public/math/reference.mjs

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1// Teaching examples for OTHER representations. Not called by the STG-Lite pass.
2// Inputs use ordinary arrays and double precision; no model/checkpoint loader.
3function normalize(v) {
4  const length = Math.hypot(...v);
5  if (!(length > 0)) throw new Error('Cannot normalize a zero vector');
6  return v.map(x => x / length);
7}
8
9export function decodeDeformation(base, deltaPosition, deltaLogScale, deltaQuaternion) {
10  // Example choice of heads; not a claim about every deformation implementation.
11  return {
12    position: base.position.map((v, i) => v + deltaPosition[i]),
13    scale: base.logScale.map((v, i) => Math.exp(v + deltaLogScale[i])),
14    quaternion: normalize(base.quaternion.map((v, i) => v + deltaQuaternion[i])),
15  };
16}
17
18export function condition4D(meanSpace, meanTime, A, b, c, time) {
19  if (!(c > 0)) throw new Error('Time variance must be positive');
20  // Caller supplies a positive-definite joint covariance.
21  const dt = time - meanTime;
22  return {
23    mean: meanSpace.map((v, i) => v + b[i] * dt / c),
24    covariance: A.map((row, i) => row.map((v, j) => v - b[i] * b[j] / c)),
25    timeWeight: Math.exp(-0.5 * dt * dt / c),
26  };
27}
28
29export function evaluateSH1(coefficients, direction) {
30  // Four RGB coefficients, Graphdeco real-SH signs/order. Raw sum, no +0.5/clamp.
31  const [x, y, z] = normalize(direction);
32  const c0 = 1 / Math.sqrt(4 * Math.PI);
33  const c1 = Math.sqrt(3 / (4 * Math.PI));
34  const basis = [c0, -c1 * y, c1 * z, -c1 * x];
35  return [0, 1, 2].map(channel =>
36    basis.reduce((sum, value, index) => sum + value * coefficients[index][channel], 0));
37}
38
39export function compositeFeatures(alphas, features, background) {
40  // Near to far; any feature dimension, including ordinary RGB.
41  const result = background.map(() => 0);
42  let transmittance = 1;
43  for (let i = 0; i < alphas.length; i++) {
44    for (let d = 0; d < result.length; d++) {
45      result[d] += transmittance * alphas[i] * features[i][d];
46    }
47    transmittance *= 1 - alphas[i];
48  }
49  return result.map((v, d) => v + transmittance * background[d]);
50}
51