By Guillaume Damiand, Pascal Lienhardt.
"Although they're much less widely recognized than different types, combinatorial maps are very robust info constructions and will be invaluable in lots of functions, together with special effects and snapshot processing. The ebook introduces those information buildings, describes algorithms and knowledge buildings linked to them, makes connections to different universal buildings, and demonstrates the best way to use those buildings in geometric modeling and photo processing. the information constructions and algorithms brought within the e-book may be on hand in a C++ library at the authors' website"-- Read more...
Introduction Subdivisions of Geometric items particular Representations of Subdivisions a number of constructions mobile buildings initial Notions simple Topological Notions Paper Surfaces category of Paper Surfaces Manifolds, Quasi-Manifolds, Pseudo-Manifolds, Complexes Discrete constructions prevalence Graphs Intuitive Presentation n-maps n-Gmaps n-Gmaps easy Definitions simple Operations Completeness, Multi-Incidence info buildings, Iterators, and Algorithms enhances n-maps easy Definitions uncomplicated Operations Completeness, Multi-Incidence information buildings, Iterators, and Algorithms enhances Operations Closure removing Contraction Insertion growth Chamfering Extrusion Triangulation Embedding for Geometric Modeling and picture Processing Embedding Geometric Modeling photo Processing mobile buildings as based Simplicial constructions Simplicial buildings Numbered Simplicial constructions and mobile buildings a few results comparability with different mobile facts constructions historical past of Combinatorial Maps orientated mobile Quasi-Manifolds Orientable and Nonorientable mobile Quasi-Manifolds Concluding feedback Bibliography Index
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Extra info for Combinatorial maps : efficient data structures for computer graphics and image processing
The exchange theorem states that T Sb,q,g = T Sb,q−2,g+1 when q ≥ 3. For instance, 4 It is a Klein bottle, although the relation with the Klein bottle with one boundary depicted in Fig. 15(a) is not obvious! Nevertheless, it is possible to transform the second one to get the first one. Note that in order to get a proof of equivalence, it would be necessary to prove that the transformations do not change the topology... 16 (a) An annulus. (b) A torus with one boundary. (c) A Klein bottle with one boundary.
9). So a paper surface can be made of a single face, or by many faces glued by identifying several pairs of edges. e. partitioned) into vertices, edges and faces. Incidence and adjacency relations The “boundary” relation corresponds to the incidence relation: more precisely, an edge (resp. a vertex) which belongs to the boundary of a face is incident to the face, and conversely, the face is incident to the edge (resp. to the vertex). e. the vertex meets the edge), the vertex and the edge are incident to each other.
For instance, all polygons depicted in Fig. 7 have one boundary; their Euler characteristic is equal to 1, they are orientable, so their orientability factor is equal to 0, and their genus is null. All polygons have these characteristics (all have one boundary, they are orientable, their Euler characteristic is equal to 1, since they have one face, and vertices and edges in equal numbers), but other surfaces too, for instance the gluing of a square and a triangle, or the gluing of two squares: cf.
Combinatorial maps : efficient data structures for computer graphics and image processing by Guillaume Damiand, Pascal Lienhardt.