We are currently implementing a discrete lattice-free model for simulating the growth of fungi, and our implementation could really benefit from built-in functions for determining the intersection between lines, a line and a polyhedron, and so on. Unfortunately, such computational geometry features do not seem to be built-in in Mathematica.
Anyone who is aware of a dedicated package that cover classical computational geometry functionalities.
I found a computational geometry package that may be able to help you. CompG allows you to find intersections between lines and the strength of the intersection. I believe you can also use this package to find intersections between a line and a polyhedron as well. Here is the link to the page in the Wolfram Library Archive: