Team geometrica

Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities

Section: New Results



Two major new releases of cgal , versions 3.6 and 3.7, have been been made available in 2010. These releases contain the following new features, involving Geometrica researchers:

Algebraic Kernel [36] . This package, introduced in cgal 3.6, is targeted to provide black-box implementations of state-of-the-art algorithms to determine, compare and approximate real roots of univariate polynomials and bivariate polynomial systems. So far the package only provides models for the univariate kernel. Nevertheless, it already defines concepts for the bivariate kernel, since this settles the interface for upcoming implementations.

3D Periodic Alpha-Shapes. The packages 3D alpha-shapes [38] and 3D periodic triangulations [37] have been interfaced in cgal 3.6, which allows to compute 3D periodic alpha-shapes.

3D Mesh Generation. The mesh generation package was introduced in cgal 3.5. From release cgal 3.6, the package proposes, after Delaunay refinement phase, an optimization phase to improve the quality of the mesh, in particular to get rid of slivers (see figure 10 ). The release cgal 3.7 includes a demo of the mesh generation package and the code has been optimized for efficiency [35] .

Figure 10. A mesh generated from a 3D segmented medical image of a liver. On the left part, the histograms of dihedral angles in the mesh are shown repectively before optimization (top), after ODT smoothing (middle), after ODT smoothing and vertex perturbation (bottom). The figures correspond in each case to the measure in degrees of the smallest and the biggest dihedral angles in the mesh.

The new release also contains new packages implemented by our cgal partners and improvements to some existing packages: a detailed list can be found on the cgal web site.

A one-week cgal developers meeting has been organized in June at INRIA by Monique Teillaud. There were 18 participants.


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