Segmenting a surface mesh into pants using Morse theory

Segmenting a Surface Mesh into Pants Using Morse Theory

A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple closed curves embedded in the surface that decompose the surface into pants. In this paper we present two Morse theory based algorithms for pants decomposition of a surface mesh. Both algorithms operates on a choice of...

Morse Theory for Implicit Surface Modeling

Morse theory describes the relationship between a function's critical points and the homotopy type of the function's domain. The theorems of Morse theory were developed speci cally for functions on a manifold. This work adapts these theorems for use with parameterized families of implicit surfaces in computer graphics. The result is a theoretical basis for the determination of the global topolo...

A Generalized Morse Theory

1. Abstract theory. Let M be a C-Riemannian manifold without boundary modeled on a separable Hubert space (see Lang [3]). For pÇzM we denote by ( , )p the inner product in the tangent space Mp and we define a function || || on the tangent bundle T(M) by ||z>|| = (v, v)J for vÇzMp. Given p and q in the same component of M we define p(p, q)==lnïfl\\<r'(t)\\dtt where the Inf is over all C 1 paths ...

A ug 2 00 5 Immersions of Pants into a Fixed Hyperbolic Surface

Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...

Morse Theory