@thi.ng/geom-splines/cubic-hobby.js

nD cubic & quadratic curve analysis, conversion, interpolation, splitting

import { THIRD, TWO_THIRD } from "@thi.ng/math/api";
import { solveTridiagonal } from "@thi.ng/math/solve";
import {
  angleBetween2,
  mag2
} from "@thi.ng/vectors";
import { add2 } from "@thi.ng/vectors/add";
import { normalize2 } from "@thi.ng/vectors/normalize";
import { rotate } from "@thi.ng/vectors/rotate";
import { sub2 } from "@thi.ng/vectors/sub";
import { set2 } from "@thi.ng/vectors/set";
const cubicHobby2 = (points, closed = false, omega = 1) => {
  const nump = points.length;
  if (closed) {
    points = points.slice(nump - 3).concat(points, points.slice(0, 3));
  }
  const n = points.length - 1;
  const chords = new Array(n);
  const d = new Array(n);
  const alpha = new Array(n + 1);
  const gamma = new Array(n + 1);
  const A = new Array(n + 1);
  const B = new Array(n + 1);
  const C = new Array(n + 1);
  for (let i = 0; i < n; i++) {
    const delta = chords[i] = sub2([], points[i + 1], points[i]);
    d[i] = mag2(delta);
    i > 0 && (gamma[i] = angleBetween2(chords[i - 1], delta));
  }
  B[0] = B[n] = 2 + omega;
  C[0] = A[n] = 2 * omega + 1;
  alpha[0] = -C[0] * gamma[1];
  alpha[n] = gamma[n] = 0;
  for (let i = 1; i < n; i++) {
    const dprev = d[i - 1];
    const dcurr = d[i];
    const invD = 1 / (dprev * dcurr);
    A[i] = 1 / dprev;
    B[i] = (2 * dprev + 2 * dcurr) * invD;
    C[i] = 1 / dcurr;
    alpha[i] = -(2 * gamma[i] * dcurr + gamma[i + 1] * dprev) * invD;
  }
  solveTridiagonal(A, B, C, alpha);
  const res = [];
  const [from, to] = closed ? [3, 3 + nump] : [0, n];
  for (let i = from; i < to; i++) {
    const a = alpha[i];
    const b = i < n - 1 ? -gamma[i + 1] - alpha[i + 1] : -alpha[n];
    const c = chords[i];
    const cosA = Math.cos(a);
    const cosB = Math.cos(b);
    const scale = TWO_THIRD * d[i];
    res.push([
      set2([], points[i]),
      add2(
        null,
        normalize2(null, rotate([], c, a), __rho(cosA, cosB, scale)),
        points[i]
      ),
      add2(
        null,
        // reuse chord vector for result to avoid extraneous allocation
        normalize2(
          null,
          rotate(null, c, -b),
          -__rho(cosB, cosA, scale)
        ),
        points[i + 1]
      ),
      set2([], points[i + 1])
    ]);
  }
  return res;
};
const __rho = (cosA, cosB, scale) => scale / (1 + THIRD * cosA + TWO_THIRD * cosB);
export {
  cubicHobby2
};