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Table of Contents
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Short Table of Contents
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Package Overview
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Bibliography
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Index
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Title Page
CGAL User and Reference Manual
Table of Contents
Title Page
Bibliography
Package Overview
Index
Table of Contents
Short Table of Contents
I General Introduction
1 General Introduction
1.1
License Issues
1.2
Third Party Software
1.3
Advanced
1.4
Namespace CGAL
1.5
Inclusion Order of Header Files
1.6
Compile-time Flags to Control Inlining
1.7
Checks
II Kernels
2 2D and 3D Kernel
User Manual
2.1
Introduction
2.2
Kernel Representations
2.3
Kernel Geometry
2.4
Predicates and Constructions
2.5
Extensible Kernel
2.6
Kernel Related Tools
Reference Manual
2.7
Concepts
2.8
Kernel Classes and Operations
2.9
Predefined Kernels
2.10
Kernel Objects
2.11
Constants and Enumerations
2.12
Global Functions
2.13
Kernel Function Object Concepts
2.14
Tag Classes
3 dD Kernel
User Manual
3.1
Introduction
3.2
Kernel Representations
3.3
Kernel Geometry
3.4
Predicates and Constructions
Reference Manual
3.5
Linear Algebra Concepts and Classes
3.6
Kernel Objects
3.7
Global Kernel Functions
3.8
Kernel Concept
4 2D Circular Kernel
User Manual
4.1
Introduction
4.2
Software Design
4.3
Examples
4.4
Design and Implementation History
Reference Manual
4.5
Geometric Concepts
4.6
Algebraic Concepts
4.7
Geometric Kernels and Classes
4.8
Algebraic Kernel and Classes
4.9
Traits Classes for C
GAL
Arrangements
4.10
Alphabetical List of Reference Pages
III Convex Hull Algorithms
5 2D Convex Hulls and Extreme Points
User Manual
5.1
Introduction
5.2
Convex Hull
5.3
Example using Graham-Andrew's Algorithm
5.4
Extreme Points and Hull Subsequences
5.5
Traits Classes
5.6
Convexity Checking
Reference Manual
5.7
Classified Reference Pages
5.8
Alphabetical List of Reference Pages
6 3D Convex Hulls
User Manual
6.1
Introduction
6.2
Static Convex Hull Construction
6.3
Incremental Convex Hull Construction
6.4
Dynamic Convex Hull Construction
Reference Manual
6.5
Classified Reference Pages
6.6
Alphabetical List of Reference Pages
7 dD Convex Hulls and Delaunay Triangulations
User Manual
7.1
Introduction
7.2
dD Convex Hull
7.3
Delaunay Triangulation
Reference Manual
7.4
Classified Reference Pages
7.5
Alphabetical List of Reference Pages
IV Polygons and Polyhedra
8 2D Polygons
User Manual
8.1
Introduction
8.2
Example
Reference Manual
8.3
Classified Reference Pages
8.4
Alphabetical List of Reference Pages
9 2D Polygon Partitioning
User Manual
9.1
Introduction
9.2
Monotone Partitioning
9.3
Convex Partitioning
Reference Manual
9.4
Classified Reference Pages
9.5
Alphabetical List of Reference Pages
10 3D Polyhedral Surfaces
User Manual
10.1
Introduction
10.2
Definition
10.3
Example Programs
10.4
File I/O
10.5
Extending Vertices, Halfedges, and Facets
10.6
Advanced Example Programs
Reference Manual
10.7
Classified Reference Pages
10.8
Alphabetical List of Reference Pages
11 Halfedge Data Structures
User Manual
11.1
Introduction
11.2
Software Design
11.3
Example Programs
Reference Manual
11.4
Classified Reference Pages
11.5
Alphabetical List of Reference Pages
V Polygon and Polyhedron Operations
12 2D Regularized Boolean Set-Operations
User Manual
12.1
Introduction
12.2
Boolean Set-Operations on Linear Polygons
12.3
Boolean Set-Operations on General Polygons
Reference Manual
12.4
Classified Reference Pages
12.5
Alphabetical List of Reference Pages
13 2D Boolean Operations on Nef Polygons
User Manual
13.1
Introduction
13.2
Construction and Composition
13.3
Exploration
13.4
Traits Classes
13.5
Implementation
Reference Manual
13.6
Classified Reference Pages
13.7
Alphabetical List of Reference Pages
14 2D Boolean Operations on Nef Polygons Embedded on the Sphere
User Manual
14.1
Introduction
14.2
Restricted Spherical Geometry
14.3
Example Programs
Reference Manual
14.4
Classified Reference Pages
14.5
Alphabetical List of Reference Pages
15 3D Boolean Operations on Nef Polyhedra
User Manual
15.1
Introduction
15.2
Definition
15.3
Infimaximal Box
15.4
Regularized Set Operations
15.5
Example Programs
15.6
File I/O
15.7
Further Example Programs
15.8
Visualization
Reference Manual
15.9
Classified Reference Pages
15.10
Alphabetical List of Reference Pages
16 2D Straight Skeleton and Polygon Offsetting
User Manual
16.1
Definitions
16.2
Representation
16.3
API
16.4
Straight Skeletons, Medial Axis and Voronoi Diagrams
16.5
Usages of the Straight Skeletons
16.6
Straight Skeleton of a General Figure in the Plane
Reference Manual
16.7
Classified Reference Pages
16.8
Alphabetical List of Reference Pages
VI Arrangements
17 2D Arrangements
User Manual
17.1
Introduction
17.2
The Main Arrangement Class
17.3
Issuing Queries on an Arrangement
17.4
Free Functions in the Arrangement Package
17.5
Traits Classes
17.6
The Notification Mechanism
17.7
Extending the D
CEL
17.8
Overlaying Arrangements
17.9
Storing the Curve History
17.10
Input/Output Functions
17.11
Adapting to B
OOST
Graphs
17.12
How To Speed Up Your Computation
Reference Manual
17.13
Classified Reference Pages
17.14
Alphabetical List of Reference Pages
18 2D Intersection of Curves
User Manual
18.1
Introduction
Reference Manual
18.2
Alphabetical List of Reference Pages
19 2D Snap Rounding
User Manual
19.1
Introduction
19.2
What is Snap Rounding/Iterated Snap Rounding
19.3
Terms and Software Design
19.4
Four Line Segment Example
Reference Manual
19.5
Alphabetical List of Reference Pages
VII Triangulations and Delaunay Triangulations
20 2D Triangulations
User Manual
20.1
Definitions
20.2
Representation
20.3
Software Design
20.4
Basic Triangulations
20.5
Delaunay Triangulations
20.6
Regular Triangulations
20.7
Constrained Triangulations
20.8
Constrained Delaunay Triangulations
20.9
Constrained Triangulations Plus
20.10
The Triangulation Hierarchy
20.11
Flexibility: Using Customized Vertices and Faces
20.12
Design and Implementation History
Reference Manual
20.13
Classified Reference Pages
20.14
Alphabetical List of Reference Pages
21 2D Triangulation Data Structure
User Manual
21.1
Definition
21.2
The Concept of Triangulation Data Structure
21.3
The Default Triangulation Data Structure
Reference Manual
21.4
Classified Reference Pages
21.5
Alphabetical List of Reference Pages
22 3D Triangulations
User Manual
22.1
Representation
22.2
Delaunay Triangulation
22.3
Regular Triangulation
22.4
Triangulation Hierarchy
22.5
Software Design
22.6
Examples
22.7
Design and Implementation History
Reference Manual
22.8
Classified Reference Pages
22.9
Alphabetical List of Reference Pages
23 3D Triangulation Data Structure
User Manual
23.1
Representation
23.2
Software Design
23.3
Examples
23.4
Design and Implementation History
Reference Manual
23.5
Classified Reference Pages
23.6
Alphabetical List of Reference Pages
24 2D Alpha Shapes
User Manual
24.1
Definitions
24.2
Functionality
24.3
Concepts and Models
24.4
Examples
Reference Manual
24.5
Classified Reference Pages
24.6
Alphabetical List of Reference Pages
25 3D Alpha Shapes
User Manual
25.1
Definitions
25.2
Functionality
25.3
Concepts and Models
25.4
Examples
Reference Manual
25.5
Classified Reference Pages
25.6
Alphabetical List of Reference Pages
VIII Voronoi Diagrams
26 2D Segment Delaunay Graphs
User Manual
26.1
Definitions
26.2
Software Design
26.3
The Geometric Traits
26.4
The Segment Delaunay Graph Hierarchy
26.5
Examples
Reference Manual
26.6
Classified Reference Pages
26.7
Alphabetical List of Reference Pages
27 2D Apollonius Graphs (Delaunay Graphs of Disks)
User Manual
27.1
Definitions
27.2
Software Design
27.3
The Geometric Traits
27.4
The Apollonius Graph Hierarchy
27.5
Examples
Reference Manual
27.6
Classified Reference Pages
27.7
Alphabetical List of Reference Pages
28 2D Voronoi Diagram Adaptor
User Manual
28.1
Introduction
28.2
Software Design
28.3
The Adaptation Traits
28.4
The Adaptation Policy
28.5
Examples
Reference Manual
28.6
Classified Reference Pages
28.7
Alphabetical List of Reference Pages
IX Meshing
29 2D Conforming Triangulations and Meshes
User Manual
29.1
Conforming Triangulations
29.2
Meshes
Reference Manual
29.3
Classified Reference Pages
29.4
Alphabetical List of Reference Pages
30 3D Surface Mesher
User Manual
30.1
Introduction
30.2
The Surface Mesher Interface
30.3
Examples
30.4
Meshing Criteria, Guarantees and Variations
30.5
Design and Implementation History
Reference Manual
30.6
Classified Reference Pages
30.7
Alphabetical List of Reference Pages
31 3D Surface Subdivision Methods
User Manual
31.1
Introduction
31.2
Subdivision Method
31.3
A Quick Example: Catmull-Clark Subdivision
31.4
Catmull-Clark Subdivision
31.5
Refinement Host
31.6
Geometry Policy
31.7
The Four Subdivision Methods
31.8
Other Subdivision Methods
Reference Manual
31.9
Classified Reference Pages
31.10
Alphabetical List of Reference Pages
32 Planar Parameterization of Triangulated Surface Meshes
User Manual
32.1
Introduction
32.2
Basics
32.3
Surface Parameterization Methods
32.4
Sparse Linear Algebra
32.5
Cutting a Mesh
32.6
Output
32.7
Complexity and Guarantees
32.8
Software Design
32.9
Extending the Package and Reusing Code