swOperation/node_modules/@antv/path-util/src/get-arc-params.ts

const mod = function (n: number, m: number): number {
  return ((n % m) + m) % m;
};

// 向量长度
function vMag(v) {
  return Math.sqrt(v[0] * v[0] + v[1] * v[1]);
}

// u.v/|u||v|，计算夹角的余弦值
function vRatio(u, v) {
  // 当存在一个向量的长度为 0 时，夹角也为 0，即夹角的余弦值为 1
  return vMag(u) * vMag(v) ? (u[0] * v[0] + u[1] * v[1]) / (vMag(u) * vMag(v)) : 1;
}

// 向量角度
function vAngle(u, v) {
  return (u[0] * v[1] < u[1] * v[0] ? -1 : 1) * Math.acos(vRatio(u, v));
}

/**
 * 判断两个点是否重合，点坐标的格式为 [x, y]
 * @param {Array} point1 第一个点
 * @param {Array} point2 第二个点
 */
export function isSamePoint(point1, point2) {
  return point1[0] === point2[0] && point1[1] === point2[1];
}

// A 0:rx 1:ry 2:x-axis-rotation 3:large-arc-flag 4:sweep-flag 5: x 6: y
export default function getArcParams(startPoint, params) {
  let rx = params[1];
  let ry = params[2];
  const xRotation = mod((params[3] * Math.PI) / 180, Math.PI * 2);
  const arcFlag = params[4];
  const sweepFlag = params[5];
  // 弧形起点坐标
  const x1 = startPoint[0];
  const y1 = startPoint[1];
  // 弧形终点坐标
  const x2 = params[6];
  const y2 = params[7];
  const xp = (Math.cos(xRotation) * (x1 - x2)) / 2.0 + (Math.sin(xRotation) * (y1 - y2)) / 2.0;
  const yp = (-1 * Math.sin(xRotation) * (x1 - x2)) / 2.0 + (Math.cos(xRotation) * (y1 - y2)) / 2.0;
  const lambda = (xp * xp) / (rx * rx) + (yp * yp) / (ry * ry);

  if (lambda > 1) {
    rx *= Math.sqrt(lambda);
    ry *= Math.sqrt(lambda);
  }
  const diff = rx * rx * (yp * yp) + ry * ry * (xp * xp);

  let f = diff ? Math.sqrt((rx * rx * (ry * ry) - diff) / diff) : 1;

  if (arcFlag === sweepFlag) {
    f *= -1;
  }
  if (isNaN(f)) {
    f = 0;
  }

  // 旋转前的起点坐标，且当长半轴和短半轴的长度为 0 时，坐标按 (0, 0) 处理
  const cxp = ry ? (f * rx * yp) / ry : 0;
  const cyp = rx ? (f * -ry * xp) / rx : 0;

  // 椭圆圆心坐标
  const cx = (x1 + x2) / 2.0 + Math.cos(xRotation) * cxp - Math.sin(xRotation) * cyp;
  const cy = (y1 + y2) / 2.0 + Math.sin(xRotation) * cxp + Math.cos(xRotation) * cyp;

  // 起始点的单位向量
  const u = [(xp - cxp) / rx, (yp - cyp) / ry];
  // 终止点的单位向量
  const v = [(-1 * xp - cxp) / rx, (-1 * yp - cyp) / ry];
  // 计算起始点和圆心的连线，与 x 轴正方向的夹角
  const theta = vAngle([1, 0], u);

  // 计算圆弧起始点和终止点与椭圆圆心连线的夹角
  let dTheta = vAngle(u, v);

  if (vRatio(u, v) <= -1) {
    dTheta = Math.PI;
  }
  if (vRatio(u, v) >= 1) {
    dTheta = 0;
  }
  if (sweepFlag === 0 && dTheta > 0) {
    dTheta = dTheta - 2 * Math.PI;
  }
  if (sweepFlag === 1 && dTheta < 0) {
    dTheta = dTheta + 2 * Math.PI;
  }
  return {
    cx,
    cy,
    // 弧形的起点和终点相同时，长轴和短轴的长度按 0 处理
    rx: isSamePoint(startPoint, [x2, y2]) ? 0 : rx,
    ry: isSamePoint(startPoint, [x2, y2]) ? 0 : ry,
    startAngle: theta,
    endAngle: theta + dTheta,
    xRotation,
    arcFlag,
    sweepFlag,
  };
}