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E-raamat: Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing

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  • Formaat: 404 pages
  • Ilmumisaeg: 19-Sep-2014
  • Kirjastus: Apple Academic Press Inc.
  • Keel: eng
  • ISBN-13: 9781040073650
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Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image ProcessingSuurem pilt
  • Formaat: 404 pages
  • Ilmumisaeg: 19-Sep-2014
  • Kirjastus: Apple Academic Press Inc.
  • Keel: eng
  • ISBN-13: 9781040073650
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"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"--

Damaind and Lienhardt focus mainly on two subclasses of combinatorial maps: n-Gmaps and n-maps to present a versatile framework for handling subdivided geometric objects. They cover preliminary notions, intuitive presentations, operations, embedding for geometric modeling and image processing, cellular structures as structured simplicial structures, and comparing other cellular data structures. The material is suitable for researchers and graduate students in geometric modeling, computational and discrete geometry, computer graphics, and imaging processing and analysis. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

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.

Arvustused

"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

Acknowledgements xi
List of Algorithms
xiii
List of Figures
xvii
1 Introduction
1(16)
1.1 Subdivisions of Geometric Objects
1(4)
1.1.1 Subdivided Objects
1(3)
1.1.2 Different Subdivisions
4(1)
1.2 Explicit Representations of Subdivisions
5(2)
1.2.1 Why Explicit Representations?
5(1)
1.2.2 Some Interests of Explicit Representations
6(1)
1.3 Numerous Structures
7(4)
1.3.1 Why Numerous Structures?
9(2)
1.3.2 Some Interests of Many Structures
11(1)
1.4 Cellular Structures
11(6)
1.4.1 Some Historical Milestones
13(1)
1.4.2 Outline
14(3)
2 Preliminary Notions
17(36)
2.1 Basic Topological Notions
17(5)
2.1.1 Basic Elements
17(2)
2.1.2 Continuous Map, Homeomorphism
19(3)
2.2 Paper Surfaces
22(6)
2.2.1 Basic Elements
22(1)
2.2.2 Basic Construction Operation: Identification of Edges
23(5)
2.3 Classification of Paper Surfaces
28(8)
2.3.1 Topological Surfaces
28(6)
2.3.2 Constructing any Subdivision of Any Surface
34(2)
2.4 Manifolds, Quasi-manifolds, Pseudo-manifolds, Complexes
36(6)
2.5 Discrete Structures
42(8)
2.5.1 Discrete Mappings
43(4)
2.5.2 Hypermaps, Group of Permutations, Orbits
47(1)
2.5.3 Partial Functions, Partial Permutations, Partial Involutions and Related Notions
48(2)
2.6 Incidence Graphs
50(3)
3 Intuitive Presentation
53(30)
3.1 n-Gmaps
53(16)
3.1.1 Objects without Boundary
53(9)
3.1.2 Objects with Boundary
62(6)
3.1.3 Generalization in Any Dimension
68(1)
3.2 n-Gmaps
69(14)
3.2.1 Objects without Boundary
70(6)
3.2.2 Objects with Boundary
76(3)
3.2.3 Generalization in Any Dimension
79(4)
4 n-Gmaps
83(50)
4.1 Basic Definitions
83(4)
4.2 Basic Operations
87(10)
4.2.1 Basic Tools
88(2)
4.2.2 Sew Operations
90(6)
4.2.3 Unsew Operations
96(1)
4.3 Completeness, Multi-Incidence
97(11)
4.3.1 Construction by Increasing Dimensions
97(3)
4.3.2 Construction Directly in a Given Dimension
100(4)
4.3.3 Completeness
104(1)
4.3.4 Multi-Incidence
105(3)
4.4 Data Structures, Iterators and Algorithms
108(15)
4.4.1 Data Structures
108(3)
4.4.2 Iterators
111(4)
4.4.3 Basic Tools
115(4)
4.4.4 Sew/Unsew Operations
119(4)
4.5 Complements
123(10)
4.5.1 Boundary Map
123(2)
4.5.2 Duality
125(2)
4.5.3 Orientability
127(3)
4.5.4 Classification of 2-Gmaps
130(3)
5 n-maps
133(52)
5.1 Basic Definitions
133(5)
5.2 Basic Operations
138(9)
5.2.1 Basic Tools
139(2)
5.2.2 Sew Operations
141(5)
5.2.3 Unsew Operations
146(1)
5.3 Completeness, Multi-Incidence
147(11)
5.3.1 Construction by Increasing Dimensions
148(3)
5.3.2 Construction Directly in a Given Dimension
151(2)
5.3.3 Completeness
153(1)
5.3.4 Multi-Incidence
154(4)
5.4 Data Structures, Iterators and Algorithms
158(16)
5.4.1 Data Structures
158(3)
5.4.2 Iterators
161(4)
5.4.3 Basic Tools
165(6)
5.4.4 Sew/Unsew Operations
171(3)
5.5 Complements
174(11)
5.5.1 Boundary Map
175(3)
5.5.2 Links between n-maps and n-Gmaps
178(3)
5.5.3 Classification of 2-maps
181(1)
5.5.4 Duality
182(3)
6 Operations
185(66)
6.1 Closure
185(13)
6.1.1 For n-Gmaps
186(6)
6.1.2 For n-maps
192(6)
6.2 Removal
198(16)
6.2.1 For n-Gmaps
199(6)
6.2.2 For n-maps
205(9)
6.3 Contraction
214(10)
6.3.1 For n-Gmaps
214(5)
6.3.2 For n-maps
219(5)
6.4 Insertion
224(6)
6.5 Expansion
230(3)
6.6 Chamfering
233(7)
6.7 Extrusion
240(5)
6.8 Triangulation
245(6)
7 Embedding for Geometric Modeling and Image Processing
251(44)
7.1 Embedding
251(4)
7.2 Geometric Modeling
255(17)
7.2.1 Embedding of n-Gmaps in Rd
255(3)
7.2.2 Geometric Operations
258(5)
7.2.3 Example of Modeling of an Object
263(9)
7.3 Image Processing
272(23)
7.3.1 Preliminary Notions
272(1)
7.3.2 2D Topological Map
273(4)
7.3.3 Operations
277(18)
8 Cellular Structures as Structured Simplicial Structures
295(40)
8.1 Simplicial Structures
297(11)
8.1.1 Abstract Simplicial Complexes
297(5)
8.1.2 Semi-Simplicial Sets
302(5)
8.1.3 Conversions of Simplicial Structures
307(1)
8.2 Numbered Simplicial Structures and Cellular Structures
308(17)
8.2.1 Numbered Simplicial Structures
308(5)
8.2.2 Simplicial Interpretation of n-Gmaps
313(7)
8.2.3 Simplicial Interpretation of Incidence Graphs
320(2)
8.2.4 n-Gmaps and Incidence Graphs
322(3)
8.3 Some Consequences
325(10)
8.3.1 Chain of Maps
325(4)
8.3.2 Euler-Poincare Characteristic for Combinatorial Maps
329(6)
9 Comparison with Other Cellular Data Structures
335(16)
9.1 History of Combinatorial Maps
336(2)
9.2 Oriented Cellular Quasi-Manifolds
338(7)
9.2.1 Winged-edge
338(2)
9.2.2 Half-edge
340(2)
9.2.3 Radial-edge
342(2)
9.2.4 Handle-face
344(1)
9.2.5 Nef Polyhedron
345(1)
9.3 Orientable and Nonorientable Cellular Quasi-Manifolds
345(6)
9.3.1 Quad-edge
345(2)
9.3.2 Facet-edge
347(1)
9.3.3 Cell-tuple
348(3)
10 Concluding Remarks
351(8)
Bibliography 359(20)
Index 379
Damiand, Guillaume; Lienhardt, Pascal
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