@thi.ng/geom-arc/from-endpoints.js

2D circular / elliptic arc operations

import { EPS, TAU } from "@thi.ng/math/api";
import { abs2 } from "@thi.ng/vectors/abs";
import { angleBetween2 } from "@thi.ng/vectors/angle-between";
import { X2 } from "@thi.ng/vectors/api";
import { div2 } from "@thi.ng/vectors/div";
import { eqDelta2 } from "@thi.ng/vectors/eqdelta";
import { mulN2 } from "@thi.ng/vectors/muln";
import { neg } from "@thi.ng/vectors/neg";
import { powN2 } from "@thi.ng/vectors/pown";
import { sub2 } from "@thi.ng/vectors/sub";
import { submN2 } from "@thi.ng/vectors/submn";
const fromEndPoints = (a, b, radii, axis = 0, xl = false, cw = false) => {
  const r = abs2([], radii);
  if (eqDelta2(a, b) || r[0] < EPS || r[1] < EPS) {
    return;
  }
  axis %= TAU;
  const d = submN2([], a, b, 0.5);
  const c = Math.cos(axis);
  const s = Math.sin(axis);
  const tp = [c * d[0] + s * d[1], -s * d[0] + c * d[1]];
  const [tx2, ty2] = powN2([], tp, 2);
  const rc = tx2 / (r[0] * r[0]) + ty2 / (r[1] * r[1]);
  rc > 1 && mulN2(r, r, Math.sqrt(rc));
  const [rx, ry] = r;
  const rx2 = rx * rx;
  const ry2 = ry * ry;
  const radicant = Math.max(
    0,
    (rx2 * ry2 - rx2 * ty2 - ry2 * tx2) / (rx2 * ty2 + ry2 * tx2)
  );
  const coeff = (xl !== cw ? 1 : -1) * Math.sqrt(radicant);
  const tc = [coeff * (rx * tp[1] / ry), coeff * (-(ry * tp[0]) / rx)];
  const center = [
    c * tc[0] - s * tc[1] + (a[0] + b[0]) / 2,
    s * tc[0] + c * tc[1] + (a[1] + b[1]) / 2
  ];
  const ta = div2(null, sub2([], tp, tc), r);
  const tb = div2(null, sub2(null, neg([], tp), tc), r);
  const start = angleBetween2(X2, ta);
  let sweep = angleBetween2(ta, tb);
  if (!cw && sweep > 0) {
    sweep -= TAU;
  } else if (cw && sweep < 0) {
    sweep += TAU;
  }
  sweep %= TAU;
  return {
    center,
    r,
    axis,
    start,
    end: start + sweep,
    xl,
    cw
  };
};
export {
  fromEndPoints
};