Discrete Models for Geometric Objects

Pere Brunet

Universitat Politecnica de Catalunya
Barcelona, Spain


This lecture presents and discusses the use of discrete models for modelinggeometric objects. Discrete models (voxel representations, octrees, KD-trees,interval solids or even point representations) are emerging as a flexibletool for geometric modeling. These algorithms exploit the trade-off betweenrobustness and memory. The availability at low cost of large amounts ofmemory affords thus completely robust models. Discrete bands can be used for instance for reconstructing valid closed models from point clouds, and to obtain different kinds of smooth Boundary Representations. On the other hand, discrete representations are specially well suited for error-boundedgeometry and topology simplification, being also useful for occlusion culling in the inspection and navigation of very large virtual environments. Basic tools for modeling, surface extraction and visualization, simplification andrelaxation will be described, and a number of potential applications will be presented.


Pere Brunet is professor of Computer Science at the Polytechnical Universityof Catalonia in Barcelona. He received an engineering degree and a PhD.in the same University in 1976. He is responsible for the Computer GraphicsGroup in the department of software, and he has been vice-president forresearch of the Polytechnical University of Catalonia from 1988 to 1992.His research interests include Computer-Aided Geometric Design, Solid Modeling,Octree Representations and Virtual Reality. His group is working in differentresearch activities and projects including CAD and piping for ship design,free form surface design, rendering algorithms and volume modeling andvisualization for medical applications. He promoted the Virtual Reality Center of Barcelona and is presently the UPC responsible of the Center.He is a member of the editorial board of the international journals Computer-Aided Design, Computer-Aided Geometric Design, IEEE Transactions on Visualization and Computer Graphics and Computers & Graphics. He has published refereed papers in well-known international research journals and has participated actively in many International Conferences. He has been the chairman of the Spanish Chapter of Eurographics since its creation in 1986 until 1990, and a member of the Eurographics Executive Committee since 1989. He was the Chairman of the Eurographics '93 Conference, Vice-Chairman of the Eurographics Association from 1990 to 1995, co-chair of tutorials at Eurographics '97, co-chair of the International Programme Committee at Eurographics '99 and member of the Siggraph '2000 courses committee. He is presently the chairman of the Eurographics Association and a member of the Spanish Academy of Engineering. Pere Brunet Professor, Software Department Universitat Politecnica de Catalunya Barcelona, Spain

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