Added convex hull demo
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361
canvas/convex-hull.js
Normal file
361
canvas/convex-hull.js
Normal file
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// This file is mostly written by ChatGPT 5.2
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// Renders 3D polylines (arrays of Vec3 points) onto a 2D canvas using a perspective frustum.
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// - ctx: CanvasRenderingContext2D
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// - polylines: Array<Array<{x:number,y:number,z:number}>>
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// - camera: {
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// eye:{x,y,z}, target:{x,y,z}, up:{x,y,z},
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// fovY:number (radians), aspect:number, near:number, far:number
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// }
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// - viewport: { x:number, y:number, w:number, h:number } // canvas rect in pixels
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function renderFrustumPolylines(ctx, polylines, camera, viewport)
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{
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const V = mat4LookAt(camera.eye, camera.target, camera.up);
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const P = mat4Perspective(camera.fovY, camera.aspect, camera.near, camera.far);
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const VP = mat4Mul(P, V);
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ctx.beginPath();
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for (const poly of polylines)
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{
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if (!poly || poly.length < 2) continue;
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for (let i = 0; i < poly.length - 1; i++)
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{
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const a = poly[i];
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const b = poly[i + 1];
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const ca = mat4MulVec4(VP, [a.x, a.y, a.z, 1]);
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const cb = mat4MulVec4(VP, [b.x, b.y, b.z, 1]);
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const clipped = clipLineClipSpace(ca, cb);
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if (!clipped) continue;
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const [p0, p1] = clipped;
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// Perspective divide -> NDC
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const ndc0 = [p0[0] / p0[3], p0[1] / p0[3], p0[2] / p0[3]];
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const ndc1 = [p1[0] / p1[3], p1[1] / p1[3], p1[2] / p1[3]];
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// NDC [-1..1] -> screen pixels
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const s0 = ndcToScreen(ndc0, viewport);
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const s1 = ndcToScreen(ndc1, viewport);
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ctx.moveTo(s0[0], s0[1]);
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ctx.lineTo(s1[0], s1[1]);
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}
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}
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ctx.stroke();
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}
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function ndcToScreen(ndc, vp)
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{
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// Canvas y-axis points down; NDC y-axis points up.
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const x = vp.x + (ndc[0] * 0.5 + 0.5) * vp.w;
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const y = vp.y + (1 - (ndc[1] * 0.5 + 0.5)) * vp.h;
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return [x, y];
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}
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// --- Homogeneous line clipping in clip space ---
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// Clip space constraints (OpenGL-style):
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// -w <= x <= w
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// -w <= y <= w
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// -w <= z <= w
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//
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// Returns null if fully outside, else returns [p0,p1] (both vec4 in clip space).
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function clipLineClipSpace(p0, p1)
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{
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let t0 = 0, t1 = 1;
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const d = [p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2], p1[3] - p0[3]];
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// For each plane: (a·p + b >= 0). In homogeneous clip space:
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// x + w >= 0, -x + w >= 0, y + w >= 0, -y + w >= 0, z + w >= 0, -z + w >= 0.
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const planes = [
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[ 1, 0, 0, 1], // x + w >= 0
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[-1, 0, 0, 1], // -x + w >= 0
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[ 0, 1, 0, 1], // y + w >= 0
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[ 0, -1, 0, 1], // -y + w >= 0
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[ 0, 0, 1, 1], // z + w >= 0
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[ 0, 0, -1, 1] // -z + w >= 0
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];
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for (const pl of planes)
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{
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const f0 = pl[0]*p0[0] + pl[1]*p0[1] + pl[2]*p0[2] + pl[3]*p0[3];
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const f1 = pl[0]*p1[0] + pl[1]*p1[1] + pl[2]*p1[2] + pl[3]*p1[3];
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const df = f1 - f0;
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if (df === 0)
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{
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if (f0 < 0) return null; // parallel and outside
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continue;
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}
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const t = -f0 / df;
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if (df > 0)
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{
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// entering
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if (t > t0) t0 = t;
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}
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else
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{
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// leaving
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if (t < t1) t1 = t;
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}
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if (t0 > t1) return null;
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}
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const q0 = [
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p0[0] + d[0]*t0, p0[1] + d[1]*t0, p0[2] + d[2]*t0, p0[3] + d[3]*t0
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];
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const q1 = [
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p0[0] + d[0]*t1, p0[1] + d[1]*t1, p0[2] + d[2]*t1, p0[3] + d[3]*t1
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];
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// Also reject if w is non-positive after clipping (avoid invalid perspective divide)
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if (q0[3] <= 0 && q1[3] <= 0) return null;
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return [q0, q1];
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}
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// --- Minimal 4x4 matrix helpers (column-major, WebGL-style) ---
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function mat4Mul(A, B)
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{
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// C = A * B
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const C = new Float32Array(16);
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for (let c = 0; c < 4; c++)
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{
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for (let r = 0; r < 4; r++)
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{
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C[c*4 + r] =
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A[0*4 + r] * B[c*4 + 0] +
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A[1*4 + r] * B[c*4 + 1] +
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A[2*4 + r] * B[c*4 + 2] +
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A[3*4 + r] * B[c*4 + 3];
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}
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}
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return C;
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}
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function mat4MulVec4(M, v)
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{
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return [
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M[0]*v[0] + M[4]*v[1] + M[8]*v[2] + M[12]*v[3],
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M[1]*v[0] + M[5]*v[1] + M[9]*v[2] + M[13]*v[3],
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M[2]*v[0] + M[6]*v[1] + M[10]*v[2] + M[14]*v[3],
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M[3]*v[0] + M[7]*v[1] + M[11]*v[2] + M[15]*v[3]
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];
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}
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function mat4Perspective(fovY, aspect, near, far)
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{
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const f = 1 / Math.tan(fovY * 0.5);
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const nf = 1 / (near - far);
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const M = new Float32Array(16);
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M[0] = f / aspect; M[4] = 0; M[8] = 0; M[12] = 0;
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M[1] = 0; M[5] = f; M[9] = 0; M[13] = 0;
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M[2] = 0; M[6] = 0; M[10] = (far + near) * nf; M[14] = (2 * far * near) * nf;
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M[3] = 0; M[7] = 0; M[11] = -1; M[15] = 0;
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return M;
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}
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function mat4LookAt(eye, target, up)
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{
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const z = normalize3(sub3(eye, target)); // forward (camera looks down -Z in view space)
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const x = normalize3(cross3(up, z)); // right
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const y = cross3(z, x); // true up
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const M = new Float32Array(16);
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M[0] = x.x; M[4] = x.y; M[8] = x.z; M[12] = -dot3(x, eye);
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M[1] = y.x; M[5] = y.y; M[9] = y.z; M[13] = -dot3(y, eye);
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M[2] = z.x; M[6] = z.y; M[10] = z.z; M[14] = -dot3(z, eye);
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M[3] = 0; M[7] = 0; M[11] = 0; M[15] = 1;
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return M;
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}
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// --- Vec3 helpers ---
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function scale3(v, s) { return { x: v.x * s, y: v.y * s, z: v.z * s}; }
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function sub3(a, b) { return { x: a.x - b.x, y: a.y - b.y, z: a.z - b.z }; }
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function dot3(a, b) { return a.x*b.x + a.y*b.y + a.z*b.z; }
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function cross3(a, b)
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{
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return {
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x: a.y*b.z - a.z*b.y,
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y: a.z*b.x - a.x*b.z,
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z: a.x*b.y - a.y*b.x
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};
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}
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function normalize3(v)
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{
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const len = Math.hypot(v.x, v.y, v.z) || 1;
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return { x: v.x / len, y: v.y / len, z: v.z / len };
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}
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function rotateVecY(v, angle)
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{
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const c = Math.cos(angle);
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const s = Math.sin(angle);
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return {
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x: v.x * c - v.z * s,
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y: v.y,
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z: v.x * s + v.z * c
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};
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}
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class Plane {
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constructor(position, normal) {
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Object.assign(this, { position, normal: normalize3(normal)} );
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}
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intersect_with(other) {
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const n1 = this.normal;
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const n2 = other.normal;
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// Direction of intersection line
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const dir = cross3(n1, n2);
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const dirLen2 = dot3(dir, dir);
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// Parallel (or nearly)
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if (dirLen2 < 1e-8)
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return null;
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// Plane constants: n·x + d = 0
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const d1 = -dot3(n1, this.position);
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const d2 = -dot3(n2, other.position);
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// Compute point on line
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// x = ( (d2*n1 - d1*n2) × dir ) / |dir|²
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const tmp = sub3(
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scale3(n1, d2),
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scale3(n2, d1)
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);
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const point = scale3(
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cross3(tmp, dir),
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1 / dirLen2
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);
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return {
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point, // point on the line
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direction: normalize3(dir)
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};
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};
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}
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function create_convex_hull() {
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const ph1 = performance.now()*0.007 % (Math.PI * 2);
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const ph2 = performance.now()*0.005 % (Math.PI * 2);
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const sides = [
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// Top
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new Plane({x:0, y:-2, z:0}, {x:0, y:-1, z:0}),
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new Plane({x:-2, y:0, z:0}, {x:-3, y:1, z:0}),
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new Plane({x: 2, y:0, z:0}, {x: 3, y:1, z:0}),
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new Plane({x:0, y:0, z:-2}, {x:0, y:1, z:-3}),
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new Plane({x:0, y:0, z: 2}, {x:0, y:1, z: 3}),
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// Bottom
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new Plane({x:0, y:2, z:0}, {x:Math.sin(ph1)*.2, y:1, z:Math.sin(ph2)*.2}),
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];
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const hull = [];
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const EPS = 1e-6;
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for (let i = 0; i < sides.length - 1; i++) {
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for (let j = i + 1; j < sides.length; j++) {
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const line = sides[i].intersect_with(sides[j]);
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if (!line) continue;
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let tMin = -Infinity;
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let tMax = +Infinity;
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for (let k = 0; k < sides.length; k++) {
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if (k === i || k === j) continue;
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const pl = sides[k];
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// inside: dot(n, x - p0) <= 0
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const a = dot3(pl.normal, line.direction);
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const c = dot3(pl.normal, sub3(line.point, pl.position));
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// Parallel to plane
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if (Math.abs(a) < EPS) {
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if (c > 0) { // entirely outside
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tMin = 1;
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tMax = 0;
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break;
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}
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continue;
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}
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const tHit = -c / a;
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if (a > 0) {
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// t <= tHit
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if (tHit < tMax) tMax = tHit;
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} else {
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// t >= tHit
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if (tHit > tMin) tMin = tHit;
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}
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if (tMin > tMax) break;
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}
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if (tMin <= tMax) {
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const p0 = {
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x: line.point.x + line.direction.x * tMin,
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y: line.point.y + line.direction.y * tMin,
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z: line.point.z + line.direction.z * tMin
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};
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const p1 = {
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x: line.point.x + line.direction.x * tMax,
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y: line.point.y + line.direction.y * tMax,
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z: line.point.z + line.direction.z * tMax
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};
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hull.push([p0, p1]);
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}
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}
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}
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return hull;
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}
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function demo_convex_hull() {
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const hull = create_convex_hull();
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const eye = rotateVecY({x:0,y:2,z:10}, performance.now()*0.001 % (Math.PI * 2));
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C.clearRect(0, 0, W, H);
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renderFrustumPolylines(
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C,
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hull,
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{
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eye,
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target:{x:0,y:0,z:0},
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up:{x:0,y:1,z:0},
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fovY:Math.PI/4,
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aspect:canvas.width/canvas.height,
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near:0.1,
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far:100
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},
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{ x:0, y:0, w:canvas.width, h:canvas.height }
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);
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window.requestAnimationFrame(demo_convex_hull);
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}
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window.requestAnimationFrame(demo_convex_hull);
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