# Determine whether or not a point lies within a rotated rectangle

I need some maths help for a 2D game I am programming. In this game I have a rectangle, specified by its centers' X and Y coordinates, and its width and height. I then rotate this rectangle via

halfWidth = width / 2;
halfHeight = height / 2;

x1 = -halfWidth * cos - (-halfHeight) * sin;
y1 = -halfWidth * sin + (-halfHeight) * cos;
x2 =  halfWidth * cos - (-halfHeight) * sin;
y2 =  halfWidth * sin + (-halfHeight) * cos;
x3 =  halfWidth * cos - halfHeight * sin;
y3 =  halfWidth * sin + halfHeight * cos;
x4 = -halfWidth * cos - halfHeight * sin;
y4 = -halfWidth * sin + halfHeight * cos;

x1 += x;
y1 += y;
x2 += x;
y2 += y;
x3 += x;
y3 += y;
x4 += x;
y4 += y;


That is working fine.

Additionally I have a point in the same Cartesian coordinate space, specified by pointX and pointY. Now I want check whether or not this point lies within the boudaries of the rotated rectangle -- but unfortunately I do not have a clue how to achieve this :)

Can you help me with this question?

Kind regards, Matthias

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Just for the record, I have found two interesting links on that topic: ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html http://www.visibone.com/inpoly/ Cheers! –  Matthias Jul 30 '11 at 13:56