Topological quadrangulations of closed triangulated surfaces using the Reeb graph

Authors:
Franck Hétroy;Dominique Attali
Affiliations:
LIS Laboratory, Domaine Universitaire, BP 46, 38402 Saint Martin d' Hères cedex, France;LIS Laboratory, Domaine Universitaire, BP 46, 38402 Saint Martin d' Hères cedex, France
Venue:
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Year:
2003

Citing 17
Cited 6

Graphs and algorithms

Graphs and algorithms
Minimal quadrangulations of orientable surfaces

Journal of Combinatorial Theory Series B
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms

ACM Transactions on Graphics (TOG)
Computational complexity of combinatorial surfaces

SCG '90 Proceedings of the sixth annual symposium on Computational geometry
C1-surface splines

SIAM Journal on Numerical Analysis
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

SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Scattered Data Interpolation Using C2 Supersplines of Degree Six

SIAM Journal on Numerical Analysis
A feature-based approach for smooth surfaces

SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Contour trees and small seed sets for isosurface traversal

SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing homology groups of simplicial complexes in R3

Journal of the ACM (JACM)
Level set diagrams of polyhedral objects

Proceedings of the fifth ACM symposium on Solid modeling and applications
Computing contour trees in all dimensions

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Semi-regular mesh extraction from volumes

Proceedings of the conference on Visualization '00
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
Surface Coding Based on Morse Theory

IEEE Computer Graphics and Applications

Reeb graphs for shape analysis and applications

Theoretical Computer Science
Describing shapes by geometrical-topological properties of real functions

ACM Computing Surveys (CSUR)
Efficient algorithms for computing Reeb graphs

Computational Geometry: Theory and Applications
A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes

Proceedings of the twenty-sixth annual symposium on Computational geometry
Quading triangular meshes with certain topological constraints

Journal of Computational and Applied Mathematics
Technical Section: Topological saliency

Computers and Graphics

Quantified Score

Hi-index	0.01

Visualization

Abstract

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 for the construction of coarse topological quadrangulations of closed triangulated surfaces, based on Morse theory. In order to construct on the surface a quadrangulation of its canonical polygonal schema, we compute first a Reeb graph then a canonical set of generators embedded on the surface. Some results are shown on different surfaces.