trainsim/math/path.ts

import { Vector } from "doodler";

export class ComplexPath {

  points: Vector[] = [];

  radius = 50;

  ctx?: CanvasRenderingContext2D;

  constructor(points?: Vector[]) {
    points && (this.points = points);
  }

  setContext(ctx: CanvasRenderingContext2D) {
    this.ctx = ctx;
  }

  draw() {
    if (!this.ctx || !this.points.length) return;
    const ctx = this.ctx;

    ctx.save();
    ctx.lineWidth = 2;
    ctx.strokeStyle = 'white';
    ctx.setLineDash([21, 6])

    let last = this.points[this.points.length - 1]

    for (const point of this.points) {
      ctx.beginPath();
      ctx.moveTo(last.x, last.y);
      ctx.lineTo(point.x, point.y);
      ctx.stroke();
      last = point;
    }
    ctx.restore();
  }
}

export class PathSegment {
  points: [Vector, Vector, Vector, Vector]
  ctx?: CanvasRenderingContext2D;

  length: number;

  constructor(points: [Vector, Vector, Vector, Vector]) {
    this.points = points;
    this.length = this.calculateApproxLength(100);
  }

  setContext(ctx: CanvasRenderingContext2D) {
    this.ctx = ctx;
  }

  draw() {
    const [a, b, c, d] = this.points;
    doodler.drawBezier(a, b, c, d, {
      strokeColor: '#ffffff50'
    })
    // if (!this.ctx) return;
    // const ctx = this.ctx;

    // ctx.save();
    // ctx.beginPath();
    // ctx.moveTo(this.points[0].x, this.points[0].y);

    // ctx.bezierCurveTo(
    //   this.points[1].x,
    //   this.points[1].y,
    //   this.points[2].x,
    //   this.points[2].y,
    //   this.points[3].x,
    //   this.points[3].y,
    // );

    // ctx.strokeStyle = '#ffffff50';
    // ctx.lineWidth = 2;
    // ctx.stroke();
    // ctx.restore();
  }

  getPointAtT(t: number) {
    const [a, b, c, d] = this.points;
    const res = a.copy();

    res.add(Vector.add(a.copy().mult(-3), b.copy().mult(3)).mult(t))
    res.add(Vector.add(Vector.add(a.copy().mult(3), b.copy().mult(-6)), c.copy().mult(3)).mult(Math.pow(t, 2)));
    res.add(Vector.add(Vector.add(a.copy().mult(-1), b.copy().mult(3)), Vector.add(c.copy().mult(-3), d.copy())).mult(Math.pow(t, 3)));

    return res;
  }

  getClosestPoint(v: Vector): [Vector, number, number] {
    const samples = 25;
    const resolution = 1 / samples;
    let closest = this.points[0];
    let closestDistance = this.points[0].dist(v);
    let closestT = 0;

    for (let i = 0; i < samples; i++) {
      const point = this.getPointAtT(i * resolution);
      const distance = v.dist(point);
      if (distance < closestDistance) {
        closest = point;
        closestDistance = distance;
        closestT = i * resolution;
      }
    }

    return [closest, closestDistance, closestT];
  }

  getPointsWithinRadius(v: Vector, r: number) {
    const points: [number, PathSegment][] = [];
    const samples = 25;
    const resolution = 1 / samples;

    for (let i = 0; i < samples; i++) {
      const point = this.getPointAtT(i * resolution);
      const distance = v.dist(point);
      if (distance < r) {
        points.push([i * resolution, this]);
      }
    }
    return points
  }

  tangent(t: number) {
    // dP(t) / dt =  -3(1-t)^2 * P0 + 3(1-t)^2 * P1 - 6t(1-t) * P1 - 3t^2 * P2 + 6t(1-t) * P2 + 3t^2 * P3 
    const [a, b, c, d] = this.points;

    const res = Vector.sub(b, a).mult(3 * Math.pow(1 - t, 2));
    res.add(Vector.add(Vector.sub(c, b).mult(6 * (1 - t) * t), Vector.sub(d, c).mult(3 * Math.pow(t, 2))));

    return res;
  }

  doesIntersectCircle(x: number, y: number, r: number) {
    const v = new Vector(x, y);
    const samples = 25;
    const resolution = 1 / samples;

    let distance = Infinity;
    let t;

    for (let i = 0; i < samples; i++) {
      if (i !== samples - 1) {
        const a = this.getPointAtT(i * resolution);
        const b = this.getPointAtT((i + 1) * resolution);
        const ac = Vector.sub(v, a);
        const ab = Vector.sub(b, a);

        const d = Vector.add(Vector.vectorProjection(ac, ab), a);
        const ad = Vector.sub(d, a);

        const k = Math.abs(ab.x) > Math.abs(ab.y) ? ad.x / ab.x : ad.y / ab.y;

        let dist;
        if (k <= 0.0) {
          dist = Vector.hypot2(v, a)
        } else if (k >= 1.0) {
          dist = Vector.hypot2(v, b)
        }

        dist = Vector.hypot2(v, d)

        if (dist < distance) {
          distance = dist;
          t = i * resolution;
        }
      }
    }

    if (distance < r) return t;

    return false;
  }

  calculateApproxLength(resolution = 25) {
    const stepSize = 1 / resolution;
    const points: Vector[] = []
    for (let i = 0; i <= resolution; i++) {
      const current = stepSize * i;
      points.push(this.getPointAtT(current))
    }
    return points.reduce((acc: { prev?: Vector, length: number }, cur) => {
      const prev = acc.prev;
      acc.prev = cur;
      if (!prev) return acc;
      acc.length += cur.dist(prev);
      return acc;
    }, { prev: undefined, length: 0 }).length
  }

  calculateEvenlySpacedPoints(spacing: number, resolution = 1) {
    const points: Vector[] = []

    points.push(this.points[0]);
    let prev = points[0];
    let distSinceLastEvenPoint = 0

    let t = 0;

    const div = Math.ceil(this.length * resolution * 10);
    while (t < 1) {
      t += 1 / div;
      const point = this.getPointAtT(t);
      distSinceLastEvenPoint += prev.dist(point);


      if (distSinceLastEvenPoint >= spacing) {
        const overshoot = distSinceLastEvenPoint - spacing;
        const evenPoint = Vector.add(point, Vector.sub(point, prev).normalize().mult(overshoot))
        distSinceLastEvenPoint = overshoot;
        points.push(evenPoint);
        prev = evenPoint;
      }

      prev = point;
    }

    return points;
  }
}