Kink-free deformations of polygons
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Constructive Hopf's Theorem: Or How to Untangle Closed Planar Curves
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Determining contractibility of curves
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Algorithms for manifolds and simplicial complexes in Euclidean 3-space (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Computing homology groups of simplicial complexes in R3
Journal of the ACM (JACM)
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Topological Quadrangulations of Closed Triangulated Surfaces Using the Reeb Graph
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Graph based topological analysis of tessellated surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Topological quadrangulations of closed triangulated surfaces using the Reeb graph
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Cycle bases of graphs and sampled manifolds
Computer Aided Geometric Design
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Graph and map isomorphism and all polyhedral embeddings in linear time
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Computational Geometry: Theory and Applications
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
Algorithms and theory of computation handbook
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Space complexity of perfect matching in bounded genus bipartite graphs
Journal of Computer and System Sciences
Measuring similarity between curves on 2-manifolds via homotopy area
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We investigate the computational problems associated with combinatorial surfaces. Specifically, we present an algorithm (based on the Brahana-Dehn-Heegaard approach) for transforming the polygonal schema of a closed triangulated surface into its canonical form in &Ogr;(n log n) time, where n is the total number of vertices, edges and faces. We also give an &Ogr;(n log n + gn) algorithm for constructing canonical generators of the fundamental group of a surface of genus g. This is useful in constructing homeomorphisms between combinatorial surfaces.