Combinatorial maps : efficient data structures for computer by Guillaume Damiand, Pascal Lienhardt.

By Guillaume Damiand, Pascal Lienhardt.

"Although they're much less widely recognized than different versions, combinatorial maps are very robust facts buildings and will be helpful in lots of functions, together with special effects and photograph processing. The ebook introduces those facts constructions, describes algorithms and information buildings linked to them, makes connections to different universal buildings, and demonstrates the way to use those constructions in geometric modeling  Read more...

Introduction Subdivisions of Geometric items particular Representations of Subdivisions a number of constructions mobile constructions initial Notions uncomplicated Topological Notions Paper Surfaces category of Paper Surfaces Manifolds, Quasi-Manifolds, Pseudo-Manifolds, Complexes Discrete buildings prevalence Graphs Intuitive Presentation n-maps n-Gmaps n-Gmaps uncomplicated Definitions uncomplicated Operations Completeness, Multi-Incidence facts constructions, Iterators, and Algorithms enhances n-maps easy Definitions simple Operations Completeness, Multi-Incidence information constructions, Iterators, and Algorithms enhances Operations Closure removing Contraction Insertion growth Chamfering Extrusion Triangulation Embedding for Geometric Modeling and photograph Processing Embedding Geometric Modeling snapshot Processing mobile constructions as established Simplicial buildings Simplicial buildings Numbered Simplicial buildings and mobile constructions a few results comparability with different mobile information constructions heritage of Combinatorial Maps orientated mobile Quasi-Manifolds Orientable and Nonorientable mobile Quasi-Manifolds Concluding feedback Bibliography Index

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Combinatorial maps : efficient data structures for computer graphics and image processing

"Although they're much less widely recognized than different versions, combinatorial maps are very robust facts constructions and will be precious in lots of functions, together with special effects and photo processing. The ebook introduces those info constructions, describes algorithms and knowledge buildings linked to them, makes connections to different universal buildings, and demonstrates the right way to use those buildings in geometric modeling and photo processing.

Visual and Spatial Analysis

Complicated visible research and challenge fixing has been performed effectively for millennia. The Pythagorean Theorem used to be confirmed utilizing visible potential greater than 2000 years in the past. within the nineteenth century, John Snow stopped a cholera epidemic in London through featuring particular water pump be close down. He came across that pump via visually correlating facts on a urban map.

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Removing a boundary: Fig. 13. Let e and e be such that they belong to a same boundary, and they share their two extremity vertices v and v : so their incident boundary contains only e and e . There is only one possible way to identify e and e , since loops are not allowed, and the boundary vanishes. So b = b − 1. This identification removes one edge (e and e are identified), so c = c + 1. The orientability is not modified. If S is orientable, it can be coherently oriented: assume e is oriented from v to v ; thus e is oriented from v to v, since they are consecutive in their incident boundary, and this boundary is coherently oriented; so the edge resulting from the identification of e and e is coherently oriented with respect to its incident faces.

E. being homeomorphic to an nsimplex), is homeomorphic to a closed n-ball, so it is a manifold with one boundary. We will see later that other definitions of n-cells do not involve this property (cf. 20 (a) A closed 1-cell. (b) A closed 2-cell. (c) A closed 3-cell. (d) Two closed 2-cells; arrows at left denote the homeomorphism between two 1-cells, leading to their identification.

Faces: the initial twenty-four edges are identified into the resulting twelve sewn edges of the cube. Unnecessary constraints In order to simplify the study of surface construction, assume the boundary of any face contains at least three edges and three vertices. Similarly, assume that the boundary of an edge contains at least, and thus exactly, two vertices (in other words, no edge is a loop). Moreover, when two edges are identified, they belong to the boundaries of two distinct faces: in other words, it is forbidden to identify two edges incident to a same face.

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