Determining contractibility of curves
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
Transforming curves on surfaces
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics
Computing shortest cycles using universal covering space
The Visual Computer: International Journal of Computer Graphics
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
IEEE Transactions on Visualization and Computer Graphics
Surface Mapping Using Consistent Pants Decomposition
IEEE Transactions on Visualization and Computer Graphics
Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
A Level Set Formulation of Geodesic Curvature Flow on Simplicial Surfaces
IEEE Transactions on Visualization and Computer Graphics
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shortest cut graph of a surface with prescribed vertex set
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Computing shortest words via shortest loops on hyperbolic surfaces
Computer-Aided Design
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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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.