Effective Computational Geometry for Curves and Surfaces
Shared-cost RTD (FET Open) Project No IST-2000-26473
This project is focused on effectively handling curved objects.
Geometric algorithms for curves and surfaces. We intend to revisit the field of Computational Geometry in order to understand how structures that are well-known for linear objects behave when defined on curves and surfaces.
Algebraic issues. Several operations on nonlinear geometric objects, often lying at the algorithm's bottleneck, are equivalent to manipulating polynomials. A fundamental question is the solution of algebraic systems, ubiquitous in the construction of new objects, such as intersections. Another crucial goal is the implementation of primitives with Boolean or discrete output, such as an object is contained in some bounding object.
Robustness issues. Geometric programs are notorious for their non-robustness: algorithms are designed for a model of computation where real numbers are dealt with exactly and geometric algorithms are frequently only formulated for inputs in general position. This is not simply an academic problem. It is easy to crash any commercial CAD-system. Progress has been made only in recent years. A significant part of the progress was made by the proposers and centers around the so-called exact computation paradigm. We will extend this paradigm to curved objects.
Approximating curves and surfaces. Since algorithms for curves and surfaces are more involved, more difficult to make robust and typically several orders of magnitude slower than their linear counterparts, there is a need for approximate representations. Our objective is to provide robust and quality guaranteed approximations of curves and surfaces.
|INRIA Sophia Antipolis - France (coordinator)||Prisme/Geometrica and Galaad Groups.||Project Manager: Jean-Daniel Boissonnat
Technical Project Manager: Monique Teillaud
|ETH Zürich - Switzerland||Theory of Combinatorial Algorithms Group||Site leader: Emo Welzl|
|Freie Universität Berlin - Germany||Group Theoretical Computer Science||Site leader: Günter Rote|
|Rijksuniversiteit Groningen - Netherlands||High-Performance Computing and Imaging Group||Site leader: Gert Vegter|
|MPI Saarbrücken - Germany||Algorithms and Complexity Group||Site leader: Kurt Mehlhorn|
|Tel Aviv University - Israel||School of Computer Science||Site leader: Dan Halperin|