Geometric Modeling: Theory and Practice The State of the Art

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.

I Mathematical Tools.- Variational Design with Boundary Conditions and Parameter Optimized Surface Fitting.- Special Applications in Surface Fitting.- A Synthesis Process for Fair Free-Form Surfaces.- Computing Minimal Surfaces with Particle Systems.- Orthogonality Relations for Cardinal B-Splines over Bounded Intervals.- Optimizing CNC Programs Using Spline Techniques.- New Approximation Methods for Planar Offset and Convolution Curves.- Detection and Computation of Degenerate Normal Vectors on Tensor Product Polynomial Surfaces.- Surfaces Intersection for Solid Algebra: A Classification Algorithm.- A Degree-of-Freedom Graph Approach.- II Representations.- Multiple-View Feature Modelling and Conversion.- A Knowledge Representation Perspective on Geometric Modeling.- Projection Operation for Multidimensional Geometric Modeling with Real Functions.- Breps as Displayable-Selectable Models in Interactive Design of Families of Geometric Objects.- Synthesis of a Unified Approach to Shape Modeling.- Virtual Topology Construction and Applications.- Generalization of Modified Octrees for Geometric Modeling.- Boundary Generation from Voxel-based Volume Representations.- Conversion of Binary Space Partitioning Trees to Boundary Representation.- A Formal Approach to Multiresolution Hypersurface Modeling.- Generation of Multiresolution Models from CAD-Data for Real Time Rendering.- Piecewise Linear Approximation for Scientific Data.- III Systems.- Provision of an Explicit Constraints Schema in the STEP Standard.- MicroStation Modeler: The Design and Implementation of an Extensible Solid Modeling System.- Contour Edge Analysis for Polyhedron Projections.- IV Automated Assembly.- Atlas: An Automatic Assembly Sequencing and Fixturing System.- Geometrical and Physical Reasoning for Stable Assembly Sequence Planning.