Turning by any angle (sin and cos)

A quarter turn swaps coordinates. For any angle a we need numbers between: that is what cos and sin are for. Here is where the formula comes from, in two sentences:

• Turning by a sends the point (1, 0) to (cos a, sin a), and the point (0, 1) to (-sin a, cos a).
• Any point (x, y) is x steps of the first plus y steps of the second: (x*cos a − y*sin a, x*sin a + y*cos a).

Sanity checks: a = 0 gives cos = 1, sin = 0, so nothing changes. A quarter turn (a = 1.5708) gives cos = 0, sin = 1, so (x, y) becomes (-y, x), exactly the swap you just used.

float a = 0.5;                  // angle in radians (a full turn is 6.28318)
float c = cos(a);
float s = sin(a);
p = float2(c * p.x - s * p.y,  s * p.x + c * p.y);

Do not worry about memorising it. Everyone copies this snippet. What matters is understanding that it is applied to the pixel's position, before the shape is measured.