Generative Modeling for Computer Graphics and Cad (eBook)

Symbolic Shape Design Using Interval Analysis

John M. SNYDER (Autor)

eBook Download: PDF

2014 | 1. Auflage
334 Seiten
Elsevier Science (Verlag)
978-1-4832-6035-8 (ISBN)

Infos

Generative Modeling for Computer Graphics and Cad: Symbolic Shape Design Using Interval Analysis presents a symbolic approach to shape representation that is useful to the CAD/CAM and computer graphics communities. This book discusses the kinds of operators useful in a geometric modeling system, including arithmetic operators, vector and matrix operators, integration, differentiation, constraint solution, and constrained minimization. Associated with each operator are several methods that compute properties about the parametric functions represented with the operators. This text also elaborates how numerous rendering and analytical operations can be supported with only three methods-evaluation of the parametric function at a point, symbolic differentiation of the parametric function, and evaluation of an inclusion function for the parametric function. This publication is intended for people working in the area of computational geometry who are interested in a robust class of algorithms for manipulating shapes and those who want to know how human beings can specify and manipulate shape.

Inhalt

Front Cover 1
Generative Modeling for Computer Graphics and CAD: Symbolic Shape Design Using Interval Analysis 4
Copyright Page 5
Table of Contents 6
Foreword 12
Preface 14
Acknowledgments 18
Index of Figures 20
Chapter 1. Introduction 24
1.1 User vs. Macliine Shape Representations 25
1.2 Criteria for Evaluation of a Shape Representation 26
1.3 Previous Work in Shape Representation 28
1.4 Areas for Improvement in Shape Representation 33
1.5 The Generative Modeling Approach 36
1.6 Generative Modeling: The State of the Art 39
Chapter 2. Shape Representation 46
2.1 Generative Models: A Domain of Shapes 46
2.2 Specifying Generative Models 49
2.3 Development of tlie Generative Modeling Representation 72
Chapter 3. Shape Specification Examples 80
3.1 GENMOD Preliminaries 80
3.2 Generative Surfaces 83
3.3 Other Generative Shapes 115
Chapter 4. Shape Rendering 120
4.1 Categorizing Generative Models for Rendering 121
4.2 Sampling Generative Models 131
4.3 Controlling Visualization of Generative Models 136
Chapter 5. Interval Methods for Shape Synthesis and Analysis 144
5.1 Why Interval Analysis? 145
5.2 Inclusion Functions 146
5.3 Constraint Solution Algorithm 161
Color Plates 178
5.4 Constrained Minimization Algorithm 189
Chapter 6. Applying Interval Methods to Geometric Modeling 194
6.1 Offset Operations 194
6.2 Approximating Implicit Curves 202
6.3 Approximating Parametric Shapes Using Adaptive Criteria 221
6.4 CSG-Like Operations with Trinuned Surfaces 228
6.5 Constructive Solid Geometry with Trinuned Surfaces 242
6.6 Approximating Implicit Surfaces 244
Chapter 7. Conclusion 250
Appendix A: The GENMOD Language 254
Appendix .: GENMOD Code Examples 286
Appendix C: Theorems in Interval Analysis 308
Bibliography 324
Index 336

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 1-4832-6035-6 / 1483260356
• ISBN-13: 978-1-4832-6035-8 / 9781483260358