Effective Computational Geometry for Curves and Surfaces

Informacje na temat projektu

ECG

Identyfikator umowy o grant: IST-2000-26473

Projekt został zamknięty

Data rozpoczęcia 1 Maja 2001

Data zakończenia 30 Kwietnia 2004

Finansowanie w ramach

• Programme for research, technological development and demonstration on a "User-friendly information society, 1998-2002"

Koszt całkowity € 1 595 600,00

Wkład UE € 1 029 000,00

Koordynowany przez

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
France

Rezultaty

Methods for approximating curves and surfaces

We have made a survey of the literature, designed algorithms, and written software implementing a few algorithms for approximating a given curve made up of several, possibly curved, pieces, by a single polygonal curve. The software is embedded in the CGAL library of geometric algorithms. This task of curve simplification has possible applications in geographic information systems, in computer graphics, in industrial design, or in any area where geometric modelling is involved. The novel feature of our approach is that it addresses curved input pieces and provides output with guaranteed error bounds (under suitable assumptions about the input). We have developed the first algorithms that can mesh surfaces with topological and geometrical guarantees. We have proposed three general algorithms and one for skin surfaces (especially useful in structural biology). The algorithms have been implemented as CGAL packages. One will be commercialised soon by GeometryFactory.

Non affine Voronoi diagrams

We invented new algorithms for constructing Voronoi diagrams of line segments, circles and general convex convex objects in the plane. These algorithms have implemented and are now commercialised by GeometryFactory. New combinatorial bounds and a new algorithm have been proposed for the Voronoi diagrams of spheres. A prototype implementation is available. For more complex objects, we established an approximation result and implemented an algorithm that produces a certified approximation of Voronoi diagrams of 3D curved objects.

Robust algorithms for constructing arrangements of curves and surfaces

We have devised a unified software platform for the robust construction and manipulation of arrangements of curves in the plane. Our implementation constitutes the state-of-the-art in planar arrangements, and has no parallel in generality, conciseness and usability.

Surface reconstruction

Several new algorithms for surface reconstruction have been developed. On the theoretical level, we made progress on the flow complex. We organized an international contest and participated in another one organized by DIMACS in the US. Our surface reconstruction codes compare favourably with the best codes that participated in the two contests.

Algebraic numbers

We devised robust and efficient methods for manipulating algebraic numbers. Some of the methods are based on separation bounds. Others use techniques like root isolation and Sturm sequences. The implementations are either going to be integrated into LEDA, or into Synaps or into CGAL.