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Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways. In 12 chapters written by leading experts, this book presents recent results which rely on the interaction of both fields. Some of these results have been obtained from a major European project in geometric modeling.
While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies
19 papers presented by international experts give a state-of-the-art survey of the relevant problems and issues in modeling, CAD/CAM, scientific visualization, and computational geometry. The following topics are treated: • surface design and fairing • subdivision schemes • variational design • NURBS • reverse engineering • physically-based modelling • medical imaging
Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre.
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.
Computer Aided techniques, Applications, Systems and tools for Geometric Modeling are extremely useful in a number of academic and industrial settings. Specifically, Computer Aided Geometric Modeling (CAGM) plays a significant role in the construction of - signing and manufacturing of various objects. In addition to its cri- cal importance in the traditional fields of automobile and aircraft manufacturing, shipbuilding, and general product design, more - cently, the CAGM methods have also proven to be indispensable in a variety of modern industries, including computer vision, robotics, medical imaging, visualization, and even media. This book aims to provide a valuable source, which focuses on - terdisciplinary methods and affiliate research in the area. It aims to provide the user community with a variety of Geometric Modeling techniques, Applications, systems and tools necessary for various real life problems in the areas such as: Font Design Medical Visualization Scientific Data Visualization Archaeology Toon Rendering Virtual Reality Body Simulation It also aims to collect and disseminate information in various dis- plines including: Curve and Surface Fitting Geometric Algorithms Scientific Visualization Shape Abstraction and Modeling Intelligent CAD Systems Computational Geometry Solid Modeling v Shape Analysis and Description Industrial Applications The major goal of this book is to stimulate views and provide a source where researchers and practitioners can find the latest dev- opments in the field of Geometric Modeling.
The second book of a two-volume work in which the author presents an overview of computer graphics as seen in the context of geometric modeling and the mathematics required to understand the subject.
The International Workshop CG '88 on "Computational Geometry" was held at the University of Würzburg, FRG, March 24-25, 1988. As the interest in the fascinating field of Computational Geometry and its Applications has grown very quickly in recent years the organizers felt the need to have a workshop, where a suitable number of invited participants could concentrate their efforts in this field to cover a broad spectrum of topics and to communicate in a stimulating atmosphere. This workshop was attended by some fifty invited scientists. The scientific program consisted of 22 contributions, of which 18 papers with one additional paper (M. Reichling) are contained in the present volume. The contributions covered important areas not only of fundamental aspects of Computational Geometry but a lot of interesting and most promising applications: Algorithmic Aspects of Geometry, Arrangements, Nearest-Neighbor-Problems and Abstract Voronoi-Diagrams, Data Structures for Geometric Objects, Geo-Relational Algebra, Geometric Modeling, Clustering and Visualizing Geometric Objects, Finite Element Methods, Triangulating in Parallel, Animation and Ray Tracing, Robotics: Motion Planning, Collision Avoidance, Visibility, Smooth Surfaces, Basic Models of Geometric Computations, Automatizing Geometric Proofs and Constructions.
This book constitutes the refereed proceedings of the 4th International Conference on Geometric Modeling and Processing, GMP 2006, held in Pittsburgh, PA, USA in July 2006. The 36 revised full papers and 21 revised short papers presented were carefully reviewed and selected from a total of 84 submissions. All current issues in the area of geometric modeling and processing are addressed and the impact in such areas as computer graphics, computer vision, machining, robotics, and scientific visualization is shown. The papers are organized in topical sections on shape reconstruction, curves and surfaces, geometric processing, shape deformation, shape description, shape recognition, geometric modeling, subdivision surfaces, and engineering applications.