When alpha-complexes collapse onto codimension-1 submanifolds
When alpha-complexes collapse onto codimension-1 submanifolds
Given a finite set of points $P$ sampling an unknown smooth surface $\mathcal{M} \subseteq \mathbb{R}^3$, our goal is to triangulate $\mathcal{M}$ based solely on $P$. Assuming $\mathcal{M}$ is a smooth orientable submanifold of codimension 1 in $\mathbb{R}^d$, we introduce a simple algorithm, Naive Squash, which simplifies the $\alpha$-complex of $P$ …