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# Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing

A K Peters/CRC Press, September 2014

Abstract: A Versatile Framework for Handling Subdivided Geometric Objects. Combinatorial 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 and n-maps. Suitable for researchers and graduate students in geometric modeling, computational and discrete geometry, computer graphics, and image processing and analysis, the book presents the data structures, operations, and algorithms that are useful in handling subdivided geometric objects. It shows how to study data structures for the explicit representation of subdivided geometric objects and describes operations for handling the structures. The book also illustrates results of the design of data structures and operations.

Keywords: Combinatorial maps; Generalized Maps; Data-structures; Operations; Computer graphics; Image processing.

## BibTex references

@Book{DamLie14,
author = {Damiand, G. and Lienhardt, P.},
title = {Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing},
month = {September},
year = {2014},
publisher = {A K Peters/CRC Press}
}

## Table des matières :

1. Introduction
1. Subdivisions of Geometric Objects
2. Explicit Representations of Subdivisions
3. Numerous Structures
4. Cellular Structures
2. Preliminary Notions
1. Basic Topological Notions
2. Paper Surfaces
3. Classification of Paper Surfaces
4. Manifolds, Quasi-Manifolds, Pseudo-Manifolds, Complexes
5. Discrete Structures
6. Incidence Graphs
3. Intuitive Presentation
1. n-maps
2. n-Gmaps
4. n-Gmaps
1. Basic Definitions
2. Basic Operations
3. Completeness, Multi-Incidence
4. Data Structures, Iterators, and Algorithms
5. Complements
5. n-maps
1. Basic Definitions
2. Basic Operations
3. Completeness, Multi-Incidence
4. Data Structures, Iterators, and Algorithms
5. Complements
6. Operations
1. Closure
2. Removal
3. Contraction
4. Insertion
5. Expansion
6. Chamfering
7. Extrusion
8. Triangulation
7. Embedding for Geometric Modeling and Image Processing
1. Embedding
2. Geometric Modeling
3. Image Processing
8. Cellular Structures as Structured Simplicial Structures
1. Simplicial Structures
2. Numbered Simplicial Structures and Cellular Structures
3. Some Consequences
9. Comparison with Other Cellular Data Structures
1. History of Combinatorial Maps
2. Oriented Cellular Quasi-Manifolds
3. Orientable and Nonorientable Cellular Quasi-Manifolds
10. Concluding Remarks
• Bibliography
• Index

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