Graphs and algorithms
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Journal of Combinatorial Theory Series B
Computational complexity of combinatorial surfaces
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Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
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Contour trees and small seed sets for isosurface traversal
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Journal of the ACM (JACM)
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Surface Coding Based on Morse Theory
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Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method to construct coarse topological quadrangulations of closed triangulated surfaces, based on theoretical results about topological classification of surfaces and Morse theory. In order to compute a canonical set of generators, a Reeb graph is constructed on the surface using Dijkstra's algorithm. Some results are shown on different surfaces.