geometricNormal.js

import { vec3 } from 'gl-matrix';

/*
  Construct a [ position, normal ] from parametric function and (u, v) coordinate.
  Reference: ThreeJS.
*/

export function geometricNormal(fn, u, v) {
  const EPS = 0.00001;
  const pu = [];
  const pv = [];
  const p0 = fn(u, v);
  if (u - EPS >= 0) {
    const p1 = fn(u - EPS, v);
    vec3.sub(pu, p0, p1);
  } else {
    const p1 = fn(u + EPS, v);
    vec3.sub(pu, p1, p0);
  }
  if (v - EPS >= 0) {
    const p1 = fn(u, v - EPS);
    vec3.sub(pv, p0, p1);
  } else {
    const p1 = fn(u, v + EPS);
    vec3.sub(pv, p1, p0);
  }

  // cross product of tangent vectors returns surface normal
  const normal = vec3.cross([], pu, pv);
  vec3.normalize(normal, normal);
  vec3.normalize(pu, pu);
  vec3.normalize(pv, pv);
  return [p0, normal];
}