2D Euclidean vector rotations

Question

I have a euclidean vector a sitting at the coordinates (0, 1). I want to rotate a by 90 degrees (clockwise) around the origin: (0, 0).

If I have a proper understanding of how this should work, the resultant (x, y) coordinates after the rotation should be (1, 0). If I were to rotate it by 45 degrees (still clockwise) instead, I would have expected the resultant coordinates to be (0.707, 0.707).

theta = deg2rad(angle);  cs = cos(theta); sn = sin(theta);  x = x * cs - y * sn; y = x * sn + y * cs; 

Using the above code, with an angle value of 90.0 degrees, the resultant coordinates are: (-1, 1). And I am so damn confused. The examples seen in the following links represent the same formula shown above surely?

What have I done wrong? Or have I misunderstood how a vector is to be rotated?

Answer 1

Rotating a vector 90 degrees is particularily simple.

(x, y) rotated 90 degrees around (0, 0) is (-y, x).

If you want to rotate clockwise, you simply do it the other way around, getting (y, -x).

Answer 2

you should remove the vars from the function:

x = x * cs - y * sn; // now x is something different than original vector x y = x * sn + y * cs; 

create new coordinates becomes, to avoid calculation of x before it reaches the second line:

px = x * cs - y * sn;  py = x * sn + y * cs;