Engineer at Mapbox, creator of Leaflet, algorithms geek, open source enthusiast, musician, father of twin girls, Ukrainian. 🇺🇦
Published
Edited
Sep 24, 2019
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When Does the Barbell Tip Over?One-Rep Max Formulas ShowdownKinematics of Reverse Angle Parking3D planets with Three.jsUV-mapping an icosphereCollatz conjecture (3x + 1)Chroma Key CompositingHilbert Curve PackingDrawing logarithmic spiralsApproximating Geometric SlerpPixelmatch DemoMARTINI: Real-Time RTIN Terrain MeshRobust Arithmetic in Computational Geometry
Fast Icosphere Mesh
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Algorithms & Math
icosphere = (order = 0) => {
// set up a 20-triangle icosahedron
const f = (1 + 5 ** 0.5) / 2;
const T = 4 ** order;
const vertices = new Float32Array((10 * T + 2) * 3);
vertices.set(Float32Array.of(
-1, f, 0, 1, f, 0, -1, -f, 0, 1, -f, 0,
0, -1, f, 0, 1, f, 0, -1, -f, 0, 1, -f,
f, 0, -1, f, 0, 1, -f, 0, -1, -f, 0, 1));
let triangles = Uint32Array.of(
0, 11, 5, 0, 5, 1, 0, 1, 7, 0, 7, 10, 0, 10, 11,
11, 10, 2, 5, 11, 4, 1, 5, 9, 7, 1, 8, 10, 7, 6,
3, 9, 4, 3, 4, 2, 3, 2, 6, 3, 6, 8, 3, 8, 9,
9, 8, 1, 4, 9, 5, 2, 4, 11, 6, 2, 10, 8, 6, 7);
let v = 12;
const midCache = order ? new Map() : null; // midpoint vertices cache to avoid duplicating shared vertices
function addMidPoint(a, b) {
const key = Math.floor((a + b) * (a + b + 1) / 2) + Math.min(a, b); // Cantor's pairing function
let i = midCache.get(key);
if (i !== undefined) { midCache.delete(key); return i; }
midCache.set(key, v);
for (let k = 0; k < 3; k++) vertices[3 * v + k] = (vertices[3 * a + k] + vertices[3 * b + k]) / 2;
i = v++;
return i;
}
let trianglesPrev = triangles;
for (let i = 0; i < order; i++) {
// subdivide each triangle into 4 triangles
triangles = new Uint32Array(trianglesPrev.length * 4);
for (let k = 0; k < trianglesPrev.length; k += 3) {
const v1 = trianglesPrev[k + 0];
const v2 = trianglesPrev[k + 1];
const v3 = trianglesPrev[k + 2];
const a = addMidPoint(v1, v2);
const b = addMidPoint(v2, v3);
const c = addMidPoint(v3, v1);
let t = k * 4;
triangles[t++] = v1; triangles[t++] = a; triangles[t++] = c;
triangles[t++] = v2; triangles[t++] = b; triangles[t++] = a;
triangles[t++] = v3; triangles[t++] = c; triangles[t++] = b;
triangles[t++] = a; triangles[t++] = b; triangles[t++] = c;
}
trianglesPrev = triangles;
}
// normalize vertices
for (let i = 0; i < vertices.length; i += 3) {
const m = 1 / Math.hypot(vertices[i + 0], vertices[i + 1], vertices[i + 2]);
vertices[i + 0] *= m;
vertices[i + 1] *= m;
vertices[i + 2] *= m;
}
return {vertices, triangles};
}
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