Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Transforming curves on surfaces
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Using generic programming for designing a data structure for polyhedral surfaces
Computational Geometry: Theory and Applications - Special issue on applications and challenges
The Delaunay tetrahedralization from Delaunay triangulated surfaces
Proceedings of the eighteenth annual symposium on Computational geometry
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
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
Transforming 3D mesh surfaces into images by parameterization
Integrated image and graphics technologies
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
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
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
Conformal virtual colon flattening
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Splitting (complicated) surfaces is hard
Proceedings of the twenty-second annual symposium on Computational geometry
Planar parameterization for closed 2-manifold genus-1 meshes
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Plumber: a method for a multi-scale decomposition of 3D shapes into tubular primitives and bodies
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Generating smooth parting lines for mold design for meshes
Proceedings of the 2007 ACM symposium on Solid and physical modeling
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)
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Graph and map isomorphism and all polyhedral embeddings in linear time
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
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
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Shortest cut graph of a surface with prescribed vertex set
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Algorithms and theory of computation handbook
Drawing graphs in the plane with a prescribed outer face and polynomial area
GD'10 Proceedings of the 18th international conference on Graph drawing
The tight orthogonal homotopic bases of closed oriented triangulated surfaces and their computing
Computers & Mathematics with Applications
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
Planar drawings of higher-genus graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
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A closed orientable surface of genus $g$ can be obtained by appropriat e identification of pairs of edges of a $4g$-gon (the polygonal schema). The identified edges form $2g$ loops on the surface, that are disjoint except for their common end-point. These loops are generators of both the fundamental group and the homology group of the surface. The inverse problem is concerned with finding a set of $2g$ loops on a triangulated surface, such that cutting the surface along these loops yields a (canonical) polygonal schema. We present two optimal algorithms for this inverse problem. Both algorithms have been implemented using the CGAL polyhedron data structure.