A new representation of orientable 2-manifold polygonal surfaces for geometric modelling
Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modern point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used data structures are also presented in terms of time and space efficiency.
Key wordsShape representation Combinatorial data structure Computational topology
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- Baumgart, B.G., 1972. Winged-edge Polyhedron Representation. Technical report, STAN-CS-320, Stanford University.Google Scholar
- Cooke, G.E., Finney, R.L., 1967. Homology of Cell Complexes. Princeton University Press.Google Scholar
- de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O., 1997. Computational Geometry: Algorithms and Applications. Springer.Google Scholar
- do Carmo, M.P., 1976. Differential Geometry for Curves and Surfaces. Prentice-Hall.Google Scholar
- Edelsbrunner, H., 1987. Algorithms in Combinatorial Geometry, EATCS Monographs on Theoretical Computer Science (Vol. 10). Springer-Veralg.Google Scholar
- Fomenko, A.T., Kunii, T.L., 1997. Topological Modelling for Visualization. Springer.Google Scholar
- Giblin, P.J., 1981. Graphs, Surfaces and Homology (2nd Ed.). Chapman and Hall.Google Scholar
- Gross, J.L., Tucker, T.W., 1987. Topological Graph Theory. Wiley-Interscience.Google Scholar
- Mantyla, M., 1988. An Introduction to Solid Modelling. Computer Science Press.Google Scholar
- Preparata, F.P., Shamos, M.I., 1985. Computational Geometry: An Introduction. Springer-Verlag.Google Scholar
- Sieradski, A.J., 1992. An Introduction to Topology and Homotopy. PWS-KENT Pub.Google Scholar