Cubic B-spline から ベジエの制御点に変換

cubicBSpline.ts

export function cubicBSpline(P0: Point, P1: Point, P2: Point, P3: Point): [Point, Point, Point, Point] {
  const x0 = (P0[0] + 4 * P1[0] + P2[0]) / 6;
  const y0 = (P0[1] + 4 * P1[1] + P2[1]) / 6;

  const x1 = (2 * P1[0] + P2[0]) / 3;
  const y1 = (2 * P1[1] + P2[1]) / 3;

  const x2 = (P1[0] + 2 * P2[0]) / 3;
  const y2 = (P1[1] + 2 * P2[1]) / 3;

  const x3 = (P1[0] + 4 * P2[0] + P3[0]) / 6;
  const y3 = (P1[1] + 4 * P2[1] + P3[1]) / 6;

  return [
    [x0, y0],
    [x1, y1],
    [x2, y2],
    [x3, y3],
  ];
}