Community Research and Development Information Service - CORDIS

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.

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