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Geometric modelling has been an important and interesting subject for many years from the purely mathematical and computer science viewpoint, and also from the standpoint of engineering and various other applications, such as CAD/CAM, entertainment, animation, and multimedia. This book focuses on the interaction between the theoretical foundation of geometric modelling and practical applications in CAD and related areas.
Geometric Modelling: Theoretical and Computational Basis towards Advanced CAD Applications starts with two position papers, discussing basic computational theory and practical system solutions. The well-organized seven review papers give a systematic overview of the current situation and deep insight for future research and development directions towards the reality of shape representation and processing. They discuss various aspects of important issues, such as geometric computation for space search and shape generation, parametric modelling, feature modelling, user interface for geometric modelling, geometric modelling for the Next Generation CAD, and geometric/shape standard. Other papers discuss features and new research directions in geometric modelling, solid modeling, free-form surface modeling, intersection calculation, mesh modeling and reverse engineering. They cover a wide range of geometric modelling issues to show the problem scope and the technological importance.
Researchers interested in the current status of geometric modelling research and developments will find this volume to be an essential reference.
Preface. International Program Committee. Invited Papers. Degeneracy and Instability in Geometric Computation; K. Sugihara. Industry Application of Geometric Modeling Technology - Major Future Issues and Some Challenges; A. Ohtaka. Keynote Papers. Medial Axis Transform (MAT) of General 2D Shapes and 3D Polyhedra for Engineering Applications; Y.-C. Chang, et al. Designing with Parametric CAD: Classification and Comparison of Construction Techniques; J.J. Shah. Semantic and Multiple-view Feature Modelling: Towards More Meaningful Product Modelling; W.F. Bronsvoort, et al. C-Space Approach to Tool-Path Generation for Sculptured Surface Machining; B.K. Choi. User Interfaces for Geometric Modeling; M. Shpitalni, H. Lipson. Required Features of CAD System as a Real Design Tool; Kunwoo Lee. Geometric Modelling: Lessons Learned from the 'STEP' Standard; M.J. Pratt. Feature and New Approaches in Geometric Modelling. Feature Management with Multiple Views Based on Convexity Properties of Shape Region; H. Kojima, M. Higashi. Evolution of Interaction in Physically-Based Modelling; M. Bordegoni, et al. Constraint Representation and Reduction based on Lie Algebra in Assembly Model; H. Tokunaga, et al. Solid Modelling. Robust Boolean Set Operation by Symbol Processing of Topology; M. Higashi, et al. Solid Modeling Using Boundary Integral Equations; Y. Ochiai. Density Spatial Model for Computer Aided Industrial Design; K. Sakita, M. Igoshi. Free-Form Surface Modelling. Streamline Modeling: Designing Free-Form Surfaces by Blending Tangent Vectors; K.T. Miura, et al. The Bernstein-Bezier Surface on the Simplex; Z. Liang, et al. An Automatic Offsetting Method of Composite Surfaces; H. Kawabata, J. Ishida. Fillet Operations with Recursive Subdivision Surfaces; Z. Xu, K. Kondo Intersection Calculation. Surface-Surface Intersection with Critical Point Detection Based on Bézier Normal Vector Surfaces; Y. Yamaguchi, et al. A Sweep Line Algorithm for Polygonal Chain Intersection and its Applications; S.C. Park, et al. Mesh Modelling and Reverse Engineering. Subdivision-based Mesh Refinement for Rapid Prototyping; H. Suzuki, et al. Reverse Engineering of 3D Models based on Image Processing and 3D Scanning Techniques; A. Manor, A. Fischer. Method to Generate Freeform Surfaces from Idea-Sketch and Three Dimensional Data; T. Kuragano, et al.