@thi.ng/geom-splines/cubic-from-breakpoints.js

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

import { cornerBisector } from "@thi.ng/vectors/bisect";
import { corner2 } from "@thi.ng/vectors/clockwise";
import { direction2 } from "@thi.ng/vectors/direction";
import { dist2 } from "@thi.ng/vectors/dist";
import { maddN2 } from "@thi.ng/vectors/maddn";
import { mulN, mulN2 } from "@thi.ng/vectors/muln";
import { perpendicularCW } from "@thi.ng/vectors/perpendicular";
import { set2 } from "@thi.ng/vectors/set";
const __buildSegments = (tangents, t, uniform) => {
  const res = [];
  for (let i = 0, num = tangents.length - 1; i < num; i++) {
    const [a, na] = tangents[i];
    const [b, nb] = tangents[i + 1];
    const d = uniform ? t : t * dist2(a, b);
    res.push([a, maddN2([], na, d, a), maddN2([], nb, -d, b), b]);
  }
  return res;
};
const closedCubicFromBreakPoints = (points, t = 1 / 3, uniform = false) => {
  const tangents = [];
  for (let num = points.length, i = num - 1, j = 0; j < num; i = j, j++) {
    const a = points[i];
    const b = points[j];
    const c = points[(j + 1) % num];
    const n = mulN(
      null,
      perpendicularCW(null, cornerBisector([], a, b, c)),
      corner2(a, b, c)
    );
    tangents.push([set2([], b), n]);
  }
  tangents.push(tangents[0]);
  return __buildSegments(tangents, t, uniform);
};
const openCubicFromBreakPoints = (points, t = 1 / 3, uniform = false) => {
  const tangents = [
    [points[0], direction2([], points[0], points[1])]
  ];
  const num = points.length - 1;
  for (let i = 1; i < num; i++) {
    const a = points[i - 1];
    const b = points[i];
    const c = points[i + 1];
    const n = mulN2(
      null,
      perpendicularCW(null, cornerBisector([], a, b, c)),
      corner2(a, b, c)
    );
    tangents.push([set2([], b), n]);
  }
  tangents.push([points[num], direction2([], points[num - 1], points[num])]);
  return __buildSegments(tangents, t, uniform);
};
export {
  closedCubicFromBreakPoints,
  openCubicFromBreakPoints
};