traffic-laser/src/graphic/Util/MathUtil.js

import Constant from "../Constant";
import bezierUtil from "./bezierUtil.js";

export default class MathUtil {
  constructor() {}

  getFixed(num, decimal) {
    if (!decimal) {
      decimal = 5;
    }
    // return Math.floor(num * 10000) / 10000;
    return parseFloat(num.toFixed(decimal));
  }

  // 求两个点的距离
  getDistance(p1, p2) {
    const x1 = p1.x;
    const y1 = p1.y;
    const x2 = p2.x;
    const y2 = p2.y;
    const num = Math.sqrt(Math.pow(x1 - x2, 2) + Math.pow(y1 - y2, 2));
    return this.getFixed(num);
  }

  createLine1(point1, point2) {
    if (point1.x == point2.x && point1.y == point2.y) {
      return null;
    } else if (this.getFixed(Math.abs(point1.x - point2.x)) == 0) {
      return { x: point1.x };
    } else if (this.getFixed(Math.abs(point1.y - point2.y)) == 0) {
      return { y: point1.y };
    }

    const parametera = (point1.y - point2.y) / (point1.x - point2.x);
    const parameterb =
      (point1.x * point2.y - point2.x * point1.y) / (point1.x - point2.x);
    if (this.getFixed(parametera) == 0) {
      return { y: this.getFixed(parameterb) };
    }
    const parameter = {
      a: this.getFixed(parametera),
      b: this.getFixed(parameterb),
    };
    return parameter;
  }

  createLine2(point, angle) {
    if (angle == 90 || angle == 270) {
      return { x: point.x };
    }
    let a = Math.tan((angle / 180) * Math.PI);
    let b = point.y - a * point.x;
    if (a != 0) {
      return { a: a, b: b };
    } else {
      return { y: point.y };
    }
  }

  // 与lineA平行并且point在线上
  createLine3(lineA, point) {
    const parameter = {};
    if (typeof lineA.a === "undefined") {
      if (typeof lineA.x !== "undefined") {
        parameter.x = point.x;
      } else if (typeof lineA.y !== "undefined") {
        parameter.y = point.y;
      }
    } else {
      parameter.a = lineA.a;
      parameter.b = point.y - point.x * lineA.a;
    }
    return parameter;
  }

  create2AngleLine(point, angle, driftAngle) {
    let line1 = this.createLine2(point, angle - driftAngle / 2);
    let line2 = this.createLine2(point, angle + driftAngle / 2);
    return { line1: line1, line2: line2 };
  }

  distanceForPoints(point1, point2) {
    return Math.sqrt(
      Math.pow(point1.x - point2.x, 2) + Math.pow(point1.y - point2.y, 2)
    );
  }

  //与line平行且两条线直接的距离是distance的两条线
  getParallelLineForDistance(line, distance) {
    let line1 = {};
    let line2 = {};
    if (!line.hasOwnProperty("a")) {
      if (line.hasOwnProperty("x")) {
        let x = line.x;
        line1.x = x + distance;
        line2.x = x - distance;
      } else if (line.hasOwnProperty("y")) {
        let y = line.y;
        line1.y = y + distance;
        line2.y = y - distance;
      }
    } else {
      line1.a = line.a;
      line1.b = line.b;

      line2.a = line.a;
      line2.b = line.b;

      let angle = Math.atan(line.a);
      let db = Math.abs(distance / Math.cos(angle));
      let b = line.b;
      line1.b = b + db;
      line2.b = b - db;
    }

    return { line1: line1, line2: line2 };
  }

  //获取扇形的两个端点
  getEndpoint(point, angle, sectorAngle) {
    const distance = 15;
    //line1是减，line2是加
    let lines1 = this.create2AngleLine(point, angle, sectorAngle);
    let line = this.createLine2(point, angle);
    line = this.getLineForPoint(line, point);
    let lines2 = this.getParallelLineForDistance(line, distance);

    let point1 = this.getIntersectionPoint(lines1.line1, lines2.line1);
    let point2 = this.getIntersectionPoint(lines1.line1, lines2.line2);
    let point3 = this.getIntersectionPoint(lines1.line2, lines2.line1);
    let point4 = this.getIntersectionPoint(lines1.line2, lines2.line2);

    let angle1 = this.Angle(point, point1, { x: point.x + 1, y: point.y });
    let angle2 = this.Angle(point, point2, { x: point.x + 1, y: point.y });
    let angle3 = this.Angle(point, point3, { x: point.x + 1, y: point.y });
    let angle4 = this.Angle(point, point4, { x: point.x + 1, y: point.y });
    if (angle > 180) {
      angle = 360 - angle;
    }
    if (
      Math.abs((angle1 + angle3) / 2 - angle) <
      Math.abs((angle2 + angle4) / 2 - angle)
    ) {
      return { p1: point1, p2: point3 };
    } else {
      return { p1: point2, p2: point4 };
    }
  }

  // true表示逆时针，false表示顺时针
  isClockwise(vertices) {
    let area = 0;
    for (let i = 0; i < vertices.length; i++) {
      const j = (i + 1) % vertices.length;
      area += vertices[i].x * vertices[j].y;
      area -= vertices[j].x * vertices[i].y;
    }
    const sub = area / 2;
    if (sub > 0) {
      // 逆时针
      return true;
    } else {
      // 顺时针
      return false;
    }
  }

  reverse(points) {
    const _points = [];
    for (let i = points.length - 1; i > -1; --i) {
      _points.push(points[i]);
    }
    return _points;
  }

  //两条线的交点
  getIntersectionPoint(parameter1, parameter2) {
    if (this.isParallel(parameter1, parameter2)) {
      return null;
    }
    if (
      typeof parameter1.a == "undefined" &&
      typeof parameter2.a != "undefined"
    ) {
      if (parameter1.x) {
        return {
          x: parameter1.x,
          y: parameter2.a * parameter1.x + parameter2.b,
        };
      } else if (parameter1.y) {
        return {
          x: (parameter1.y - parameter2.b) / parameter2.a,
          y: parameter1.y,
        };
      }
    } else if (
      typeof parameter2.a == "undefined" &&
      typeof parameter1.a != "undefined"
    ) {
      if (parameter2.x) {
        return {
          x: parameter2.x,
          y: parameter1.a * parameter2.x + parameter1.b,
        };
      } else if (parameter2.y) {
        return {
          x: (parameter2.y - parameter1.b) / parameter1.a,
          y: parameter2.y,
        };
      }
    } else if (
      typeof parameter2.a == "undefined" &&
      typeof parameter1.a == "undefined"
    ) {
      if (parameter1.hasOwnProperty("x") && parameter2.hasOwnProperty("y")) {
        return { x: parameter1.x, y: parameter2.y };
      } else if (
        parameter1.hasOwnProperty("y") &&
        parameter2.hasOwnProperty("x")
      ) {
        return { x: parameter2.x, y: parameter1.y };
      } else {
        return null;
      }
    }

    if (parameter1.a == parameter2.a) {
      return null;
    }

    let joinpointx =
      (parameter2.b - parameter1.b) / (parameter1.a - parameter2.a);
    let joinpointy =
      (parameter1.a * parameter2.b - parameter2.a * parameter1.b) /
      (parameter1.a - parameter2.a);

    let point = { x: joinpointx, y: joinpointy };
    return point;
  }

  // 直线的交点
  getIntersectionPoint2(a, b, c, d) {
    /** 1 解线性方程组, 求线段交点. **/

    // 如果分母为0 则平行或共线, 不相交
    const denominator = (b.y - a.y) * (d.x - c.x) - (a.x - b.x) * (c.y - d.y);
    if (denominator == 0) {
      return null;
    }

    // 线段所在直线的交点坐标 (x , y)
    const x =
      ((b.x - a.x) * (d.x - c.x) * (c.y - a.y) +
        (b.y - a.y) * (d.x - c.x) * a.x -
        (d.y - c.y) * (b.x - a.x) * c.x) /
      denominator;
    const y =
      -(
        (b.y - a.y) * (d.y - c.y) * (c.x - a.x) +
        (b.x - a.x) * (d.y - c.y) * a.y -
        (d.x - c.x) * (b.y - a.y) * c.y
      ) / denominator;

    return { x: x, y: y };
  }

  //两条线段交点
  getIntersectionPoint3(a, b, c, d) {
    const join = this.getIntersectionPoint2(a, b, c, d);
    if (join) {
      const x = join.x;
      const y = join.y; // 交点在线段1上 且交点也在线段2上
      /** 2 判断交点是否在两条线段上 **/
      if (
        (x - a.x) * (x - b.x) <= 0.001 &&
        (y - a.y) * (y - b.y) <= 0.001 &&
        (x - c.x) * (x - d.x) <= 0.001 &&
        (y - c.y) * (y - d.y) <= 0.001
      ) {
        // 返回交点p
        return {
          x: x,
          y: y,
        };
      }
      return null;
    }
    return null;
  }

  // 线段和直线是否相交
  getIntersectionPoint4(point1, point2, line) {
    const line1 = this.createLine1(point1, point2);
    const join = this.getIntersectionPoint(line1, line);
    if (join == null) {
      return null;
    }
    if (this.PointInSegment(join, point1, point2)) {
      return join; // 相交
    } else {
      return null;
    }
  }

  //返回true表示平行
  isParallel(line1, line2) {
    if (typeof line1.a == "undefined" && typeof line2.a == "undefined") {
      if (line1.hasOwnProperty("x") && line2.hasOwnProperty("x")) {
        return true;
      } else if (line1.hasOwnProperty("y") && line2.hasOwnProperty("y")) {
        return true;
      } else {
        return false;
      }
    } else if (typeof line1.a == "undefined" || typeof line2.a == "undefined") {
      return false;
    } else if (this.getFixed(line1.a) == this.getFixed(line2.a)) {
      return true;
    } else {
      return false;
    }
  }

  //两条相交的线段的夹角，永远小于180度
  Angle(o, s, e) {
    let cosfi = 0,
      fi = 0,
      norm = 0;
    let dsx = s.x - o.x;
    let dsy = s.y - o.y;
    let dex = e.x - o.x;
    let dey = e.y - o.y;

    cosfi = dsx * dex + dsy * dey;
    norm = (dsx * dsx + dsy * dsy) * (dex * dex + dey * dey);
    cosfi /= Math.sqrt(norm);

    if (cosfi >= 1.0) return 0;
    //if (cosfi <= -1.0) return Math.PI;
    if (cosfi <= -1.0) return 180;
    fi = Math.acos(cosfi);

    if ((180 * fi) / Math.PI < 180) {
      //return 180 * fi / Math.PI;
      return (fi * 180) / Math.PI;
    } else {
      //return 360 - 180 * fi / Math.PI;
      return ((2 * Math.PI - fi) * 180) / Math.PI;
    }
  }

  getArrow(start, end, ange = 30, L = 20) {
    let a = Math.atan2(end.y - start.y, end.x - start.x);
    let xC = end.x - L * Math.cos(a + (ange * Math.PI) / 180); // θ=30
    let yC = end.y - L * Math.sin(a + (ange * Math.PI) / 180);
    let xD = end.x - L * Math.cos(a - (ange * Math.PI) / 180);
    let yD = end.y - L * Math.sin(a - (ange * Math.PI) / 180);

    return [{ x: xC, y: yC }, end, { x: xD, y: yD }];
  }

  //经过point且与line垂直的线
  getLineForPoint(line, point) {
    let parameter = {};
    if (line.a == 0 || typeof line.a == "undefined") {
      if (line.hasOwnProperty("x")) {
        parameter.x = line.x;
        parameter.y = point.y;
      } else if (line.hasOwnProperty("y")) {
        parameter.x = point.x;
        parameter.y = line.y;
      }
    } else {
      parameter.a = -1 / line.a;
      parameter.b = point.y - point.x * parameter.a;
    }
    return parameter;
  }

  // 经过point且与line垂直的直线，该直线与line的交点
  getJoinLinePoint(point, line) {
    const verticalLine = this.getVerticalLine(line, point);
    const join = this.getIntersectionPoint(line, verticalLine);
    return join;
  }

  // 点到直线的距离
  getDisForPoinLine(point, line) {
    const join = this.getJoinLinePoint(point, line);
    return this.getDistance(point, join);
  }

  // 垂直线
  getVerticalLine(line, point) {
    if (typeof line.a === "undefined") {
      if (line.hasOwnProperty("x")) {
        return { y: point.y };
      } else if (line.hasOwnProperty("y")) {
        return { x: point.x };
      } else {
        return null;
      }
    } else if (line.a == 0) {
      return { x: point.x };
    } else {
      const tl = {};
      tl.a = -1 / line.a;
      const result = this.createLine3(tl, point);
      return result;
    }
  }

  //point在直线上，只是不确定是否在线段上
  //方法：point到startPoint和endPoint的距离之和与startPoint和endPoint之间的距离对比
  isContainForSegment(point, startPoint, endPoint, minDis) {
    if (!minDis) {
      minDis = Constant.minLen;
    }
    let dis1 =
      this.getDistance(startPoint, point) + this.getDistance(endPoint, point);
    let dis2 = this.getDistance(startPoint, endPoint);
    if (Math.abs(dis1 - dis2) < minDis) {
      return true;
    } else {
      return false;
    }
  }

  /*
    //minDis
    isPointInPoly(point, points, minDis) {
        if (!minDis) {
            minDis = Constant.minRealDis
        }
        const x = point.x
        const y = point.y

        let inside = false

        // 是否在顶点附近
        for (let i = 0; i < points.length; ++i) {
            let distance = this.getDistance(point, points[i])
            if (distance < minDis) {
                return true
            }
        }

        // 是否在边沿
        for (let i = 0, j = points.length - 1; i < points.length; j = i++) {
            let pt1 = points[i]
            let pt2 = points[j]
            const flag = this.isContainForSegment(point, pt1, pt2, minDis)
            if (flag) {
                return true
            }
        }

        for (let i = 0, j = points.length - 1; i < points.length; j = i++) {
            let pt1 = points[i]
            let pt2 = points[j]
            const xi = pt1.x
            const yi = pt1.y
            const xj = pt2.x
            const yj = pt2.y

            const intersect = yi > y != yj > y && x < ((xj - xi) * (y - yi)) / (yj - yi) + xi
            if (intersect) inside = !inside
        }

        return inside
    }
    */

  isPointInPoly(point, points) {
    const x = point.x;
    const y = point.y;

    let inside = false;

    for (let i = 0, j = points.length - 1; i < points.length; j = i++) {
      let pt1 = points[i];
      let pt2 = points[j];
      const xi = pt1.x;
      const yi = pt1.y;
      const xj = pt2.x;
      const yj = pt2.y;

      const intersect =
        yi > y != yj > y && x < ((xj - xi) * (y - yi)) / (yj - yi) + xi;
      if (intersect) inside = !inside;
    }

    return inside;
  }

  // 点到线段的距离
  // 在minDistance范围内，会吸附到point1/point2上
  // 返回值：type是1表示吸附在point1，是2表示吸附在point2，是0表示在线段point1-point2上；
  getDisForPoinSegment(point, point1, point2, minDistance) {
    const line = this.createLine1(point1, point2);
    const join = this.getJoinLinePoint(point, line);
    const dis = this.getDistance(point1, point2);
    const dis1 = this.getDistance(join, point1);
    const dis2 = this.getDistance(join, point2);
    if (
      this.getDistance(join, point1) > dis ||
      this.getDistance(join, point2) > dis
    ) {
      // 在线段外
      if (dis1 < dis2 && dis1 < minDistance) {
        return { type: 1, join: point1 };
      } else if (dis2 < dis1 && dis2 < minDistance) {
        return { type: 2, join: point2 };
      } else {
        return null;
      }
    } else {
      if (dis1 < minDistance) {
        return { type: 1, join: point1 };
      } else if (dis2 < minDistance) {
        return { type: 2, join: point2 };
      } else if (this.getDistance(point, join) < minDistance) {
        return { type: 0, join: join };
      }
    }
  }

  PointInSegment(Q, pi, pj, minDis) {
    if (
      this.getDistance(Q, pi) < Constant.minAdsorbPix ||
      this.getDistance(Q, pj) < Constant.minAdsorbPix
    ) {
      return true;
    }

    if (!minDis) {
      minDis = 0.1;
    }
    minDis = minDis / 2;

    const offset1 = (Q.x - pi.x) * (pj.y - pi.y) - (pj.x - pi.x) * (Q.y - pi.y);
    const offset2 = Math.min(pi.x, pj.x) - Q.x;
    const offset3 = Q.x - Math.max(pi.x, pj.x);
    const offset4 = Math.min(pi.y, pj.y) - Q.y;
    const offset5 = Q.y - Math.max(pi.y, pj.y);

    if (
      Math.abs(offset1) < minDis &&
      (offset2 <= 0 || Math.abs(offset2) < minDis) &&
      (offset3 <= 0 || Math.abs(offset3) < minDis) &&
      (offset4 <= 0 || Math.abs(offset4) < minDis) &&
      (offset5 <= 0 || Math.abs(offset5) < minDis)
    ) {
      return true;
    } else {
      return false;
    }
  }

  //点p是否在线段AB上
  isPointOnSegment(p, A, B) {
    // 计算向量 AP 和 BP
    const AP = {
      x: p.x - A.x,
      y: p.y - A.y,
    };
    const BP = {
      x: p.x - B.x,
      y: p.y - B.y,
    };

    // 计算向量 AB 的长度和方向
    const AB = {
      x: B.x - A.x,
      y: B.y - A.y,
    };
    const AB_length = this.getDistance(A, B);
    const AB_direction = {
      x: AB.x / AB_length,
      y: AB.y / AB_length,
    };

    // 检查 AP 和 BP 的方向是否与 AB 相同，并检查它们的长度是否小于等于 AB 的长度
    const dot_product_AP = AP.x * AB_direction.x + AP.y * AB_direction.y;
    const dot_product_BP = BP.x * AB_direction.x + BP.y * AB_direction.y;
    //return dot_product_AP >= 0 && dot_product_BP <= 0 && Math.abs(AP.x * BP.y - AP.y * BP.x) <= AB_length * Number.EPSILON;
    return (
      dot_product_AP >= 0 &&
      dot_product_BP <= 0 &&
      Math.abs(AP.x * BP.y - AP.y * BP.x) <= 0.01
    );
  }

  clonePoint(p1, p2) {
    p1.x = p2.x;
    p1.y = p2.y;
  }

  equalPoint(p1, p2) {
    if (p1.x == p2.x && p1.y == p2.y) {
      return true;
    } else {
      return false;
    }
  }

  crossTwoLines(point1, point2, point3, point4, dis) {
    if (typeof dis == "undefined") {
      dis = Constant.minAdsorbPix;
    }
    const join = this.getIntersectionPoint2(point1, point2, point3, point4);
    if (join != null) {
      if (
        this.getDistance(point1, join) > dis &&
        this.getDistance(point2, join) > dis &&
        this.getDistance(point3, join) > dis &&
        this.getDistance(point4, join) > dis
      ) {
        if (
          this.getDistance(point1, join) < this.getDistance(point1, point2) &&
          this.getDistance(point2, join) < this.getDistance(point1, point2) &&
          this.getDistance(point3, join) < this.getDistance(point3, point4) &&
          this.getDistance(point4, join) < this.getDistance(point3, point4)
        ) {
          return true;
        } else {
          return false;
        }
      }
    } else {
      if (
        this.PointInSegment(point1, point3, point4) ||
        this.PointInSegment(point2, point3, point4)
      ) {
        return true;
      }
    }
    return false;
  }

  getDisPointsLine(line, point, distance1, distance2) {
    const newpoint1 = {};
    const newpoint2 = {};
    const result = {};
    if (line.hasOwnProperty("x")) {
      newpoint1.x = line.x;
      newpoint1.y = point.y - distance1;
      newpoint2.x = line.x;
      newpoint2.y = point.y + distance2;
    } else if (line.hasOwnProperty("y")) {
      newpoint1.y = line.y;
      newpoint1.x = point.x - distance1;
      newpoint2.y = line.y;
      newpoint2.x = point.x + distance2;
    } else {
      const a = Math.atan(line.a);
      const t_line = { a: -1 / line.a };
      const line_ab2 = this.createLine3(t_line, point);
      const join = this.getIntersectionPoint(line, line_ab2);

      newpoint1.x = join.x - distance1 * Math.cos(a);
      newpoint1.y = join.y - distance1 * Math.sin(a);

      newpoint2.x = join.x + distance2 * Math.cos(a);
      newpoint2.y = join.y + distance2 * Math.sin(a);
    }
    result.newpoint1 = newpoint1;
    result.newpoint2 = newpoint2;
    return result;
  }

  getBoundingBox(points) {
    let minX = points[0].x;
    let maxX = points[0].x;
    let minY = points[0].y;
    let maxY = points[0].y;

    for (let i = 1; i < points.length; ++i) {
      const point = points[i];
      if (minX > point.x) {
        minX = point.x;
      }
      if (minY > point.y) {
        minY = point.y;
      }
      if (maxX < point.x) {
        maxX = point.x;
      }
      if (maxY < point.y) {
        maxY = point.y;
      }
    }

    const box = {};
    box.minX = minX;
    box.minY = minY;
    box.maxX = maxX;
    box.maxY = maxY;

    return box;
  }

  getBoundingBox2(points) {
    let minX = null;
    let maxX = null;
    let minY = null;
    let maxY = null;

    for (let key in points) {
      const point = points[key];
      if (minX == null || minX > point.x) {
        minX = point.x;
      }
      if (minY == null || minY > point.y) {
        minY = point.y;
      }
      if (maxX == null || maxX < point.x) {
        maxX = point.x;
      }
      if (maxY == null || maxY < point.y) {
        maxY = point.y;
      }
    }

    const box = {};
    box.minX = minX;
    box.minY = minY;
    box.maxX = maxX;
    box.maxY = maxY;

    return box;
  }

  ComputePolygonArea(points) {
    const point_num = points.length;
    if (point_num < 3) {
      return 0;
    }
    let s = points[0].y * (points[point_num - 1].x - points[1].x);
    for (let i = 1; i < point_num; ++i)
      s += points[i].y * (points[i - 1].x - points[(i + 1) % point_num].x);
    return Math.abs(s / 2.0);
  }

  // 获取多边形重心
  getPolygonCore(points) {
    function Area(p0, p1, p2) {
      let area = 0.0;
      area =
        p0.x * p1.y +
        p1.x * p2.y +
        p2.x * p0.y -
        p1.x * p0.y -
        p2.x * p1.y -
        p0.x * p2.y;
      return area / 2;
    }

    let sum_x = 0;
    let sum_y = 0;
    let sum_area = 0;
    let p1 = points[1];
    for (let i = 2; i < points.length; i++) {
      const p2 = points[i];
      const area = Area(points[0], p1, p2);
      sum_area += area;
      sum_x += (points[0].x + p1.x + p2.x) * area;
      sum_y += (points[0].y + p1.y + p2.y) * area;
      p1 = p2;
    }
    const xx = sum_x / sum_area / 3;
    const yy = sum_y / sum_area / 3;
    return {
      x: xx,
      y: yy,
    };
  }

  // points1是否在points2里
  isPolyInPoly(points1, points2, minDis) {
    for (let i = 0; i < points1.length; ++i) {
      let flag = false;
      for (let j = 0; j < points2.length; ++j) {
        if (this.equalPoint(points1[i], points2[j])) {
          flag = true;
          break;
        }
      }
      if (!flag) {
        if (!this.isPointInPoly(points1[i], points2, minDis)) {
          return false;
        }
      } else {
        const nextIndex = i == points1.length - 1 ? 0 : i + 1;
        const mid = {
          x: (points1[i].x + points1[nextIndex].x) / 2,
          y: (points1[i].y + points1[nextIndex].y) / 2,
        };
        if (!this.isPointInPoly(mid, points2, minDis)) {
          return false;
        }
      }
    }
    return true;
  }

  dotPoints(pt1, pt2, point1, point2) {
    let vt1 = {};
    let vt2 = {};
    vt1.start = {};
    vt1.end = {};
    vt1.start.x = 0;
    vt1.start.y = 0;
    vt1.end.x = pt2.x - pt1.x;
    vt1.end.y = pt2.y - pt1.y;

    vt2.start = {};
    vt2.end = {};
    vt2.start.x = 0;
    vt2.start.y = 0;
    vt2.end.x = point2.x - point1.x;
    vt2.end.y = point2.y - point1.y;

    let result = vt1.end.x * vt2.end.x + vt1.end.y * vt2.end.y;
    return result;
  }

  //start是起点，target是朝着目标移动，distance是移动的距离
  translate(start, target, point, distance) {
    let dx = target.x - start.x;
    let dy = target.y - start.y;
    let dis = Math.sqrt(Math.pow(dx, 2) + Math.pow(dy, 2));

    let result = {
      x: point.x + (dx * distance) / dis,
      y: point.y + (dy * distance) / dis,
    };

    return result;
  }

  //射线与线段相交
  // intersection(rayStart, rayEnd, segmentStart, segmentEnd) {
  //     // 计算射线和线段的方向向量
  //     const rayDirection = {
  //         x:rayEnd.x - rayStart.x,
  //         y:rayEnd.y - rayStart.y,
  //     };
  //     const segmentDirection = {
  //         x:segmentEnd.x - segmentStart.x,
  //         y:segmentEnd.y - segmentStart.y,
  //     };

  //     // 计算射线和线段的起点之间的向量
  //     const startPointVector = {
  //         x:rayStart.x - segmentStart.x,
  //         y:rayStart.y - segmentStart.y,
  //     };

  //     // 计算射线和线段的叉积
  //     const crossProduct = rayDirection.x * segmentDirection.y - rayDirection.y * segmentDirection.x;

  //     // 如果叉积为0，则表示射线和线段平行
  //     if (crossProduct === 0) {
  //       return null;
  //     }

  //     // 计算线段起点到射线的交点的向量
  //     const t = (startPointVector.x * segmentDirection.y - startPointVector.y * segmentDirection.x) / crossProduct;

  //     // 如果t的值小于0，则交点在射线的起点之后
  //     if (t < 0) {
  //       return null;
  //     }

  //     // 计算交点的坐标
  //     const intersectionX = rayStart.x + t * rayDirection.x;
  //     const intersectionY = rayStart.y + t * rayDirection.y;

  //     // 如果交点在线段的范围内，则返回交点坐标
  //     if ((intersectionX >= Math.min(segmentStart.x, segmentEnd.x)) &&
  //         (intersectionX <= Math.max(segmentStart.x, segmentEnd.x)) &&
  //         (intersectionY >= Math.min(segmentStart.y, segmentEnd.y)) &&
  //         (intersectionY <= Math.max(segmentStart.y, segmentEnd.y))) {
  //       //return [intersectionX, intersectionY];
  //       return {
  //         x:intersectionX,
  //         y:intersectionY,
  //       };
  //     }

  //     // 否则返回null
  //     return null;
  //   }
  // raySegmentIntersection(rayOrigin, rayDirection, segmentStart, segmentEnd) {
  //     // 计算射线和线段的交点
  //     const x1 = rayOrigin.x
  //     const y1 = rayOrigin.y
  //     const x2 = segmentStart.x
  //     const y2 = segmentStart.y
  //     const dx1 = rayDirection.x
  //     const dy1 = rayDirection.y
  //     const dx2 = segmentEnd.x - x2
  //     const dy2 = segmentEnd.y - y2

  //     const crossProduct = dx1 * dy2 - dx2 * dy1
  //     if (Math.abs(crossProduct) < 1e-8) {
  //         // 射线和线段平行或共线
  //         return null
  //     }

  //     const t1 = (dx2 * (y1 - y2) - dy2 * (x1 - x2)) / crossProduct
  //     const t2 = (dx1 * (y1 - y2) - dy1 * (x1 - x2)) / crossProduct

  //     if (t1 >= 0 && t2 >= 0 && t2 <= 1) {
  //         // 有交点，计算交点坐标
  //         const intersectionX = x1 + t1 * dx1
  //         const intersectionY = y1 + t1 * dy1
  //         return {
  //             x: intersectionX,
  //             y: intersectionY,
  //         }
  //     } else {
  //         // 没有交点
  //         return null
  //     }
  // }
  raySegmentIntersection(rayOrigin, rayDirection, segmentStart, segmentEnd) {
    const end = {
      x: rayOrigin.x + rayDirection.x,
      y: rayOrigin.y - rayDirection.z,
    };
    const line = this.createLine1(rayOrigin, end);
    const join = this.getIntersectionPoint4(segmentStart, segmentEnd, line);
    if (join == null) {
      return null;
    } else {
      const dis = this.getDistance(end, join);
      const dis1 = this.getDistance(rayOrigin, join);
      const dis2 = this.getDistance(rayOrigin, end);
      if (dis - (dis1 + dis2) + 0.01 > 0) {
        return null;
      } else {
        return join;
      }
    }
  }

  RectangleVertex(startPoint, endPoint, width) {
    let line = this.createLine1(startPoint, endPoint);
    let lines = this.getParallelLineForDistance(line, width / 2);

    let leftEdgeStart, rightEdgeStart, rightEdgeEnd, leftEdgeEnd;

    let point = null;
    let points = [];

    //先计算start部分
    point = startPoint;
    points.push(endPoint);
    points.push(startPoint);
    let point1 = this.getJoinLinePoint(point, lines.line1);
    let point2 = this.getJoinLinePoint(point, lines.line2);
    points[2] = point1;

    if (this.isClockwise(points)) {
      rightEdgeStart = point1;
      leftEdgeStart = point2;
    } else {
      rightEdgeStart = point2;
      leftEdgeStart = point1;
    }

    //再计算end部分
    points = [];
    point = endPoint;
    points.push(startPoint);
    points.push(endPoint);
    point1 = this.getJoinLinePoint(point, lines.line1);
    point2 = this.getJoinLinePoint(point, lines.line2);
    points[2] = point1;

    if (this.isClockwise(points)) {
      rightEdgeEnd = point2;
      leftEdgeEnd = point1;
    } else {
      rightEdgeEnd = point1;
      leftEdgeEnd = point2;
    }
    return {
      leftEdgeStart: leftEdgeStart,
      rightEdgeStart: rightEdgeStart,
      rightEdgeEnd: rightEdgeEnd,
      leftEdgeEnd: leftEdgeEnd,
    };
  }

  //start到end的射线中取一点point，start-end和end-point的距离相同
  getPositionForExtendedLine(start, end) {
    const dx = end.x - start.x;
    const dy = end.y - start.y;
    const point = {
      x: end.x + dx,
      y: end.y + dy,
    };
    return point;
  }

  isOnRay(start, dir, position) {
    const v1 = { x: dir.x - start.x, y: dir.y - start.y };
    const v2 = { x: position.x - start.x, y: position.y - start.y };
    return v1.x * v2.y - v1.y * v2.x;
  }

  //向量是否同样的方向
  isSameDirForVector(point1, point2, p1, p2) {
    const v1 = {
      x: point2.x - point1.x,
      y: point2.y - point1.y,
    };
    const v2 = {
      x: p2.x - p1.x,
      y: p2.y - p1.y,
    };

    const value = this.dot(v1, v2);
    if (value > 0) {
      return true;
    }
    {
      return false;
    }
  }

  //生成五角星
  createFivePointedStar(position, r) {
    let deg = Math.PI / 180; //角度
    let points = [];
    points[0] = {
      x: position.x - r * Math.cos(54 * deg),
      y: position.y + r * Math.sin(54 * deg),
    };
    points[1] = {
      x: position.x,
      y: position.y - r,
    };
    points[2] = {
      x: position.x + r * Math.cos(54 * deg),
      y: position.y + r * Math.sin(54 * deg),
    };
    points[3] = {
      x: position.x - r * Math.cos(18 * deg),
      y: position.y - r * Math.sin(18 * deg),
    };
    points[4] = {
      x: position.x + r * Math.cos(18 * deg),
      y: position.y - r * Math.sin(18 * deg),
    };
    return points;
  }

  //求圆和直线之间的交点
  /**
   * 求圆和直线之间的交点
   * 直线方程：y = kx + b
   * 圆的方程：(x - m)² + (x - n)² = r²
   * x1, y1 = 线坐标1, x2, y2 = 线坐标2, m, n = 圆坐标, r = 半径
   */
  getInsertPointBetweenCircleAndLine(x1, y1, x2, y2, m, n, radius) {
    let insertPoints = [];
    if (Math.abs(x1 - x2) < 0.5) {
      insertPoints[0] = {
        x: x1,
        y: n - Math.sqrt(radius * radius - Math.pow(x1 - m, 2)),
      };
      insertPoints[1] = {
        x: x1,
        y: n + Math.sqrt(radius * radius - Math.pow(x1 - m, 2)),
      };
      return insertPoints;
    }
    // console.log(x1, y1, x2, y2, m, n, radius)
    let kbArr = this.binaryEquationGetKB(x1, y1, x2, y2);
    let k = kbArr[0];
    let b = kbArr[1];

    let aX = 1 + k * k;
    let bX = 2 * k * (b - n) - 2 * m;
    let cX = m * m + (b - n) * (b - n) - radius * radius;

    let xArr = this.quadEquationGetX(aX, bX, cX);
    xArr.forEach((x) => {
      let y = k * x + b;
      insertPoints.push({ x: x, y: y });
    });
    return insertPoints;
  }

  /**
   * 求二元一次方程的系数
   * y1 = k * x1 + b => k = (y1 - b) / x1
   * y2 = k * x2 + b => y2 = ((y1 - b) / x1) * x2 + b
   */
  binaryEquationGetKB(x1, y1, x2, y2) {
    let k = (y1 - y2) / (x1 - x2);
    let b = (x1 * y2 - x2 * y1) / (x1 - x2);
    return [k, b];
  }

  /**
   * 一元二次方程求根
   * ax² + bx + c = 0
   */
  quadEquationGetX(a, b, c) {
    let xArr = [];
    let result = Math.pow(b, 2) - 4 * a * c;
    if (result > 0) {
      xArr.push((-b + Math.sqrt(result)) / (2 * a));
      xArr.push((-b - Math.sqrt(result)) / (2 * a));
    }
    //else if (result == 0) {
    else {
      xArr.push(-b / (2 * a));
    }
    return xArr;
  }

  angleTo(v1, v2) {
    const denominator = Math.sqrt(this.lengthSq(v1) * this.lengthSq(v2));
    if (denominator === 0) return 90;
    const theta = this.dot(v1, v2) / denominator;
    //return Math.acos(this.clamp(theta, -1, 1));
    return (Math.acos(this.clamp(theta, -1, 1)) / Math.PI) * 180;
  }

  //点乘
  dot(v1, v2) {
    return v1.x * v2.x + v1.y * v2.y;
  }

  //叉乘
  cross(v1, v2) {
    return v1.x * v2.y - v1.y * v2.x;
  }

  // 两点相减
  pointMinus(v1, v2) {
    return {
      x: v1.x - v2.x,
      y: v1.y - v2.y,
    };
  }
  // 两点相加
  pointPlus(v1, v2) {
    return {
      x: v1.x + v2.x,
      y: v1.y + v2.y,
    };
  }
  // 点放大
  pointScale(v, a) {
    return {
      x: v.x * a,
      y: v.y * a,
    };
  }

  clamp(value, min, max) {
    return Math.max(min, Math.min(max, value));
  }

  lengthSq(v) {
    return v.x * v.x + v.y * v.y;
  }

  // 当前点 下一个点 下下个点
  getCurvesControls(p1, pt, p2, scale = 0.3) {
    const vec1T = this.pointMinus(p1, pt);
    const vecT2 = this.pointMinus(p1, pt);
    const len1 = Math.hypot(vec1T.x, vec1T.y);
    const len2 = Math.hypot(vecT2.x, vecT2.y);
    const v = len1 / len2;

    let delta;
    if (v > 1) {
      delta = this.pointMinus(
        p1,
        this.pointPlus(pt, this.pointScale(this.pointMinus(p2, pt), 1 / v))
      );
    } else {
      delta = this.pointMinus(
        this.pointPlus(pt, this.pointScale(this.pointMinus(p1, pt), v)),
        p2
      );
    }
    delta = this.pointScale(delta, scale);

    const control1 = {
      x: this.pointPlus(pt, delta).x,
      y: this.pointPlus(pt, delta).y,
    };
    const control2 = {
      x: this.pointMinus(pt, delta).x,
      y: this.pointMinus(pt, delta).y,
    };
    return { control1, control2 };
  }

  getCurvesByPoints(points, scale = 0.2) {
    const curves = [];
    let preControl1, preControl2;
    for (let i = 0; i < points.length - 2; i++) {
      const { control1, control2 } = this.getCurvesControls(
        points[i],
        points[i + 1],
        points[i + 2],
        scale
      );

      curves.push({
        start: points[i],
        end: points[i + 1],
        controls: i === 0 ? [control1] : [preControl2, control1],
      });
      preControl1 = control1;
      preControl2 = control2;
    }
    curves.push({
      start: points[points.length - 2],
      controls: [preControl2],
      end: points[points.length - 1],
    });
    return curves;
  }

  /**
   * 已知四个控制点，及曲线中的某一个点的 x/y，反推求 t
   * @param {number} x1 起点 x/y
   * @param {number} x2 控制点1 x/y
   * @param {number} x3 控制点2 x/y
   * @param {number} x4 终点 x/y
   * @param {number} X 曲线中的某个点 x/y
   * @returns {number[]} t[]
   */
  getThreeBezierT(x1, x2, x3, x4, X) {
    const a = -x1 + 3 * x2 - 3 * x3 + x4;
    const b = 3 * x1 - 6 * x2 + 3 * x3;
    const c = -3 * x1 + 3 * x2;
    const d = x1 - X;

    // 盛金公式, 预先需满足, a !== 0
    // 判别式
    const A = Math.pow(b, 2) - 3 * a * c;
    const B = b * c - 9 * a * d;
    const C = Math.pow(c, 2) - 3 * b * d;
    const delta = Math.pow(B, 2) - 4 * A * C;

    let t1 = -100,
      t2 = -100,
      t3 = -100;

    // 3个相同实数根
    if (A === B && A === 0) {
      t1 = -b / (3 * a);
      t2 = -c / b;
      t3 = (-3 * d) / c;
      return [t1, t2, t3];
    }

    // 1个实数根和1对共轭复数根
    if (delta > 0) {
      const v = Math.pow(B, 2) - 4 * A * C;
      const xsv = v < 0 ? -1 : 1;

      const m1 = A * b + (3 * a * (-B + (v * xsv) ** (1 / 2) * xsv)) / 2;
      const m2 = A * b + (3 * a * (-B - (v * xsv) ** (1 / 2) * xsv)) / 2;

      const xs1 = m1 < 0 ? -1 : 1;
      const xs2 = m2 < 0 ? -1 : 1;

      t1 =
        (-b - (m1 * xs1) ** (1 / 3) * xs1 - (m2 * xs2) ** (1 / 3) * xs2) /
        (3 * a);
      // 涉及虚数，可不考虑。i ** 2 = -1
    }

    // 3个实数根
    if (delta === 0) {
      const K = B / A;
      t1 = -b / a + K;
      t2 = t3 = -K / 2;
    }

    // 3个不相等实数根
    if (delta < 0) {
      const xsA = A < 0 ? -1 : 1;
      const T = (2 * A * b - 3 * a * B) / (2 * (A * xsA) ** (3 / 2) * xsA);
      const theta = Math.acos(T);

      if (A > 0 && T < 1 && T > -1) {
        t1 = (-b - 2 * A ** (1 / 2) * Math.cos(theta / 3)) / (3 * a);
        t2 =
          (-b +
            A ** (1 / 2) *
              (Math.cos(theta / 3) + 3 ** (1 / 2) * Math.sin(theta / 3))) /
          (3 * a);
        t3 =
          (-b +
            A ** (1 / 2) *
              (Math.cos(theta / 3) - 3 ** (1 / 2) * Math.sin(theta / 3))) /
          (3 * a);
      }
    }
    return [t1, t2, t3];
  }

  /**
   * @desc 获取三阶贝塞尔曲线的线上坐标
   * B(t) = P0 * (1-t)^3 + 3 * P1 * t * (1-t)^2 + 3 * P2 * t^2 * (1-t) + P3 * t^3, t ∈ [0,1]
   * @param {number} t 当前百分比
   * @param {Array} p1 起点坐标
   * @param {Array} p2 终点坐标
   * @param {Array} cp1 控制点1
   * @param {Array} cp2 控制点2
   */
  getThreeBezierPoint(t, p1, cp1, cp2, p2) {
    const { x: x1, y: y1 } = p1;
    const { x: x2, y: y2 } = p2;
    const { x: cx1, y: cy1 } = cp1;
    const { x: cx2, y: cy2 } = cp2;

    const x =
      x1 * (1 - t) * (1 - t) * (1 - t) +
      3 * cx1 * t * (1 - t) * (1 - t) +
      3 * cx2 * t * t * (1 - t) +
      x2 * t * t * t;
    const y =
      y1 * (1 - t) * (1 - t) * (1 - t) +
      3 * cy1 * t * (1 - t) * (1 - t) +
      3 * cy2 * t * t * (1 - t) +
      y2 * t * t * t;
    return { x, y };
  }

  getHitInfoForThreeBezier(position, curve, rang = 3) {
    const { x: offsetX, y: offsetY } = position;
    // 用 x 求出对应的 t，用 t 求相应位置的 y，再比较得出的 y 与 offsetY 之间的差值
    const tsx = this.getThreeBezierT(
      curve.start.x,
      curve.controls[0].x,
      curve.controls[1].x,
      curve.end.x,
      offsetX
    );
    for (let x = 0; x < 3; x++) {
      if (tsx[x] <= 1 && tsx[x] >= 0) {
        const point = this.getThreeBezierPoint(
          tsx[x],
          curve.start,
          curve.controls[0],
          curve.controls[1],
          curve.end
        );
        if (Math.abs(point.y - offsetY) < rang) {
          return {
            position: point,
            distance: this.getDistance(point, position),
          };
        }
      }
    }
    // 如果上述没有结果，则用 y 求出对应的 t，再用 t 求出对应的 x，与 offsetX 进行匹配
    const tsy = this.getThreeBezierT(
      curve.start.y,
      curve.controls[0].y,
      curve.controls[1].y,
      curve.end.y,
      offsetY
    );
    for (let y = 0; y < 3; y++) {
      if (tsy[y] <= 1 && tsy[y] >= 0) {
        const point = this.getThreeBezierPoint(
          tsy[y],
          curve.start,
          curve.controls[0],
          curve.controls[1],
          curve.end
        );
        if (Math.abs(point.x - offsetX) < rang) {
          return {
            position: point,
            distance: this.getDistance(point, position),
          };
        }
      }
    }
  }

  // 二次曲线
  getHitInfoForTwoBezier(position, curve) {
    let bezierData = [];
    bezierData.push(curve.start.x);
    bezierData.push(curve.start.y);
    bezierData.push(curve.controls[0].x);
    bezierData.push(curve.controls[0].y);
    bezierData.push(curve.end.x);
    bezierData.push(curve.end.y);
    const { isHit, getInfo } = bezierUtil.measureBezier(...bezierData);
    const { point } = getInfo(position);
    return {
      position: {
        x: point[0],
        y: point[1],
      },
      distance: this.getDistance(position, {
        x: point[0],
        y: point[1],
      }),
    };
  }

  getHitInfoForCurves(pos, curves, roadWidth) {
    let joinInfo;
    for (const curve of curves) {
      const tempJoinInfo =
        curve.controls.length === 2
          ? this.getHitInfoForThreeBezier(pos, curve, roadWidth / 2)
          : this.getHitInfoForTwoBezier(pos, curve);

      if (
        !joinInfo ||
        (tempJoinInfo && tempJoinInfo.distance < joinInfo.distance)
      ) {
        joinInfo = tempJoinInfo;
      }
    }
    return joinInfo;
  }

  getHitInfoForCurve(pos, curve, roadWidth) {
    let joinInfo;
    const tempJoinInfo =
      curve.controls.length === 2
        ? this.getHitInfoForThreeBezier(pos, curve, roadWidth / 2)
        : this.getHitInfoForTwoBezier(pos, curve);

    if (
      !joinInfo ||
      (tempJoinInfo && tempJoinInfo.distance < joinInfo.distance)
    ) {
      joinInfo = tempJoinInfo;
    }
    return joinInfo;
  }

  getIndexForCurvesPoints(position, points) {
    let minDis = null;
    let index = -1;
    for (let i = 0; i < points.length - 1; ++i) {
      const line = this.createLine1(points[i], points[i + 1]);
      const join = this.getJoinLinePoint(position, line);
      const dis = this.getDistance(position, join);
      if (this.isContainForSegment(join, points[i], points[i + 1])) {
        if (minDis == null || minDis > dis) {
          minDis = dis;
          index = i;
        }
      }
    }
    return index;
  }

  // //获取一组点的偏移
  // getOffset(points, leftWidth, rightWidth, dir) {
  //   //斜边长度d已知，角度angle已知
  //   //对边长度就是y的偏移量 就是 d * sin(angle) ==> d * Math.sin(angle * Math.PI / 180)
  //   //邻边长度就是x的偏移量 就是 d * cos(angle) ==> d * Math.cos(angle * Math.PI / 180)
  //   let result = {};
  //   if (dir == "left" || !dir) {
  //     let angle = 90;
  //     let d = leftWidth;
  //     result.leftEdgePoints = points.map((coords) => {
  //       let ox = d * Math.cos((angle * Math.PI) / 180);
  //       let oy = d * Math.sin((angle * Math.PI) / 180);
  //       return {
  //         x: coords.x + ox,
  //         y: coords.y + oy,
  //       };
  //     });
  //   }

  //   if (dir == "right" || !dir) {
  //     let angle = -90;
  //     let d = rightWidth;

  //     result.rightEdgePoints = points.map((coords) => {
  //       let ox = d * Math.cos((angle * Math.PI) / 180);
  //       let oy = d * Math.sin((angle * Math.PI) / 180);
  //       return {
  //         x: coords.x + ox,
  //         y: coords.y + oy,
  //       };
  //     });
  //   }
  //   return result;
  // }

  getOffset(points, leftWidth, rightWidth, dir) {
    let leftEdgePoints = [];
    let rightEdgePoints = [];
    for (let i = 0; i < points.length - 1; ++i) {
      if (dir == "left" || !dir) {
        let leftEdgePoins1 = this.RectangleVertex(
          points[i],
          points[i + 1],
          leftWidth * 2
        );
        let leftLine1 = mathUtil.createLine1(
          leftEdgePoins1.leftEdgeStart,
          leftEdgePoins1.leftEdgeEnd
        );
        if (i != points.length - 2) {
          let leftEdgePoins2 = this.RectangleVertex(
            points[i + 1],
            points[i + 2],
            leftWidth * 2
          );

          let leftLine2 = mathUtil.createLine1(
            leftEdgePoins2.leftEdgeStart,
            leftEdgePoins2.leftEdgeEnd
          );
          let join = mathUtil.getIntersectionPoint(leftLine1, leftLine2);
          if (join != null) {
            leftEdgePoints[i + 1] = join;
          } else {
            leftEdgePoints[i + 1] = mathUtil.getJoinLinePoint(
              points[i + 1],
              leftLine1
            );
          }
        } else {
          leftEdgePoints[i + 1] = mathUtil.getJoinLinePoint(
            points[i + 1],
            leftLine1
          );
        }
        if (!leftEdgePoints[0]) {
          leftEdgePoints[0] = mathUtil.getJoinLinePoint(points[0], leftLine1);
        }
      }

      if (dir == "right" || !dir) {
        let rightEdgePoins1 = this.RectangleVertex(
          points[i],
          points[i + 1],
          rightWidth * 2
        );
        let rightLine1 = mathUtil.createLine1(
          rightEdgePoins1.rightEdgeStart,
          rightEdgePoins1.rightEdgeEnd
        );
        if (i != points.length - 2) {
          let rightEdgePoins2 = this.RectangleVertex(
            points[i + 1],
            points[i + 2],
            rightWidth * 2
          );

          let rightLine2 = mathUtil.createLine1(
            rightEdgePoins2.rightEdgeStart,
            rightEdgePoins2.rightEdgeEnd
          );
          let join = mathUtil.getIntersectionPoint(rightLine1, rightLine2);
          if (join != null) {
            rightEdgePoints[i + 1] = join;
          } else {
            rightEdgePoints[i + 1] = mathUtil.getJoinLinePoint(
              points[i + 1],
              rightLine1
            );
          }
        } else {
          rightEdgePoints[i + 1] = mathUtil.getJoinLinePoint(
            points[i + 1],
            rightLine1
          );
        }

        if (!rightEdgePoints[0]) {
          rightEdgePoints[0] = mathUtil.getJoinLinePoint(points[0], rightLine1);
        }
      }
    }

    return {
      leftEdgePoints: leftEdgePoints,
      rightEdgePoints: rightEdgePoints,
    };
  }

  twoOrderBezier(t, p1, cp, p2) {
    //参数分别是t,起始点,控制点和终点
    var x1 = p1.x;
    var y1 = p1.y;

    var cx = cp.x;
    var cy = cp.y;

    var x2 = p2.x;
    var y2 = p2.y;
    // var [x1, y1] = p1,
    //   [cx, cy] = cp,
    //   [x2, y2] = p2;
    var x = (1 - t) * (1 - t) * x1 + 2 * t * (1 - t) * cx + t * t * x2,
      y = (1 - t) * (1 - t) * y1 + 2 * t * (1 - t) * cy + t * t * y2;
    return {
      x: x,
      y: y,
    };
  }

  //t是0.5，求cp。p是曲线上的点
  twoOrderBezier2(t, p1, p, p2) {
    var x1 = p1.x;
    var y1 = p1.y;

    var x2 = p2.x;
    var y2 = p2.y;

    let cx = (p.x - t * t * x2 - (1 - t) * (1 - t) * x1) / (2 * t * (1 - t));
    let cy = (p.y - t * t * y2 - (1 - t) * (1 - t) * y1) / (2 * t * (1 - t));
    return {
      x: cx,
      y: cy,
    };
  }

  rgb() {
    //rgb颜色随机
    const r = Math.floor(Math.random() * 256);
    const g = Math.floor(Math.random() * 256);
    const b = Math.floor(Math.random() * 256);
    return `rgb(${r},${g},${b})`;
  }
}

const mathUtil = new MathUtil();
export { mathUtil };