## Geometric Modeling: Theory and Practice: The State of the ArtWolfgang Straßer, Reinhard Klein, Rene Rau The Blaubeuren Conference "Theory and Practice of Geometric Modeling" has become a meeting place for leading experts from industrial and academic research institutions, CAD system developers and experienced users to exchange new ideas and to discuss new concepts and future directions in geometric modeling. The relaxed and calm atmosphere of the Heinrich-Fabri-Institute in Blaubeuren provides the appropriate environment for profound and engaged discussions that are not equally possible on other occasions. Real problems from current industrial projects as well as theoretical issues are addressed on a high scientific level. This book is the result of the lectures and discussions during the conference which took place from October 14th to 18th, 1996. The contents is structured in 4 parts: Mathematical Tools Representations Systems Automated Assembly. The editors express their sincere appreciation to the contributing authors, and to the members of the program committee for their cooperation, the careful reviewing and their active participation that made the conference and this book a success. |

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### Contents

Variational Design with Boundary Conditions and Parameter Optimized | 3 |

A Synthesis Process for Fair FreeForm Surfaces | 32 |

Computing Minimal Surfaces with Particle Systems | 52 |

Copyright | |

19 other sections not shown

### Common terms and phrases

algebraic algorithm applications approach approximation error assembly planning assembly sequences B-rep B-spline boundary representation Brep BSP-Tree complex components Computer Graphics construction contour edges control points convex convolution curve corresponding d-simplexes data structure defined definition degenerate normal vectors degrees of freedom Delaunay triangulation dependency graph dimension domain elements equation evaluation face octree feature model Figure fixels fixture function fuzzy G-Rep geometric entities geometric modeling given hole hyperplane insertion interactive interpolation intersection knowledge representation linear lower dimensional method MicroStation MicroStation Modeler minimal morphological multiresolution model node normal vector octree operations parametric planar plane polygon polyhedra polyhedron polynomial problem projection protrusive zones quadrilaterals queries refinement relations represented result segments shape simplexes solid modeling solution space specified spline step subassemblies subdivision subset tangent tessellation tion topological tree valid vertex vertices volume voxels