Ebook: 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.

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The state of the art of geometric modeling is described and discussed in this volume, based on the international conference held in Blaubeuren, Germany, in October 1996. The contributions cover the most relevant topics in the field at an advanced level and are authored by leading experts from universities, CAD system vendors, and users of geometric modelers. The book is organized into parts dealing with: mathematical tools for geometric modeling, including variational design, particle systems, and interpolation and approximation methods; representations in solid modeling and conversion problems; requirements to be met by a modeler for the automotive industry; and applications like automated assembly. The readability and clarity of the text is supported by fine illustrations.

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The state of the art of geometric modeling is described and discussed in this volume, based on the international conference held in Blaubeuren, Germany, in October 1996. The contributions cover the most relevant topics in the field at an advanced level and are authored by leading experts from universities, CAD system vendors, and users of geometric modelers. The book is organized into parts dealing with: mathematical tools for geometric modeling, including variational design, particle systems, and interpolation and approximation methods; representations in solid modeling and conversion problems; requirements to be met by a modeler for the automotive industry; and applications like automated assembly. The readability and clarity of the text is supported by fine illustrations.
Content:
Front Matter....Pages I-IX
Front Matter....Pages 1-1
Variational Design with Boundary Conditions and Parameter Optimized Surface Fitting....Pages 3-13
Special Applications in Surface Fitting....Pages 14-31
A Synthesis Process for Fair Free-Form Surfaces....Pages 32-51
Computing Minimal Surfaces with Particle Systems....Pages 52-58
Orthogonality Relations for Cardinal B-Splines over Bounded Intervals....Pages 59-69
Optimizing CNC Programs Using Spline Techniques....Pages 70-82
New Approximation Methods for Planar Offset and Convolution Curves....Pages 83-101
Detection and Computation of Degenerate Normal Vectors on Tensor Product Polynomial Surfaces....Pages 102-113
Surfaces Intersection for Solid Algebra: A Classification Algorithm....Pages 114-131
A Degree-of-Freedom Graph Approach....Pages 132-155
Front Matter....Pages 157-157
Multiple-View Feature Modelling and Conversion....Pages 159-174
A Knowledge Representation Perspective on Geometric Modeling....Pages 175-196
Projection Operation for Multidimensional Geometric Modeling with Real Functions....Pages 197-205
Breps as Displayable-Selectable Models in Interactive Design of Families of Geometric Objects....Pages 206-225
Synthesis of a Unified Approach to Shape Modeling....Pages 226-236
Virtual Topology Construction and Applications....Pages 247-259
Generalization of Modified Octrees for Geometric Modeling....Pages 260-272
Boundary Generation from Voxel-based Volume Representations....Pages 273-285
Conversion of Binary Space Partitioning Trees to Boundary Representation....Pages 286-301
A Formal Approach to Multiresolution Hypersurface Modeling....Pages 302-323
Front Matter....Pages 157-157
Generation of Multiresolution Models from CAD-Data for Real Time Rendering....Pages 324-334
Piecewise Linear Approximation for Scientific Data....Pages 335-341
Front Matter....Pages 343-343
Provision of an Explicit Constraints Schema in the STEP Standard....Pages 345-362
MicroStation Modeler: The Design and Implementation of an Extensible Solid Modeling System....Pages 363-378
Contour Edge Analysis for Polyhedron Projections....Pages 379-394
Front Matter....Pages 395-395
Atlas: An Automatic Assembly Sequencing and Fixturing System....Pages 397-415
Geometrical and Physical Reasoning for Stable Assembly Sequence Planning....Pages 416-434

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The state of the art of geometric modeling is described and discussed in this volume, based on the international conference held in Blaubeuren, Germany, in October 1996. The contributions cover the most relevant topics in the field at an advanced level and are authored by leading experts from universities, CAD system vendors, and users of geometric modelers. The book is organized into parts dealing with: mathematical tools for geometric modeling, including variational design, particle systems, and interpolation and approximation methods; representations in solid modeling and conversion problems; requirements to be met by a modeler for the automotive industry; and applications like automated assembly. The readability and clarity of the text is supported by fine illustrations.
Content:
Front Matter....Pages I-IX
Front Matter....Pages 1-1
Variational Design with Boundary Conditions and Parameter Optimized Surface Fitting....Pages 3-13
Special Applications in Surface Fitting....Pages 14-31
A Synthesis Process for Fair Free-Form Surfaces....Pages 32-51
Computing Minimal Surfaces with Particle Systems....Pages 52-58
Orthogonality Relations for Cardinal B-Splines over Bounded Intervals....Pages 59-69
Optimizing CNC Programs Using Spline Techniques....Pages 70-82
New Approximation Methods for Planar Offset and Convolution Curves....Pages 83-101
Detection and Computation of Degenerate Normal Vectors on Tensor Product Polynomial Surfaces....Pages 102-113
Surfaces Intersection for Solid Algebra: A Classification Algorithm....Pages 114-131
A Degree-of-Freedom Graph Approach....Pages 132-155
Front Matter....Pages 157-157
Multiple-View Feature Modelling and Conversion....Pages 159-174
A Knowledge Representation Perspective on Geometric Modeling....Pages 175-196
Projection Operation for Multidimensional Geometric Modeling with Real Functions....Pages 197-205
Breps as Displayable-Selectable Models in Interactive Design of Families of Geometric Objects....Pages 206-225
Synthesis of a Unified Approach to Shape Modeling....Pages 226-236
Virtual Topology Construction and Applications....Pages 247-259
Generalization of Modified Octrees for Geometric Modeling....Pages 260-272
Boundary Generation from Voxel-based Volume Representations....Pages 273-285
Conversion of Binary Space Partitioning Trees to Boundary Representation....Pages 286-301
A Formal Approach to Multiresolution Hypersurface Modeling....Pages 302-323
Front Matter....Pages 157-157
Generation of Multiresolution Models from CAD-Data for Real Time Rendering....Pages 324-334
Piecewise Linear Approximation for Scientific Data....Pages 335-341
Front Matter....Pages 343-343
Provision of an Explicit Constraints Schema in the STEP Standard....Pages 345-362
MicroStation Modeler: The Design and Implementation of an Extensible Solid Modeling System....Pages 363-378
Contour Edge Analysis for Polyhedron Projections....Pages 379-394
Front Matter....Pages 395-395
Atlas: An Automatic Assembly Sequencing and Fixturing System....Pages 397-415
Geometrical and Physical Reasoning for Stable Assembly Sequence Planning....Pages 416-434
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