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

"Although they are less widely known than other models, combinatorial maps are very powerful data structures and can be useful in many applications, including computer graphics and image processing. The book introduces these data structures, describes algorithms and data structures associated with them, makes connections to other common structures, and demonstrates how to use these structures in geometric modeling and image processing. The data structures and algorithms introduced in the book will be available in a C++ library on the authors' website"-- Read more... Introduction Subdivisions of Geometric Objects Explicit Representations of Subdivisions Numerous Structures Cellular Structures Preliminary Notions Basic Topological Notions Paper Surfaces Classification of Paper Surfaces Manifolds, Quasi-Manifolds, Pseudo-Manifolds, Complexes Discrete Structures Incidence Graphs Intuitive Presentation n-maps n-Gmaps n-Gmaps Basic Definitions Basic Operations Completeness, Multi-Incidence Data Structures, Iterators, and Algorithms Complements n-maps Basic Definitions Basic Operations Completeness, Multi-Incidence Data Structures, Iterators, and Algorithms Complements Operations Closure Removal Contraction Insertion Expansion Chamfering Extrusion Triangulation Embedding for Geometric Modeling and Image Processing Embedding Geometric Modeling Image Processing Cellular Structures as Structured Simplicial Structures Simplicial Structures Numbered Simplicial Structures and Cellular Structures Some Consequences Comparison with Other Cellular Data Structures History of Combinatorial Maps Oriented Cellular Quasi-Manifolds Orientable and Nonorientable Cellular Quasi-Manifolds Concluding Remarks Bibliography Index "An excellent technical teaching tool, especially recommended for college library mathematics and computer science shelves."--Midwest Book Review, January 2015"Guillaume Damiand and Pascal Lienhardt have produced an excellent book that discusses in full details a family of data structures for representing explicitly the connectivity of low-dimensional meshes, such as those used for some image and terrain processing or for modeling and animating geometric shapes. it provides a mathematically rigorous introduction to this area of research and gives the attentive reader a deep understanding of n-Gmaps and n-Maps, both as theoretical models and as practical data structures and associated operators."-Jarek Rossignac, Georgia Institute of Technology "Although they are less widely known than other models, combinatorial maps are very powerful data structures and can be useful in many applications, including computer graphics and image processing. The book introduces these data structures, describes algorithms and data structures associated with them, makes connections to other common structures, and demonstrates how to use these structures in geometric modeling and image processing. The data structures and algorithms introduced in the book will be available in a C++ library on the authors' website"-- Provided by publisher A Versatile Framework for Handling Subdivided Geometric ObjectsCombinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing gathers important ideas related to combinatorial maps and explains how the maps are applied in geometric modeling and image processing. It focuses on two subclasses of combinatorial maps: n-Gmaps an