Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing, 1st Edition (Hardback) book cover

Combinatorial Maps

Efficient Data Structures for Computer Graphics and Image Processing, 1st Edition

By Guillaume Damiand, Pascal Lienhardt

A K Peters/CRC Press

404 pages | 223 B/W Illus.

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Hardback: 9781482206524
pub: 2014-09-19
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Description

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.

Reviews

"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

Table of Contents

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

Subject Categories

BISAC Subject Codes/Headings:
COM012000
COMPUTERS / Computer Graphics
TEC015000
TECHNOLOGY & ENGINEERING / Imaging Systems