Section: New Results

Introduction

The presentation of our new results follows the three main directions recalled in Section 3.1

– fundamental geometric data structures and algorithms,

– robust computation and advanced programming,

– shape approximation and mesh generation.

Contributions on the first item are the construction of Voronoi diagrams of spheres, several results related to visibility and graph algorithms for reporting maximal cliques.

Work on the second research direction includes the design and a preliminary implementation of a certified curved kernel for cgal . In addition, to further extend the robustness and the efficiency of cgal , geometric constructions are now filtered in a way similar to predicates.

Work on the third axis gained momentum and is subdivided in surface approximation, mesh generation, computation and stability of geometric features, and compact data structures.

Lastly, we report on some applications in molecular biology, visualization and signal processing.