| Foreword | ||
| Preface | ||
| Acknowledgments | ||
| Index of Figures | ||
| 1 | Introduction | 1 |
| 1.1 | User vs. Machine Shape Representations | 2 |
| 1.2 | Criteria for Evaluation of a Shape Representation | 3 |
| 1.3 | Previous Work in Shape Representation | 5 |
| 1.4 | Areas for Improvement in Shape Representation | 10 |
| 1.5 | The Generative Modeling Approach | 13 |
| 1.6 | Generative Modeling: The State of the Art | 16 |
| 2 | Shape Representation | 23 |
| 2.1 | Generative Models: A Domain of Shapes | 23 |
| 2.2 | Specifying Generative Models | 26 |
| 2.3 | Development of the Generative Modeling Representation | 49 |
| 3 | Shape Specification Examples | 57 |
| 3.1 | GENMOD Preliminaries | 57 |
| 3.2 | Generative Surfaces | 60 |
| 3.3 | Other Generative Shapes | 92 |
| 4 | Shape Rendering | 97 |
| 4.1 | Categorizing Generative Models for Rendering | 98 |
| 4.2 | Sampling Generative Models | 108 |
| 4.3 | Controlling Visualization of Generative Models | 113 |
| 5 | Interval Methods for Shape Synthesis and Analysis | 121 |
| 5.1 | Why Interval Analysis? | 122 |
| 5.2 | Inclusion Functions | 123 |
| 5.3 | Constraint Solution Algorithm | 138 |
| 5.4 | Constrained Minimization Algorithm | 158 |
| 6 | Applying Interval Methods to Geometric Modeling | 163 |
| 6.1 | Offset Operations | 163 |
| 6.2 | Approximating Implicit Curves | 171 |
| 6.3 | Approximating Parametric Shapes Using Adaptive Criteria | 190 |
| 6.4 | CSG-Like Operations with Trimmed Surfaces | 197 |
| 6.5 | Constructive Solid Geometry with Trimmed Surfaces | 211 |
| 6.6 | Approximating Implicit Surfaces | 213 |
| 7 | Conclusion | 219 |
| App. A The GENMOD Language | 223 | |
| A.1 | Language Extensions | 223 |
| A.2 | Language Types | 224 |
| A.3 | Language Primitive Operators | 226 |
| A.4 | Language Extensibility: Building Higher-Level Operators | 237 |
| A.5 | Operator Libraries | 242 |
| App. B GENMOD Code Examples | 255 | |
| B.1 | Sphere/Cylinder Fillet Example | 255 |
| B.2 | Screwdriver Tip Examples | 257 |
| B.3 | Bottle Example | 260 |
| B.4 | Teddy Bear Example | 264 |
| App. C Theorems in Interval Analysis | 277 | |
| C.1 | Second Order Convergence of the Mean Value Form | 277 |
| C.2 | Convergence of the Constraint Solution Algorithm | 281 |
| C.3 | Convergence of the Minimization Algorithm | 282 |
| C.4 | Existence of Zeroes | 285 |
| C.5 | Interval Implicit Function Theorem | 290 |
| Bibliography | 293 | |
| Index | 305 |
