Computing shortest cycles using universal covering space

Authors:
Xiaotian Yin;Miao Jin;Xianfeng Gu
Affiliations:
State University of New York at Stony Brook, Computer Science Department, 11790, Stony Brook, NY, USA;State University of New York at Stony Brook, Computer Science Department, 11790, Stony Brook, NY, USA;State University of New York at Stony Brook, Computer Science Department, 11790, Stony Brook, NY, USA
Venue:
The Visual Computer: International Journal of Computer Graphics
Year:
2007

Citing 0
Cited 6

Computing geometry-aware handle and tunnel loops in 3D models

ACM SIGGRAPH 2008 papers
Computing Fundamental Group of General 3-Manifold

ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Computing handle and tunnel loops with knot linking

Computer-Aided Design
The tight orthogonal homotopic bases of closed oriented triangulated surfaces and their computing

Computers & Mathematics with Applications
Automatic generation of riemann surface meshes

GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Computing shortest homotopic cycles on polyhedral surfaces with hyperbolic uniformization metric

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we generalize the shortest path algorithm to the shortest cycles in each homotopy class on a surface with arbitrary topology, utilizing the universal covering space (UCS) in algebraic topology. In order to store and handle the UCS, we propose a two-level data structure which is efficient for storage and easy to process. We also pointed several practical applications for our shortest cycle algorithms and the UCS data structure.