yawn/server/web/assets/sculpt/mesh.js

import { unit } from "./math.js";

export function sphere(level = 5) {
  if (!Number.isInteger(level) || level < 4 || level > 6)
    throw new Error("Choose a supported resolution.");
  const t = (1 + Math.sqrt(5)) / 2;
  const vertices = [
    [-1, t, 0],
    [1, t, 0],
    [-1, -t, 0],
    [1, -t, 0],
    [0, -1, t],
    [0, 1, t],
    [0, -1, -t],
    [0, 1, -t],
    [t, 0, -1],
    [t, 0, 1],
    [-t, 0, -1],
    [-t, 0, 1],
  ].map(unit);
  let faces = [
    [0, 11, 5],
    [0, 5, 1],
    [0, 1, 7],
    [0, 7, 10],
    [0, 10, 11],
    [1, 5, 9],
    [5, 11, 4],
    [11, 10, 2],
    [10, 7, 6],
    [7, 1, 8],
    [3, 9, 4],
    [3, 4, 2],
    [3, 2, 6],
    [3, 6, 8],
    [3, 8, 9],
    [4, 9, 5],
    [2, 4, 11],
    [6, 2, 10],
    [8, 6, 7],
    [9, 8, 1],
  ];
  for (let l = 0; l < level; l++) {
    const cache = new Map();
    const midpoint = (a, b) => {
      const key = Math.min(a, b) * 100000 + Math.max(a, b);
      if (!cache.has(key)) {
        cache.set(key, vertices.length);
        vertices.push(unit(vertices[a].map((v, i) => v + vertices[b][i])));
      }
      return cache.get(key);
    };
    faces = faces.flatMap(([a, b, c]) => {
      const ab = midpoint(a, b),
        bc = midpoint(b, c),
        ca = midpoint(c, a);
      return [
        [a, ab, ca],
        [b, bc, ab],
        [c, ca, bc],
        [ab, bc, ca],
      ];
    });
  }
  const positions = new Float32Array(vertices.flat());
  const indices = new Uint32Array(faces.flat());
  const incident = Array.from({ length: vertices.length }, () => []);
  const neighbors = Array.from({ length: vertices.length }, () => new Set());
  faces.forEach((face, f) =>
    face.forEach((v) => {
      incident[v].push(f);
      for (const other of face) if (other !== v) neighbors[v].add(other);
    }),
  );
  const mesh = {
    level,
    positions,
    indices,
    normals: new Float32Array(positions.length),
    faceNormals: new Float32Array(indices.length),
    incident: incident.map((a) => Uint32Array.from(a)),
    neighbors: neighbors.map((a) => Uint32Array.from(a)),
  };
  mesh.faceMarks = new Uint32Array(faces.length);
  mesh.vertexMarks = new Uint32Array(vertices.length);
  mesh.generation = 0;
  updateNormals(mesh);
  return mesh;
}

// Include the unchanged incident faces when recomputing a boundary vertex normal.
export function updateNormals(mesh, moved) {
  const { positions: p, indices: idx, normals: n, faceNormals: fn } = mesh;
  const faces = [],
    vertices = [];
  const gen = ++mesh.generation;
  if (moved) {
    for (const v of moved)
      for (const f of mesh.incident[v]) {
        if (mesh.faceMarks[f] !== gen) {
          mesh.faceMarks[f] = gen;
          faces.push(f);
        }
      }
  } else for (let f = 0; f < idx.length / 3; f++) faces.push(f);
  for (const f of faces) {
    const a = idx[f * 3],
      b = idx[f * 3 + 1],
      c = idx[f * 3 + 2];
    const ax = p[b * 3] - p[a * 3],
      ay = p[b * 3 + 1] - p[a * 3 + 1],
      az = p[b * 3 + 2] - p[a * 3 + 2];
    const bx = p[c * 3] - p[a * 3],
      by = p[c * 3 + 1] - p[a * 3 + 1],
      bz = p[c * 3 + 2] - p[a * 3 + 2];
    fn[f * 3] = ay * bz - az * by;
    fn[f * 3 + 1] = az * bx - ax * bz;
    fn[f * 3 + 2] = ax * by - ay * bx;
    for (let j = 0; j < 3; j++) {
      const v = idx[f * 3 + j];
      if (mesh.vertexMarks[v] !== gen) {
        mesh.vertexMarks[v] = gen;
        vertices.push(v);
      }
    }
  }
  for (const v of vertices) {
    let x = 0,
      y = 0,
      z = 0;
    for (const f of mesh.incident[v]) {
      x += fn[f * 3];
      y += fn[f * 3 + 1];
      z += fn[f * 3 + 2];
    }
    const length = Math.hypot(x, y, z) || 1;
    n[v * 3] = x / length;
    n[v * 3 + 1] = y / length;
    n[v * 3 + 2] = z / length;
  }
  return { faces, vertices };
}