Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Computing geodesic spectra of surfaces
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Genus and the geometry of the cut graph
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The tight orthogonal homotopic bases of closed oriented triangulated surfaces and their computing
Computers & Mathematics with Applications
Euclidean geodesic loops on high-genus surfaces applied to the morphometry of vestibular systems
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Computing shortest words via shortest loops on hyperbolic surfaces
Computer-Aided Design
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On the connectivity preserving minimum cut problem
Journal of Computer and System Sciences
| Hi-index | 0.00 |
Every compact orientable boundaryless surface M can be cut along simple loops with a common point v0, pairwise disjoint except at v0, so that the resulting surface is a topological disk; such a set of loops is called a fundamental system of loops for M . The resulting disk is a polygon in which the edges are pairwise identified on the surface; it is called a polygonal schema. Assuming that M is triangulated, and that each edge has a given length, we are interested in a shortest (or optimal) system homotopic to a given one, drawn on the vertex-edge graph of M. We prove that each loop of such an optimal system is a shortest loop among all simple loops in its homotopy class. We give a polynomial (under some reasonable assumptions) algorithm to build such a system. As a byproduct, we get a polynomial algorithm to compute a shortest simple loop homotopic to a given simple loop.