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.
Here's an idea which may or may not help in your particular problem - but if it does it should be reasonably accurate and efficient.
Find the convex hull of your surface (there are algorithms for that for various inputs). Your book should come to rest on a facet. If there are no facets (or are too few, or they are too small) then you're in an unstable situation - think of balancing the book on a sphere.