We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its ...
Herbert Edelsbrunner, John Harer, Vijay Natarajan,...
We prove that the union complexity of a set of n constantcomplexity locally fat objects (which can be curved and/or non-convex) in the plane is O(λt+2(n) log n), where t is the m...
The paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as finite cell complexes. Th...
This paper addresses the complexity of computing the smallest-radius infinite cylinder that encloses an input set of n points in 3-space. We show that the problem can be solved in...
We present algorithms for constructing a hierarchy of increasingly coarse Morse complexes that decompose a piecewise linear 2-manifold. While Morse complexes are defined only in t...