A generalized combinatorial marching hypercube algorithm

We present a Generalized Combinatorial Marching Hypercubes algorithm to compute a cell complex approximation of a manifold of any dimension and co-dimension, that is, a manifold of dimension \(n-k\) $n-k$ embedded into an n-dimensional space. The algorithm uses combinatorial and topological methods to avoid the use of expensive lookup tables and hence is efficient in higher dimensions. We illustrate the effectiveness of our algorithm in higher dimensions and compare its performance with a similar algorithm based on a simplicial decomposition of the domain.