Question

Given a center point, width, height and angle forming an OBB, how can I find if a given point P is inside the OBB?

Thanks

Answer 1

I take it that the wrinkle in your problem is that the bounding box can be rotated? If so, the easiest solution to me seems to be to do all calculations in the rotated coordinate plane, centered on the center of the bounding box.

To calculate the coordinates of the point relative to these axes:

newy = sin(angle) * (oldy - centery) + cos(angle) * (oldx - centerx);
newx = cos(angle) * (oldx - centerx) - sin(angle) * (oldy - centery);

(you may need to adjust this depending on how angle is supposed to be measured, I’ll leave that to you, since you didn’t specify)

Then hit test, the normal way:

return (newy > centery - height / 2) && (newy < centery + height / 2) 
    && (newx > centerx - width / 2) && (newx < centerx + width / 2);