How to rotate a vertex around a certain point?

Question

Imagine you have two points in 2d space and you need to rotate one of these points by X degrees with the other point acting as a center.

float distX = Math.abs( centerX -point2X ); float distY = Math.abs( centerY -point2Y );  float dist = FloatMath.sqrt( distX*distX + distY*distY ); 

So far I just got to finding the distance between the two points... any ideas where should I go from that?

Answer 1

The easiest approach is to compose three transformations:

1. A translation that brings point 1 to the origin
2. Rotation around the origin by the required angle
3. A translation that brings point 1 back to its original position

When you work this all out, you end up with the following transformation (where x is the desired angle of rotation in radians):

newX = centerX + (point2x-centerX)*Math.cos(x) - (point2y-centerY)*Math.sin(x);  newY = centerY + (point2x-centerX)*Math.sin(x) + (point2y-centerY)*Math.cos(x); 

Note that this makes the assumption that the angle x is negative for clockwise rotation (the so-called standard or right-hand orientation for the coordinate system). If that's not the case, then you would need to reverse the sign on the terms involving sin(x).

Answer 2

You need a 2-d rotation matrix http://en.wikipedia.org/wiki/Rotation_matrix

Your new point will be

 newX = centerX + ( cosX * (point2X-centerX) + sinX * (point2Y -centerY))  newY = centerY + ( -sinX * (point2X-centerX) + cosX * (point2Y -centerY)) 

because you are rotating clockwise rather than anticlockwise