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

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

import { pointAtTheta } from "@thi.ng/geom-arc/point-at";
import { sincos } from "@thi.ng/math/angle";
import { EPS, HALF_PI, PI } from "@thi.ng/math/api";
import { roundEps } from "@thi.ng/math/prec";
import { magSq2 } from "@thi.ng/vectors/magsq";
import { cubicFromLine } from "./cubic-line.js";
const cubicFromArc = (pos, r, axis, start, end) => {
  const p = pointAtTheta(pos, r, axis, start);
  const q = pointAtTheta(pos, r, axis, end);
  const delta = end - start;
  const [rx, ry] = r;
  const [s, c] = sincos(axis);
  const dx = c * (p[0] - q[0]) / 2 + s * (p[1] - q[1]) / 2;
  const dy = -s * (p[0] - q[0]) / 2 + c * (p[1] - q[1]) / 2;
  if (Math.abs(delta) < PI && dx === 0 && dy === 0 || magSq2(r) < EPS) {
    return [cubicFromLine(p, q)];
  }
  const mapP = (x, y) => {
    x *= rx;
    y *= ry;
    return [c * x - s * y + pos[0], s * x + c * y + pos[1]];
  };
  const res = [];
  const n = Math.ceil(roundEps(Math.abs(delta) / HALF_PI, 1e-3));
  const d = delta / n;
  const t = 8 / 6 * Math.tan(0.25 * d);
  if (!isFinite(t)) {
    return [cubicFromLine(p, q)];
  }
  for (let i = n, theta = start, sc = sincos(theta); i > 0; i--, theta += d) {
    const [s1, c1] = sc;
    const [s2, c2] = sc = sincos(theta + d);
    res.push([
      mapP(c1, s1),
      mapP(c1 - s1 * t, s1 + c1 * t),
      mapP(c2 + s2 * t, s2 - c2 * t),
      mapP(c2, s2)
    ]);
  }
  return res;
};
export {
  cubicFromArc
};