Proper Trigonometry For Rotating A Point Around The Origin

Joshua picture Joshua · Jul 2, 2010 · Viewed 21.2k times · Source

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;
}

Answer

Alexandros Gezerlis picture Alexandros Gezerlis · Jul 2, 2010

From Wikipedia

To carry out a rotation using matrices the point (x, y) to be rotated is written as a vector, then multiplied by a matrix calculated from the angle, θ, like so:

https://upload.wikimedia.org/math/0/e/d/0ed0d28652a45d730d096a56e2d0d0a3.png

where (x′, y′) are the co-ordinates of the point after rotation, and the formulae for x′ and y′ can be seen to be

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