line-rectangle collision detection

Question

I have one line (two point (x,y) (x1,y1)) and a rectangle with focus point (rx,ry). I need help to find out collision point between line and rectangle, an example in C++ wil

Answer 1

Theres a lot of information out there about interectioning shapes. http://www.geometrictools.com/LibFoundation/Intersection/Intersection.html is probably a very good starting spot. In fact it contains C++ code for line-rectangle intersection. And its by Dave Eberly who is fairly well known in the computer graphics world.

Having said that what I'd do if I needed my own algorithm is something like this:

1. Find the equation of the line containing the line-segment as a x + b y - 1 = 0;
2. evaluate f(x) = a x + b y - 1 for each vertex of the rectangle
3. If all corners are > 0 or all are < 0 you have no possible intersection.
4. Intersections can only occur on edges with one vertex having f(x)>0 and the other having f(x)< 0. So perform a line-segment to line-segment intersection with all such edges and the original line-segment.

This should work for arbitrary polygons. And so rotated rectangles wont be a problem.

If you need to speed things up a bit you can improve the rejection criteria in 3, by using axis-aligned bounding rectangles for the line segment and the rectangle.