Given a polyhedral complex $P :=\bigcup_{i=1}^k P_i \in \mathbf{R}^n$ and the hyperplane $x_j = h$ where $x_j$ is one of the coordinates in $\mathbf{R}^n$. This hyperplane is basically $\in \mathbf{R}^{(n-1)}$. The polytopes $P_i$ are represented in the form of $Ax \leq b$.
I wish to find the intersection of this hyperplane and polyhedral complex and also implement it in code.
- Is there a straight-forward way to obtain the slice where this intersection happens? Ideally I would want the slice to be represented as a polyhedral complex.
Illustration of what I want, eg of a convex polyhedron:
image from : https://demonstrations.wolfram.com/IntersectionOfAConvexPolyhedronAndAPlane/