围绕原点旋转一个点的正确三角法

Proper Trigonometry For Rotating A Point Around The Origin(围绕原点旋转一个点的正确三角法)

问题描述

以下任何一种方法是否使用正确的数学方法来旋转一个点?如果有，哪一个是正确的?

Do either of the below approaches use the correct mathematics for rotating a point? If so, which one is correct?

POINT rotate_point(float cx,float cy,float angle,POINT p)
{
  float s = sin(angle);
  float c = cos(angle);

  // translate point back to origin:
  p.x -= cx;
  p.y -= cy;

  // Which One Is Correct:
  // This?
  float xnew = p.x * c - p.y * s;
  float ynew = p.x * s + p.y * c;
  // Or This?
  float xnew = p.x * c + p.y * s;
  float ynew = -p.x * s + p.y * c;

  // translate point back:
  p.x = xnew + cx;
  p.y = ynew + cy;
}

推荐答案

这取决于你如何定义angle.如果它是逆时针测量的(这是数学惯例)，那么正确的旋转是你的第一个:

It depends on how you define angle. If it is measured counterclockwise (which is the mathematical convention) then the correct rotation is your first one:

// This?
float xnew = p.x * c - p.y * s;
float ynew = p.x * s + p.y * c;

但如果是顺时针测量，那么第二个是正确的:

But if it is measured clockwise, then the second is correct:

// Or This?
float xnew = p.x * c + p.y * s;
float ynew = -p.x * s + p.y * c;

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