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Added constrained relaxation solver - but it doesn't work

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Mikael Lövqvist
2025-12-29 23:37:23 +01:00
parent a7396a100a
commit 8146f912a8
2 changed files with 620 additions and 0 deletions
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index.html
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<li><a href="standalone/gradient_editor.html">Gradient editor</a></li> <li><a href="standalone/gradient_editor.html">Gradient editor</a></li>
<li><a href="standalone/imu-1/3d.html">3D view using GravitySensor</a></li> <li><a href="standalone/imu-1/3d.html">3D view using GravitySensor</a></li>
<li><a href="standalone/delaunay.html">Delaunay dataset</a></li> <li><a href="standalone/delaunay.html">Delaunay dataset</a></li>
<li><a href="standalone/delaunay-edge-relax.html">Delaunay dataset + Edge relaxation (Currently broken)</a></li>
</ul> </ul>
</li> </li>

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standalone/delaunay-edge-relax.html Normal file
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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width,initial-scale=1" />
<title>Delaunay + Planarity Back-Pressure Relaxation</title>
<style>
html, body {
height: 100%;
margin: 0;
background: #111;
color: #ddd;
font-family: system-ui, -apple-system, Segoe UI, Roboto, Arial, sans-serif;
}
#wrap {
display: grid;
grid-template-rows: auto 1fr;
height: 100%;
}
#bar {
display: flex;
flex-wrap: wrap;
gap: 10px 14px;
align-items: center;
padding: 10px 12px;
background: #1a1a1a;
border-bottom: 1px solid #2a2a2a;
}
label { display: inline-flex; gap: 8px; align-items: center; white-space: nowrap; }
input[type="range"] { width: 220px; }
button {
background: #2a2a2a;
color: #ddd;
border: 1px solid #3a3a3a;
padding: 7px 10px;
border-radius: 6px;
cursor: pointer;
}
button:hover { background: #333; }
.small { font-size: 12px; opacity: .85; }
#c { display: block; width: 100%; height: 100%; }
</style>
</head>
<body>
<div id="wrap">
<div id="bar">
<label>
N
<input id="n" type="range" min="10" max="600" value="180" />
<span id="nVal">180</span>
</label>
<button id="regen">Regenerate + Solve Delaunay</button>
<label>
Free force
<input id="freeK" type="range" min="0" max="200" value="55" />
<span id="freeKVal">0.055</span>
</label>
<label>
Crossing bias
<input id="crossB" type="range" min="0" max="400" value="220" />
<span id="crossBVal">2.20</span>
</label>
<label>
Steps/frame
<input id="steps" type="range" min="1" max="60" value="18" />
<span id="stepsVal">18</span>
</label>
<label>
Step scalar
<input id="alpha" type="range" min="1" max="200" value="55" />
<span id="alphaVal">0.055</span>
</label>
<span class="small" id="info"></span>
</div>
<canvas id="c"></canvas>
</div>
<script>
(() => {
"use strict";
// ----------------------------
// Canvas
// ----------------------------
const canvas = document.getElementById("c");
const ctx = canvas.getContext("2d", { alpha: false });
let W = 0, H = 0, DPR = 1;
function resize() {
const r = canvas.getBoundingClientRect();
DPR = Math.max(1, Math.floor(window.devicePixelRatio || 1));
W = Math.max(1, r.width | 0);
H = Math.max(1, r.height | 0);
canvas.width = W * DPR;
canvas.height = H * DPR;
ctx.setTransform(DPR, 0, 0, DPR, 0, 0);
}
window.addEventListener("resize", resize);
// ----------------------------
// UI
// ----------------------------
const nSlider = document.getElementById("n");
const nVal = document.getElementById("nVal");
const regenBtn = document.getElementById("regen");
const freeK = document.getElementById("freeK");
const freeKVal = document.getElementById("freeKVal");
const crossB = document.getElementById("crossB");
const crossBVal = document.getElementById("crossBVal");
const steps = document.getElementById("steps");
const stepsVal = document.getElementById("stepsVal");
const alpha = document.getElementById("alpha");
const alphaVal = document.getElementById("alphaVal");
const info = document.getElementById("info");
function updateUiText() {
nVal.textContent = nSlider.value;
freeKVal.textContent = (Number(freeK.value) / 1000).toFixed(3);
crossBVal.textContent = (Number(crossB.value) / 100).toFixed(2);
stepsVal.textContent = steps.value;
alphaVal.textContent = (Number(alpha.value) / 1000).toFixed(3);
}
nSlider.addEventListener("input", updateUiText);
freeK.addEventListener("input", updateUiText);
crossB.addEventListener("input", updateUiText);
steps.addEventListener("input", updateUiText);
alpha.addEventListener("input", updateUiText);
// ----------------------------
// Geometry helpers
// ----------------------------
function orient(a, b, c) {
return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}
function circumcircleContains(a, b, c, p) {
// Determinant incircle test; expects a,b,c CCW.
const ax = a.x - p.x, ay = a.y - p.y;
const bx = b.x - p.x, by = b.y - p.y;
const cx = c.x - p.x, cy = c.y - p.y;
const a2 = ax * ax + ay * ay;
const b2 = bx * bx + by * by;
const c2 = cx * cx + cy * cy;
const det =
ax * (by * c2 - b2 * cy) -
ay * (bx * c2 - b2 * cx) +
a2 * (bx * cy - by * cx);
return det > 1e-10;
}
function edgeKey(i, j) {
return i < j ? (i + "," + j) : (j + "," + i);
}
function segIntersectParams(ax, ay, bx, by, cx, cy, dx, dy) {
// Returns {hit,t,u,ix,iy} for proper intersection (not touching/endpoints/collinear).
const rpx = bx - ax, rpy = by - ay;
const spx = dx - cx, spy = dy - cy;
const denom = rpx * spy - rpy * spx;
if (Math.abs(denom) < 1e-12) return null; // parallel or collinear
const qpx = cx - ax, qpy = cy - ay;
const t = (qpx * spy - qpy * spx) / denom;
const u = (qpx * rpy - qpy * rpx) / denom;
// Strict interior intersection to avoid fighting at shared endpoints.
if (t <= 1e-6 || t >= 1 - 1e-6 || u <= 1e-6 || u >= 1 - 1e-6) return null;
return {
t,
u,
ix: ax + t * rpx,
iy: ay + t * rpy
};
}
// ----------------------------
// Delaunay (Bowyer–Watson, one-shot)
// ----------------------------
let points = [];
let triangles = [];
let edges = [];
let edgePairs = []; // convenience array of {i,j}
let superCount = 0;
function solveDelaunay(pts) {
points = pts;
triangles = [];
edges = [];
edgePairs = [];
const cx = W * 0.5;
const cy = H * 0.5;
const s = Math.max(W, H) * 10;
const sa = points.length;
points.push({ x: cx - 2 * s, y: cy + s, super: true });
const sb = points.length;
points.push({ x: cx, y: cy - 2 * s, super: true });
const sc = points.length;
points.push({ x: cx + 2 * s, y: cy + s, super: true });
superCount = 3;
// Ensure CCW for super triangle
if (orient(points[sa], points[sb], points[sc]) < 0) {
const tmp = points[sb];
points[sb] = points[sc];
points[sc] = tmp;
}
triangles.push({ a: sa, b: sb, c: sc });
const realN = pts.length;
for (let pi = 0; pi < realN; pi++) {
const p = points[pi];
const bad = [];
for (let ti = 0; ti < triangles.length; ti++) {
const t = triangles[ti];
let A = points[t.a], B = points[t.b], C = points[t.c];
// enforce CCW for incircle test
if (orient(A, B, C) < 0) {
const tmp = B; B = C; C = tmp;
}
if (circumcircleContains(A, B, C, p)) bad.push(ti);
}
const ec = new Map();
for (let k = 0; k < bad.length; k++) {
const t = triangles[bad[k]];
const k1 = edgeKey(t.a, t.b);
const k2 = edgeKey(t.b, t.c);
const k3 = edgeKey(t.c, t.a);
ec.set(k1, (ec.get(k1) || 0) + 1);
ec.set(k2, (ec.get(k2) || 0) + 1);
ec.set(k3, (ec.get(k3) || 0) + 1);
}
bad.sort((a, b) => b - a);
for (let k = 0; k < bad.length; k++) triangles.splice(bad[k], 1);
for (const [k, c] of ec.entries()) {
if (c !== 1) continue;
const parts = k.split(",");
const i = Number(parts[0]);
const j = Number(parts[1]);
// make triangle CCW
if (orient(points[i], points[j], p) > 0)
triangles.push({ a: i, b: j, c: pi });
else
triangles.push({ a: j, b: i, c: pi });
}
}
// Remove triangles touching super vertices
triangles = triangles.filter(t =>
!points[t.a].super &&
!points[t.b].super &&
!points[t.c].super
);
// Build unique edges
const es = new Map();
for (let ti = 0; ti < triangles.length; ti++) {
const t = triangles[ti];
for (const [i, j] of [[t.a, t.b], [t.b, t.c], [t.c, t.a]]) {
es.set(edgeKey(i, j), { i, j });
}
}
edges = [...es.values()];
edgePairs = edges; // alias
}
// ----------------------------
// Relaxation with back-pressure constraints
// ----------------------------
let fx = null;
let fy = null;
function ensureForceArrays() {
if (!fx || fx.length !== points.length) {
fx = new Float32Array(points.length);
fy = new Float32Array(points.length);
}
}
function zeroForces() {
fx.fill(0);
fy.fill(0);
}
function addFreeForces(avgLen, kFree) {
// Spring equalization: for each edge, push/pull to match avgLen.
for (let ei = 0; ei < edgePairs.length; ei++) {
const e = edgePairs[ei];
const a = points[e.i];
const b = points[e.j];
let dx = b.x - a.x;
let dy = b.y - a.y;
let len = Math.hypot(dx, dy) || 1;
const nx = dx / len;
const ny = dy / len;
// positive when too long -> pull together
const delta = (len - avgLen);
// symmetric force along the edge
const f = delta * kFree;
const fxE = nx * f;
const fyE = ny * f;
fx[e.i] += fxE;
fy[e.i] += fyE;
fx[e.j] -= fxE;
fy[e.j] -= fyE;
}
}
function addBoundaryForces() {
// Soft boundary box: keep points in an inner region (to allow expansion).
// Uses weak forces rather than hard clamps.
const padX = W * 0.10;
const padY = H * 0.10;
const minX = padX;
const maxX = W - padX;
const minY = padY;
const maxY = H - padY;
const k = 0.002;
for (let i = 0; i < points.length; i++) {
const p = points[i];
if (p.super) continue;
if (p.x < minX) fx[i] += (minX - p.x) * k;
else if (p.x > maxX) fx[i] -= (p.x - maxX) * k;
if (p.y < minY) fy[i] += (minY - p.y) * k;
else if (p.y > maxY) fy[i] -= (p.y - maxY) * k;
}
}
function addCrossingBackPressure(bias) {
// For every intersecting non-adjacent edge pair:
// add forces that push the two segments apart using their normals at the intersection.
//
// This is a penalty constraint: strong when violated; zero otherwise.
let crossings = 0;
const kCross = 0.8 * bias; // base multiplier; bias comes from UI
for (let i = 0; i < edgePairs.length; i++) {
const e1 = edgePairs[i];
const a = points[e1.i];
const b = points[e1.j];
const ax = a.x, ay = a.y, bx = b.x, by = b.y;
for (let j = i + 1; j < edgePairs.length; j++) {
const e2 = edgePairs[j];
// Skip if they share a vertex (adjacent edges are allowed to meet).
if (e1.i === e2.i || e1.i === e2.j || e1.j === e2.i || e1.j === e2.j) continue;
const c = points[e2.i];
const d = points[e2.j];
const hit = segIntersectParams(ax, ay, bx, by, c.x, c.y, d.x, d.y);
if (!hit) continue;
crossings++;
// Segment directions
const r1x = bx - ax, r1y = by - ay;
const r2x = d.x - c.x, r2y = d.y - c.y;
const len1 = Math.hypot(r1x, r1y) || 1;
const len2 = Math.hypot(r2x, r2y) || 1;
// Unit normals (two choices; pick sign via side tests)
let n1x = -r1y / len1, n1y = r1x / len1;
let n2x = -r2y / len2, n2y = r2x / len2;
// Determine on which side of e1 the endpoints of e2 lie
// (they should be opposite sides for a proper crossing).
const s1 = orient(a, b, c);
const s2 = orient(a, b, d);
// Choose n1 direction so that it pushes c and d to opposite sides away from the edge
// We want to push e1 endpoints in direction that separates from e2; use c as reference.
// If c is "left" (positive), push e1 along +n1; otherwise along -n1.
const sign1 = (s1 > 0) ? 1 : -1;
// Similarly for e2 relative to e1
const t1 = orient(c, d, a);
const sign2 = (t1 > 0) ? 1 : -1;
n1x *= sign1; n1y *= sign1;
n2x *= sign2; n2y *= sign2;
// Strength: grow when intersection is near the middle (harder constraint)
// and modestly with edge lengths to avoid tiny-edge domination.
const midBoost = 1.0 + 2.0 * (0.5 - Math.abs(hit.t - 0.5)) + 2.0 * (0.5 - Math.abs(hit.u - 0.5));
const f1 = kCross * midBoost;
const f2 = kCross * midBoost;
// Apply equal & opposite "pressure" to endpoints (symmetric distribution)
// e1 endpoints move along its normal
fx[e1.i] += n1x * f1;
fy[e1.i] += n1y * f1;
fx[e1.j] += n1x * f1;
fy[e1.j] += n1y * f1;
// e2 endpoints move along its normal in the opposite direction
fx[e2.i] -= n2x * f2;
fy[e2.i] -= n2y * f2;
fx[e2.j] -= n2x * f2;
fy[e2.j] -= n2y * f2;
// Extra: also push along the other segment's normal (helps untangle faster)
// but smaller, to avoid oscillation.
const kMix = 0.35 * kCross;
fx[e1.i] += n2x * kMix;
fy[e1.i] += n2y * kMix;
fx[e1.j] += n2x * kMix;
fy[e1.j] += n2y * kMix;
fx[e2.i] -= n1x * kMix;
fy[e2.i] -= n1y * kMix;
fx[e2.j] -= n1x * kMix;
fy[e2.j] -= n1y * kMix;
}
}
return crossings;
}
function computeAverageEdgeLength() {
let sum = 0;
for (let i = 0; i < edgePairs.length; i++) {
const e = edgePairs[i];
const a = points[e.i];
const b = points[e.j];
sum += Math.hypot(b.x - a.x, b.y - a.y);
}
return sum / Math.max(1, edgePairs.length);
}
function applyForces(stepScalar) {
// Bounded move per inner iteration; small steps preserve stability.
const maxStep = 0.65;
for (let i = 0; i < points.length; i++) {
const p = points[i];
if (p.super) continue;
let dx = fx[i] * stepScalar;
let dy = fy[i] * stepScalar;
const d = Math.hypot(dx, dy);
if (d > maxStep) {
const s = maxStep / d;
dx *= s;
dy *= s;
}
p.x += dx;
p.y += dy;
}
}
// ----------------------------
// Drawing
// ----------------------------
function draw(crossingsLastFrame) {
ctx.fillStyle = "#111";
ctx.fillRect(0, 0, W, H);
// edges
ctx.strokeStyle = "rgba(200,200,200,0.55)";
ctx.lineWidth = 1;
ctx.beginPath();
for (let i = 0; i < edgePairs.length; i++) {
const e = edgePairs[i];
const a = points[e.i];
const b = points[e.j];
ctx.moveTo(a.x, a.y);
ctx.lineTo(b.x, b.y);
}
ctx.stroke();
// points
ctx.fillStyle = "#ddd";
for (let i = 0; i < points.length; i++) {
const p = points[i];
if (p.super) continue;
ctx.beginPath();
ctx.arc(p.x, p.y, 2.2, 0, Math.PI * 2);
ctx.fill();
}
info.textContent = `points ${points.length - superCount}, edges ${edgePairs.length}, crossings ${crossingsLastFrame}`;
}
// ----------------------------
// Regenerate + solve Delaunay
// ----------------------------
function regenerate() {
const N = Number(nSlider.value);
// Generate in central 50% region (25% margins) so it can expand.
const mx = W * 0.25;
const my = H * 0.25;
const pts = [];
for (let i = 0; i < N; i++) {
pts.push({
x: mx + Math.random() * (W - 2 * mx),
y: my + Math.random() * (H - 2 * my),
super: false
});
}
solveDelaunay(pts);
ensureForceArrays();
}
regenBtn.addEventListener("click", regenerate);
// ----------------------------
// Main animation loop
// ----------------------------
let crossingsLastFrame = 0;
function frame() {
if (!points.length) {
requestAnimationFrame(frame);
return;
}
const innerSteps = Number(steps.value);
const kFree = Number(freeK.value) / 1000;
const bias = Number(crossB.value) / 100;
let stepScalar = Number(alpha.value) / 1000;
// Adaptive step: if crossings persist, reduce step a bit this frame.
// (This is the scalar you described; keeps solver stable under strong back-pressure.)
if (crossingsLastFrame > 0) stepScalar *= 0.6;
// One visual frame = multiple solver iterations
let crossings = 0;
for (let it = 0; it < innerSteps; it++) {
ensureForceArrays();
zeroForces();
const avgLen = computeAverageEdgeLength();
// 1) free forces
addFreeForces(avgLen, kFree);
addBoundaryForces();
// 2) constraint back-pressure (fed back into totals)
crossings = addCrossingBackPressure(bias);
// Apply combined forces
applyForces(stepScalar);
// Early-out if stable
if (crossings === 0) break;
}
crossingsLastFrame = crossings;
draw(crossingsLastFrame);
requestAnimationFrame(frame);
}
// ----------------------------
// Boot
// ----------------------------
function boot() {
updateUiText();
resize();
regenerate();
requestAnimationFrame(frame);
}
boot();
})();
</script>
</body>
</html>