An introduction to solid modeling
An introduction to solid modeling
Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Topological design of sculptured surfaces
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Homeomorphism of 2-Complexes is Graph Isomorphism Complete
SIAM Journal on Computing
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Computing homology groups of simplicial complexes in R3
Journal of the ACM (JACM)
A fast surface-based procedure for object reconstruction from 3D scattered points
Computer Vision and Image Understanding
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
Physically-Based Stochastic Simplification of Mathematical Knots
IEEE Transactions on Visualization and Computer Graphics
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Creating volume models from edge-vertex graphs
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Computational Topology for Shape Modeling
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Using the CW-complex to represent the topological structure of implicit surfaces and solids
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
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In this paper a graph-based method is presented which not only characterizes topological classification of the tessellated surfaces but also simultaneously generates the substantial circles or generators on the surface. Canonical polygons cannot always be mapped back to the original surface in terms of the edges of the given triangles. Hence, instead of applying canonical transformation to the initial "word", an associated graph is constructed using the unique vertices in the word. The graph is then decomposed into its constituent loops and paths. Based on the type of edges present, the loops are classified into three types. The number of loops of each type in the graph is then used for counting the rank or genus and classification of the given surface as being open or closed, orientable or non-orientable. The image of the loops and paths on the original surface give the substantial circles and arcs on the surface respectively.