Javascript 几何：极坐标到笛卡尔坐标并再次返回

Question

我正在尝试创建一个程序，将极坐标值转换为笛卡尔值，然后再转换回来。我需要能够在两种类型之间切换而不需要更改数据。

我已经为 Polar 和 Cartesian 创建了类类型，并提供了在两者之间进行转换的方法。但我的数学不行。任何帮助将不胜感激！

class CartesianCoord {
  constructor(x, y) {
    this.x = x;
    this.y = y;
  }

  ToPolarCoord() {
    let p = new PolarCoord();
    p.radius = Math.sqrt(this.x * this.x + this.y * this.y);
    p.angle = Math.atan2(this.y, this.x);
    return p;
  }
}

class PolarCoord {
  constructor(radius, angle) {
    this.radius = radius;
    this.angle = angle;
    //this.angleDegree
  }
  set angleDegree(value) {
    this.angle = (value * 2 * Math.PI) / 360;
  }
  get angleDegree() {
    return (this.angle * 360) / (Math.PI * 2);
  }

  ToCartesianCoord() {
    let c = new CartesianCoord();
    c.x = this.radius * Math.cos(this.angle);
    c.y = this.radius * Math.sin(this.angle);
    return c;
  }
}

let polar = new PolarCoord(279, 18);
console.log(polar + "\n" + polar.radius + " " + polar.angle + " " + polar.angleDegree);

let cart = polar.ToCartesianCoord();
console.log(cart + "\n" + cart.x + " " + cart.y);

let polar2 = cart.ToPolarCoord();
console.log(polar2 + "\n" + polar2.radius + " " + polar2.angle + " " + polar2.angleDegree);

// I want polar and polar2 to be identical

Answer 1

由于 Math.atan2 只能返回 -Pi 和 Pi 弧度之间的角度，因此超出该范围的起始角度将不起作用。

解决此问题的一种方法是计算出初始角度中包含多少个 2Pi 的额外倍数，以便我们将角度减小到 -Pi 和 Pi 之间，这样我们就可以向输出添加那么多完整的旋转。

class CartesianCoord {
  constructor(x, y, extraCircles) {
    this.x = x;
    this.y = y;
    this.extraCircles = extraCircles;
  }

  ToPolarCoord() {
    let p = new PolarCoord();
    p.radius = Math.sqrt(this.x * this.x + this.y * this.y);
    p.angle = Math.atan2(this.y, this.x) + this.extraCircles * 2 * Math.PI;
    p.extraCircles = this.extraCircles;
    return p;
  }
}

class PolarCoord {
  constructor(radius, angle) {
    let currentAngle = angle;
    this.extraCircles = 0;
    while (currentAngle > Math.PI) {
      this.extraCircles++
      currentAngle -= 2 * Math.PI;
    }
    while (currentAngle < -Math.PI) {
      this.extraCircles--;
      currentAngle += 2 * Math.PI;
    }
    
    this.radius = radius;
    this.angle = angle;
  }
  set angleDegree(value) {
    this.angle = (value * 2 * Math.PI) / 360;
  }
  get angleDegree() {
    return (this.angle * 360) / (Math.PI * 2);
  }

  ToCartesianCoord() {
    let c = new CartesianCoord();
    c.x = this.radius * Math.cos(this.angle);
    c.y = this.radius * Math.sin(this.angle);
    c.extraCircles = this.extraCircles;
    return c;
  }
}

let polar = new PolarCoord(279, 18);
console.log(polar + "\n" + polar.radius + " " + polar.angle + " " + polar.angleDegree);

let cart = polar.ToCartesianCoord();
console.log(cart + "\n" + cart.x + " " + cart.y);

let polar2 = cart.ToPolarCoord();
console.log(polar2 + "\n" + polar2.radius + " " + polar2.angle + " " + polar2.angleDegree);

// I want polar and polar2 to be identical