G. Vegter. Computational topology. In Jacob E. Goodman and Joseph O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 28, pages 517-536. CRC Press LLC, Boca Raton, FL, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....primitives, loosing robustness. For example, 3d mesh compressions scheme as the famous EdgeBreaker has been considerably improved at a very low computational cost by topological considerations [Lop02] Computational Topology and its applications. The emerging field of computational topology [Veg97] deals actually with a broader scope of problems. Dey al. Dey99] have introduced six areas of applications: image processing, cartography, computer graphics, solid modeling, mesh generation and molecular modeling. The first Workshop on Computational Topology [Ber99] identified five other areas ....

G. Vegter. Computational topology. In J. E. Goodman and J. O'Rourke, editors, Handlebook of Discrete Computational Geometry, pages 517--536. CRC Press, 1997.

....S or the efficiency of algorithms to decide P remains to be thoroughly investigated. Computational topology deals with these algorithmic aspects of topology. Some work in the area related to this paper may be found in [5, 6, 8, 9, 17, 22] Two recent survey articles on computational topology are [7, 21]. The topological objects that we consider in this paper are surfaces or, equivalently, 2 manifolds. By a surface or 2 manifold we shall always mean a compact, connected, and boundaryless 2manifold. Everyday examples of such surfaces include spheres and tori (doughnuts) In fact, any finite object ....

G. Vegter, Computational topology, preprint, 1995.

.... to encompass both algorithmic questions in topology (for example, recognizing knots) and topological questions in algorithms (for example, whether a discrete construction preserves the topology of the underlying continuous domain) Research into computational topology has started already [Veg97] and is at present being undertaken separately by topology, computational geometry, and computer graphics communities, among others. Each of these fields has developed its own favored approaches to shape representation, manipulation, and analysis. Algorithms are often specific to certain data ....

Gert Vegter. Computational topology. In Jacob E. Goodman and Joseph O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 28, pages 517--536. CRC Press, Boca Raton, FL, 1997.

....simplicial complexes, in spaces of dimension higher than 3. ffl Find applications to real world objects. There seem interesting possibilities. Topology has long been applied in the physical sciences, and currently exciting applications are being found in molecular biology [8, 17] ffl See [3, 18] for a survey of related problems in the rapidly growing field of computational topology. Acknowledgement. We thank Tarun K. Mukherjee, Jadavpur University, Calcutta, for several motivating discussions. ....

G. Vegter, Computational topology, preprint , 1995.

....to topological objects, in particular simplicial complexes, in spaces of dimension higher than 3. ffl Find real applications. There are various possibilities. Topology has long been applied in the physical sciences, and currently exciting applications are arising in molecular biology [7, 18] See [3, 19] for a survey of related problems in the rapidly growing field of computational topology. Acknowledgement. We thank Professor Tarun K. Mukherjee of Jadavpur University, Calcutta, for several motivating discussions. We are grateful to an anonymous referee for comments that helped greatly to ....

G. Vegter, Computational topology, In Handbook of Discrete and Computational Geometry, J. E. Goodman and J. O'Rourke (ed.), CRC press, 1997.

....and that Whittlesey s criterion can be reduced efficiently to graph isomorphism. Therefore graph isomorphism and 2 complex homeomorphism are polynomial time equivalent. 1 Introduction This paper is concerned with a problem in Computational Topology: for recent surveys of the field, see [3, 10] A combinatorial surface is a topological space representable as a finite union of triangular regions, joined along edges. Examples include a sphere, a torus, a Klein bottle, and so on. More generally one can have a surface with boundary points on the boundary resemble points on the boundary ....

G. Vegter (1997). Computational Topology. In Handbook of Discrete and Computational Geometry, ed. J. E. Goodman and J. O'Rourke, CRC Press, 517--536.

....are conceivable in connection with morphing, where a suitable parametrization of 2 manifolds is provided by the disk obtained by cutting along the canonical generators. For general background material on computational topology, also in connection with applications, we refer to the surveys [5] and [9]. 2. SURFACES WITH COLLARS Triangulated surfaces will be represented by DoublyConnected Edge List, a data structure for representing subdivisions of surfaces. We refer to [3, Chapter 2] for details on this data structure. Note that every undirected edge of the triangulation corresponds to ....

G. Vegter. Computational topology. In J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 28, pages 517-536. CRC Press LLC, Boca Raton, FL, 1997.

....making it dicult to build isotopies in 3D. The vocabulary of this section is di erent from the one used in the proof of Tutte s theorem; it is more convenient to use combinatorial simplicial complexes (all simplicial complexes considered here are combinatorial, not geometric; see for example [39]) We introduce some other de nitions, generalizing those in 2D. A mapping f from a simplicial complex C into R d is a map from all the simplexes of C into P(R d ) satisfying: if fv 1 ; v p g is a simplex of C, f(fv 1 ; v p g) Convff(v 1 ) f(v p )g. An embedding of ....

G. Vegter. Computational topology. In J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 28, pages 517-536. CRC Press LLC, Boca Raton, FL, 1997.

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G. Vegter. Computational topology. In Jacob E. Goodman and Joseph O'Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 28, pages 517-536. CRC Press LLC, Boca Raton, FL, 1997.

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G. Vegter, Computational topology, in: J. E. Goodman, J. O'Rourke (Eds.), Handlebook of Discrete Computational Geometry, CRC Press, 1997, pp. 517-- 536. 17

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G. Vegter (1997). Computational Topology. In Handbook of Discrete and Computational Geometry, ed. J. E. Goodman and J. O'Rourke, CRC Press, 517--536.

No context found.

G. Vegter, Computational topology, in: J.E. Goodman, J. O'Rourke (Eds.), Handlebook of Discrete Computational Geometry, CRC Press, 1997, pp. 517--536.

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