0

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:

enter image description here

image from : https://demonstrations.wolfram.com/IntersectionOfAConvexPolyhedronAndAPlane/

stateless
  • 121
  • 8
  • @NominalAnimal if you can answer this question.. since you answered one about hypersphere intersection previously here - https://math.stackexchange.com/questions/1819802/intersection-of-hypersphere-and-hyperplane-question?rq=1 – stateless Feb 03 '23 at 06:49
  • @amd if you can answer this question.. since you answered one about hypersphere intersection previously here - https://math.stackexchange.com/questions/1819802/intersection-of-hypersphere-and-hyperplane-question?rq=1 – stateless Feb 03 '23 at 06:49

0 Answers0