获取二次贝塞尔曲线边缘点坐标

https://stackoverflow.com/questions/999549/finding-min-max-of-quadratic-bezier-with-coregraphics

function P(x,y){
  this.x = x;
  this.y = y;
}
function pointOnCurve(P1,P2,P3,t){
  if(t<=0 || 1<=t || isNaN(t))return false;
  let c1 =  new P(P1.x+(P2.x-P1.x)*t,P1.y+(P2.y-P1.y)*t);
  let c2 =  new P(P2.x+(P3.x-P2.x)*t,P2.y+(P3.y-P2.y)*t);
  return new P(c1.x+(c2.x-c1.x)*t,c1.y+(c2.y-c1.y)*t);
}
function getQCurveBounds(ax, ay, bx, by, cx, cy){
  let  P1 = new P(ax,ay);
  let  P2 = new P(bx,by);
  let  P3 = new P(cx,cy);
  let tx =  (P1.x - P2.x) / (P1.x - 2*P2.x + P3.x);
  let ty =  (P1.y - P2.y) / (P1.y - 2*P2.y + P3.y);
  let Ex = pointOnCurve(P1,P2,P3,tx);
  let xMin = Ex?Math.min(P1.x,P3.x,Ex.x):Math.min(P1.x,P3.x);
  let xMax = Ex?Math.max(P1.x,P3.x,Ex.x):Math.max(P1.x,P3.x);
  let Ey = pointOnCurve(P1,P2,P3,ty);
  let yMin = Ey?Math.min(P1.y,P3.y,Ey.y):Math.min(P1.y,P3.y);
  let yMax = Ey?Math.max(P1.y,P3.y,Ey.y):Math.max(P1.y,P3.y);
  return {x:xMin, y:yMin, width:xMax-xMin, height:yMax-yMin};
}

获取三次贝塞尔曲线边缘点坐标

https://stackoverflow.com/questions/2587751/an-algorithm-to-find-bounding-box-of-closed-bezier-curves

function getCurveBounds(ax, ay, bx, by, cx, cy, dx, dy) {
  var px, py, qx, qy, rx, ry, sx, sy, tx, ty,
    tobx, toby, tocx, tocy, todx, tody, toqx, toqy,
    torx, tory, totx, toty;
  var x, y, minx, miny, maxx, maxy;

  minx = miny = Number.POSITIVE_INFINITY;
  maxx = maxy = Number.NEGATIVE_INFINITY;

  tobx = bx - ax;  toby = by - ay;  // directions
  tocx = cx - bx;  tocy = cy - by;
  todx = dx - cx;  tody = dy - cy;
  var step = 1/40;      // precision
  for(var d=0;  d<1.001;  d+=step) {
    px = ax +d*tobx;  py = ay +d*toby;
    qx = bx +d*tocx;  qy = by +d*tocy;
    rx = cx +d*todx;  ry = cy +d*tody;
    toqx = qx - px;      toqy = qy - py;
    torx = rx - qx;      tory = ry - qy;

    sx = px +d*toqx;  sy = py +d*toqy;
    tx = qx +d*torx;  ty = qy +d*tory;
    totx = tx - sx;   toty = ty - sy;

    x = sx + d*totx;  y = sy + d*toty;
    minx = Math.min(minx, x); miny = Math.min(miny, y);
    maxx = Math.max(maxx, x); maxy = Math.max(maxy, y);
  }
  return {x:minx, y:miny, width:maxx-minx, height:maxy-miny};
}

求赛贝尔曲线坐标

https://www.jianshu.com/p/27d3071a9b17

/**
 * @param poss      贝塞尔曲线控制点坐标
 * @param precision 精度，需要计算的该条贝塞尔曲线上的点的数目
 * @return 该条贝塞尔曲线上的点（二维坐标）
const pos = bezier([
  [0, 160],
  [100, 0],
  [180, 160]
], 12);
*/
function bezier(poss, precision) {
  //贝塞尔曲线控制点数（阶数）, 不小于 2
  const number = poss.length;
  if (number < 2) {
    return null;
  }
  //维度，坐标轴数（二维坐标，三维坐标..., 至少为二维坐标系）
  const dimersion = poss[0].length;
  if (dimersion < 2) {
    return null;
  }
  let i, j, k, t, temp;

  //计算杨辉三角
  const mi = [];
  mi[0] = mi[1] = 1;
  for (i = 3; i <= number; i++) {
    t = [];
    for (j = 0; j < i - 1; j++) {
        t[j] = mi[j];
    }
    mi[0] = mi[i - 1] = 1;
    for (j = 0; j < i - 2; j++) {
        mi[j + 1] = t[j] + t[j + 1];
    }
  }
  
  //计算坐标点
  const result = [];
  for (i = 0; i < precision; i++) {
    result[i] = [];
    t = i / precision;
    for (j = 0; j < dimersion; j++) {
      temp = 0;
      for (k = 0; k < number; k++) {
        temp += Math.pow(1 - t, number - k - 1) * poss[k][j] * Math.pow(t, k) * mi[k];
      }
      result[i][j] = temp;
    }
  }
  result.push(poss[number - 1])
  return result;
}