - b2 * cy) -
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ay * (bx * c2 - b2 * cx) +
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a2 * (bx * cy - by * cx);
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// For CCW triangle, det > 0 means p is inside circumcircle.
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// Small epsilon to reduce flicker on nearly co-circular sets.
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return det > 1e-10;
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}
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function triKey(i, j) {
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return i < j ? (i + "," + j) : (j + "," + i);
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}
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// ----------------------------
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// Bowyer–Watson incremental state
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// ----------------------------
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let points = [];
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let triangles = []; // each {a,b,c} indices into points
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let superIds = null; // [sa,sb,sc]
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let insertOrder = [];
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let insertIndex = 0;
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let isRunning = false;
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let lastStepTime = 0;
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function makeRandomPoints(n) {
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const margin = 24;
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const pts = [];
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for (let i = 0; i < n; i++) {
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pts.push({
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x: margin + Math.random() * (W - 2 * margin),
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y: margin + Math.random() * (H - 2 * margin),
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isSuper: false
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});
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}
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return pts;
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}
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function initTriangulation() {
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const n = Number(nSlider.value);
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points = makeRandomPoints(n);
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// Build a super-triangle that contains the canvas comfortably.
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// Big triangle around center, scaled by max dimension.
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const cx = W * 0.5;
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const cy = H * 0.5;
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const s = Math.max(W, H) * 10;
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const sa = points.length;
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points.push({ x: cx - 2 * s, y: cy + s, isSuper: true });
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const sb = points.length;
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points.push({ x: cx, y: cy - 2 * s, isSuper: true });
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const sc = points.length;
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points.push({ x: cx + 2 * s, y: cy + s, isSuper: true });
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superIds = [sa, sb, sc];
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// Ensure CCW order for the super triangle
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if (orient2d(points[sa], points[sb], points[sc]) < 0) {
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// swap sb and sc
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superIds = [sa, sc, sb];
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}
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triangles = [{
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a: superIds[0],
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b: superIds[1],
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c: superIds[2]
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}];
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// Insert points in random order for a nicer incremental animation
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insertOrder = [];
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for (let i = 0; i < n; i++) insertOrder.push(i);
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for (let i = insertOrder.length - 1; i > 0; i--) {
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const j = (Math.random() * (i + 1)) | 0;
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const t = insertOrder[i];
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insertOrder[i] = insertOrder[j];
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insertOrder[j] = t;
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}
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insertIndex = 0;
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updateStatus();
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draw();
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}
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function stepInsertOnePoint() {
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if (insertIndex >= insertOrder.length) return false;
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const pIndex = insertOrder[insertIndex++];
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const p = points[pIndex];
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// 1) Find "bad" triangles whose circumcircle contains p
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const bad = [];
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for (let t = 0; t < triangles.length; t++) {
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const tri = triangles[t];
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const a = points[tri.a], b = points[tri.b], c = points[tri.c];
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// Ensure CCW for the incircle test
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let ia = tri.a, ib = tri.b, ic = tri.c;
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if (orient2d(a, b, c) < 0) {
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// Swap two vertices to make it CCW
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ib = tri.c;
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ic = tri.b;
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}
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const aa = points[ia], bb = points[ib], cc = points[ic];
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if (circumcircleContains(aa, bb, cc, p)) {
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bad.push(t);
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}
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}
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// 2) Find boundary edges of the polygonal hole
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// Count edges from bad triangles; boundary edges are those that appear once.
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const edgeCount = new Map(); // key "i,j" -> {i,j,count}
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for (let k = 0; k < bad.length; k++) {
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const tri = triangles[bad[k]];
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const e1 = triKey(tri.a, tri.b);
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const e2 = triKey(tri.b, tri.c);
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const e3 = triKey(tri.c, tri.a);
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for (const [key, i, j] of [
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[e1, tri.a, tri.b],
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[e2, tri.b, tri.c],
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[e3, tri.c, tri.a]
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]) {
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const cur = edgeCount.get(key);
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if (cur) cur.count++;
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else edgeCount.set(key, { i, j, count: 1 });
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}
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}
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const boundaryEdges = [];
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for (const e of edgeCount.values()) {
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if (e.count === 1) boundaryEdges.push({ i: e.i, j: e.j });
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}
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// 3) Remove bad triangles (remove in descending index order)
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bad.sort((x, y) => y - x);
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for (let k = 0; k < bad.length; k++) {
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triangles.splice(bad[k], 1);
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}
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// 4) Re-triangulate the hole by connecting p to each boundary edge
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for (let e = 0; e < boundaryEdges.length; e++) {
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const i = boundaryEdges[e].i;
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const j = boundaryEdges[e].j;
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// Make triangle (i, j, pIndex) CCW
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const A = points[i], B = points[j], C = p;
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if (orient2d(A, B, C) > 0) {
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triangles.push({ a: i, b: j, c: pIndex });
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} else {
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triangles.push({ a: j, b: i, c: pIndex });
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}
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}
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return true;
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}
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function finalizeRemoveSuperTriangle() {
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if (!superIds) return;
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const s0 = superIds[0], s1 = superIds[1], s2 = superIds[2];
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triangles = triangles.filter(t => t.a !== s0 && t.a !== s1 && t.a !== s2 &&
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t.b !== s0 && t.b !== s1 && t.b !== s2 &&
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t.c !== s0 && t.c !== s1 && t.c !== s2);
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updateStatus();
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draw();
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}
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function solveAll() {
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while (insertIndex < insertOrder.length) {
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stepInsertOnePoint();
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}
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finalizeRemoveSuperTriangle();
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}
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// ----------------------------
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// Drawing
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// ----------------------------
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function draw() {
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// Background
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ctx.fillStyle = "#111";
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ctx.fillRect(0, 0, W, H);
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// Triangles
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ctx.lineWidth = 1;
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ctx.strokeStyle = "rgba(190,190,190,0.65)";
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ctx.beginPath();
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for (let t = 0; t < triangles.length; t++) {
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const tri = triangles[t];
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const a = points[tri.a];
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const b = points[tri.b];
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const c = points[tri.c];
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// Optionally hide super triangle edges during build for clarity
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if (a.isSuper || b.isSuper || c.isSuper) continue;
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ctx.moveTo(a.x, a.y);
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ctx.lineTo(b.x, b.y);
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ctx.lineTo(c.x, c.y);
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ctx.lineTo(a.x, a.y);
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}
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ctx.stroke();
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// Points
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for (let i = 0; i < points.length; i++) {
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const p = points[i];
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if (p.isSuper) continue;
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ctx.fillStyle = "#ddd";
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ctx.beginPath();
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ctx.arc(p.x, p.y, 2.2, 0, Math.PI * 2);
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ctx.fill();
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}
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// Current insertion point highlight
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if (insertIndex < insertOrder.length) {
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const idx = insertOrder[insertIndex];
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const p = points[idx];
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ctx.strokeStyle = "rgba(255,255,255,0.9)";
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ctx.lineWidth = 2;
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ctx.beginPath();
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ctx.arc(p.x, p.y, 6, 0, Math.PI * 2);
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ctx.stroke();
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ctx.lineWidth = 1;
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}
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}
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function updateStatus() {
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const n = Number(nSlider.value);
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const inserted = Math.min(insertIndex, n);
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const done = (insertIndex >= n);
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statusEl.textContent = done
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? `done: points ${n}, triangles ${triangles.length}`
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: `inserting: ${inserted}/${n}, triangles ${triangles.length}`;
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}
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// ----------------------------
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// Animation loop
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// ----------------------------
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function tick(ts) {
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if (!isRunning) return;
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const ms = Number(stepMs.value);
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const ready = (ms === 0) ? true : (ts - lastStepTime >= ms);
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if (ready) {
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lastStepTime = ts;
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const progressed = stepInsertOnePoint();
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updateStatus();
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draw();
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if (!progressed) {
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finalizeRemoveSuperTriangle();
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isRunning = false;
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runBtn.textContent = "Start";
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solveBtn.disabled = false;
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regenBtn.disabled = false;
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nSlider.disabled = false;
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animateChk.disabled = false;
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}
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}
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requestAnimationFrame(tick);
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}
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function startStop() {
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if (!animateChk.checked) return;
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if (!isRunning) {
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isRunning = true;
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lastStepTime = 0;
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runBtn.textContent = "Stop";
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solveBtn.disabled = true;
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regenBtn.disabled = true;
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nSlider.disabled = true;
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animateChk.disabled = true;
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requestAnimationFrame(tick);
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} else {
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isRunning = false;
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runBtn.textContent = "Start";
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solveBtn.disabled = false;
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regenBtn.disabled = false;
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nSlider.disabled = false;
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animateChk.disabled = false;
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updateStatus();
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draw();
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}
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}
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// ----------------------------
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// UI handlers
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// ----------------------------
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regenBtn.addEventListener("click", () => {
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isRunning = false;
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runBtn.textContent = "Start";
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solveBtn.disabled = false;
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regenBtn.disabled = false;
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nSlider.disabled = false;
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animateChk.disabled = false;
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initTriangulation();
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});
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solveBtn.addEventListener("click", () => {
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isRunning = false;
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runBtn.textContent = "Start";
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solveAll();
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});
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runBtn.addEventListener("click", () => {
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startStop();
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});
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animateChk.addEventListener("change", () => {
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if (!animateChk.checked) {
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isRunning = false;
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runBtn.textContent = "Start";
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runBtn.disabled = true;
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} else {
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runBtn.disabled = false;
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}
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});
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// Click to add a point (optional quick test)
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canvas.addEventListener("pointerdown", (e) => {
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// Only allow adding points when not running and before solving is complete.
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if (isRunning) return;
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const n = Number(nSlider.value);
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if (insertIndex >= insertOrder.length) return;
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const rect = canvas.getBoundingClientRect();
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const x = e.clientX - rect.left;
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const y = e.clientY - rect.top;
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// Replace next-to-insert random point with clicked position for quick experimentation
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const idx = insertOrder[insertIndex];
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points[idx].x = x;
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points[idx].y = y;
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draw();
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});
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function boot() {
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nVal.textContent = nSlider.value;
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stepMsVal.textContent = stepMs.value;
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runBtn.disabled = !animateChk.checked;
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resize();
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initTriangulation();
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updateStatus();
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draw();
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}
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boot();
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})();
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</script>
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</body>
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</html>
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