I try to find the contact points of a plane when it is placed on an uneven surface. For example a book that is placed on uneven terrain, where would it touch the ground?
I already have some ideas how to approach this problem (in 3D):
- find the maximum of the surface underneath the plane
- rotate the surface until another point intersects the plane
- rotate again to find another point
Example in 2 dimensions:
Do you know mathematical methods that could help me there?
Edit:
The surface might have edges and jumps and comes from a point cloud. The plane has finite width and length. The solution doesn't need to be highly accurate (the generation of the point cloud might be noisy to begin with). A fast solution would be preferred. At the moment I try to find ways to approach this problem.