Computing shortest homotopic cycles on polyhedral surfaces with hyperbolic uniformization metric

作者：Jin Miao^*; Ding Ning; Yang Yang

来源：Computer-Aided Design, 2013, 45(2): 113-123.

DOI：10.1016/j.cad.2012.07.015

• Unique shortest homotopic cycle
• Hyperbolic uniformization metric
• Local loop shortening
• Extremal quasiconformal mapping
• Homotopy detection

The problem of computing shortest homotopic cycles on a surface has various applications in computational geometry and graphics. In general, shortest homotopic cycles are not unique, and local shortening algorithms can become stuck in local minima. For surfaces with a negative Euler characteristic that can be given a hyperbolic uniformization metric, however, we show that they are unique and can be found by a simple locally shortening algorithm. We also demonstrate two applications: constructing extremal quasiconformal mappings between surfaces with the same topology, which minimize angular distortion, and detecting homotopy between two paths or cycles on a surface. Published by Elsevier Ltd

• 出版日期2013-2