Meshing, Geometric Modeling and Numerical Simulation 1

Table of contents

1. Cover
2. Dedication
3. Title
4. Copyright
5. Foreword
6. Introduction
7. Chapter 1: Finite Elements and Shape Functions
   1. 1.1. Basic concepts
   2. 1.2. Shape functions, complete elements
   3. 1.3. Shape functions, reduced elements
   4. 1.4. Shape functions, rational elements
8. Chapter 2: Lagrange and Bézier Interpolants
   1. 2.1. Lagrange–Bézier analogy
   2. 2.2. Lagrange functions expressed in Bézier forms
   3. 2.3. Bézier polynomials expressed in Lagrangian form
   4. 2.4. Application to curves
   5. 2.5. Application to patches
   6. 2.6. Reduced elements
9. Chapter 3: Geometric Elements and Geometric Validity
   1. 3.1. Two-dimensional elements
   2. 3.2. Surface elements
   3. 3.3. Volumetric elements
   4. 3.4. Control points based on nodes
   5. 3.5. Reduced elements
   6. 3.6. Rational elements
10. Chapter 4: Triangulation
    1. 4.1. Triangulation, definitions, basic concepts and natural entities
    2. 4.2. Topology and local topological modifications
    3. 4.3. Enriched data structures
    4. 4.4. Construction of natural entities
    5. 4.5. Triangulation, construction methods
    6. 4.6. The incremental method, a generic method
11. Chapter 5: Delaunay Triangulation
    1. 5.1. History
    2. 5.2. Definitions and properties
    3. 5.3. The incremental method for Delaunay
    4. 5.4. Other methods of construction
    5. 5.5. Variants
    6. 5.6. Anisotropy
12. Chapter 6: Triangulation and Constraints
    1. 6.1. Triangulation of a domain
    2. 6.2. Delaunay Triangulation “Delaunay admissibility”
    3. 6.3. Triangulation of a variety
    4. 6.4. Topological invariants (triangles and tetrahedra)
13. Chapter 7: Geometric Modeling: Methods
    1. 7.1. Implicit or explicit form (CAD), starting from an analytical definition
    2. 7.2. Starting from a discretization or triangulation, discrete → continuous
    3. 7.3. Starting from a point cloud, discrete → discrete
    4. 7.4. Extraction of characteristic points and characteristic lines
14. Chapter 8: Geometric Modeling: Examples
    1. 8.1. Geometric modeling of parametric patches
    2. 8.2. Characteristic lines of a discrete surface
    3. 8.3. Parametrization of a surface patch through unfolding
    4. 8.4. Geometric simplification of a surface triangulation
    5. 8.5. Geometric support for a discrete surface
    6. 8.6. Discrete reconstruction of a digitized object or environment
15. Chapter 9: A Few Basic Algorithms and Formulae
    1. 9.1. Subdivision of an entity (De Casteljau)
    2. 9.2. Computing control coefficients (higher order elements)
    3. 9.3. Algorithms for the insertion of a point (Delaunay)
    4. 9.4. Construction of neighboring relationships, balls and shells
    5. 9.5. Localization problems
    6. 9.6. Some formulae
16. Conclusions and Perspectives
17. Bibliography
18. Index
19. End User License Agreement