如何在JavaScript中通过已知圆弧起点、终点、半径和圆心坐标计算弧线上的坐标？

function calculateArcPoint(cx, cy, r, x1, y1, x2, y2, theta) {
  // 坐标系转换
  const x1_prime = x1 - cx;
  const y1_prime = y1 - cy;
  const x2_prime = x2 - cx;
  const y2_prime = y2 - cy;

  // 计算起点和终点角度 (弧度)
  let theta1 = Math.atan2(y1_prime, x1_prime);
  let theta2 = Math.atan2(y2_prime, x2_prime);

  // 调整角度范围，确保 theta2 > theta1
  if (theta2 < theta1) {
    theta2 += 2 * Math.PI;
  }

  // 检查theta是否在范围内
  if (theta < theta1 || theta > theta2) {
    console.error("角度theta不在弧线范围内");
    return null;
  }

  // 计算目标点坐标
  const x_prime = r * Math.cos(theta);
  const y_prime = r * Math.sin(theta);

  // 坐标系转换回原坐标系
  const x = x_prime + cx;
  const y = y_prime + cy;

  return { x, y };
}


// 示例使用
const cx = 100, cy = 100, r = 50;
const x1 = 150, y1 = 100, x2 = 100, y2 = 150;
const theta = Math.PI / 4; // 45度

const point = calculateArcPoint(cx, cy, r, x1, y1, x2, y2, theta);
console.log(point); // 输出弧线上45度角的坐标