upstream-affine/blocksuite/affine/blocks/surface/src/utils/points-on-curve/index.ts

import type { Point } from '../rough/geometry.js';

// distance between 2 points
function distance(p1: Point, p2: Point): number {
  return Math.sqrt(distanceSq(p1, p2));
}

// distance between 2 points squared
function distanceSq(p1: Point, p2: Point): number {
  return Math.pow(p1[0] - p2[0], 2) + Math.pow(p1[1] - p2[1], 2);
}

// Sistance squared from a point p to the line segment vw
function distanceToSegmentSq(p: Point, v: Point, w: Point): number {
  const l2 = distanceSq(v, w);
  if (l2 === 0) {
    return distanceSq(p, v);
  }
  let t = ((p[0] - v[0]) * (w[0] - v[0]) + (p[1] - v[1]) * (w[1] - v[1])) / l2;
  t = Math.max(0, Math.min(1, t));
  return distanceSq(p, lerp(v, w, t));
}

function lerp(a: Point, b: Point, t: number): Point {
  return [a[0] + (b[0] - a[0]) * t, a[1] + (b[1] - a[1]) * t];
}

// Adapted from https://seant23.wordpress.com/2010/11/12/offset-bezier-curves/
function flatness(points: readonly Point[], offset: number): number {
  const p1 = points[offset + 0];
  const p2 = points[offset + 1];
  const p3 = points[offset + 2];
  const p4 = points[offset + 3];

  let ux = 3 * p2[0] - 2 * p1[0] - p4[0];
  ux *= ux;
  let uy = 3 * p2[1] - 2 * p1[1] - p4[1];
  uy *= uy;
  let vx = 3 * p3[0] - 2 * p4[0] - p1[0];
  vx *= vx;
  let vy = 3 * p3[1] - 2 * p4[1] - p1[1];
  vy *= vy;

  if (ux < vx) {
    ux = vx;
  }

  if (uy < vy) {
    uy = vy;
  }

  return ux + uy;
}

function getPointsOnBezierCurveWithSplitting(
  points: readonly Point[],
  offset: number,
  tolerance: number,
  newPoints?: Point[]
): Point[] {
  const outPoints = newPoints || [];
  if (flatness(points, offset) < tolerance) {
    const p0 = points[offset + 0];
    if (outPoints.length) {
      const d = distance(outPoints[outPoints.length - 1], p0);
      if (d > 1) {
        outPoints.push(p0);
      }
    } else {
      outPoints.push(p0);
    }
    outPoints.push(points[offset + 3]);
  } else {
    // subdivide
    const t = 0.5;
    const p1 = points[offset + 0];
    const p2 = points[offset + 1];
    const p3 = points[offset + 2];
    const p4 = points[offset + 3];

    const q1 = lerp(p1, p2, t);
    const q2 = lerp(p2, p3, t);
    const q3 = lerp(p3, p4, t);

    const r1 = lerp(q1, q2, t);
    const r2 = lerp(q2, q3, t);

    const red = lerp(r1, r2, t);

    getPointsOnBezierCurveWithSplitting(
      [p1, q1, r1, red],
      0,
      tolerance,
      outPoints
    );
    getPointsOnBezierCurveWithSplitting(
      [red, r2, q3, p4],
      0,
      tolerance,
      outPoints
    );
  }
  return outPoints;
}

export function simplify(points: readonly Point[], distance: number): Point[] {
  return simplifyPoints(points, 0, points.length, distance);
}

// Ramer–Douglas–Peucker algorithm
// https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm
function simplifyPoints(
  points: readonly Point[],
  start: number,
  end: number,
  epsilon: number,
  newPoints?: Point[]
): Point[] {
  const outPoints = newPoints || [];

  // find the most distance point from the endpoints
  const s = points[start];
  const e = points[end - 1];
  let maxDistSq = 0;
  let maxNdx = 1;
  for (let i = start + 1; i < end - 1; ++i) {
    const distSq = distanceToSegmentSq(points[i], s, e);
    if (distSq > maxDistSq) {
      maxDistSq = distSq;
      maxNdx = i;
    }
  }

  // if that point is too far, split
  if (Math.sqrt(maxDistSq) > epsilon) {
    simplifyPoints(points, start, maxNdx + 1, epsilon, outPoints);
    simplifyPoints(points, maxNdx, end, epsilon, outPoints);
  } else {
    if (!outPoints.length) {
      outPoints.push(s);
    }
    outPoints.push(e);
  }

  return outPoints;
}

export function pointsOnBezierCurves(
  points: Point[],
  tolerance = 0.15,
  distance?: number
): Point[] {
  const newPoints: Point[] = [];
  const numSegments = (points.length - 1) / 3;
  for (let i = 0; i < numSegments; i++) {
    const offset = i * 3;
    getPointsOnBezierCurveWithSplitting(points, offset, tolerance, newPoints);
  }
  if (distance && distance > 0) {
    return simplifyPoints(newPoints, 0, newPoints.length, distance);
  }
  return newPoints;
}