## Section: New Results

### Software

#### CGAL

A major new release of cgal , version 3.5, has been been made available
in October 2009. Besides improvements to existing packages, this release
contains the following new packages implemented by Geometrica :
— *3D Mesh Generation* [46] . This package
generates 3 dimensional meshes. It
computes isotropic simplicial meshes for domains or multidomains provided that
a domain descriptor, able to answer queries from a few different types on the
domain, is given. In the current version, the package generates meshes for domains
described through implicit functions, 3D images or polyhedral boundaries. The
output is a 3D mesh of the domain volume and conformal surface meshes for all
the boundary and subdividing surfaces.

— *Surface Reconstruction from Point Sets* [40] .
This package implements an
implicit surface reconstruction method: Poisson Surface Reconstruction. The
input is an unorganized point set with oriented normals.

— *3D Periodic Triangulations* [43] .
This package allows to build and handle triangulations of
point sets in the three dimensional flat torus. Triangulations are
built incrementally and can be modified by insertion or removal of
vertices. They offer point location facilities.

— *Point Set Processing* [41] . This package implements a set of algorithms for analysis, processing, and normal estimation and orientation of point sets.

— *AABB tree* [42] . This package implements a hierarchy of axis-aligned bounding boxes (an AABB tree) for efficient intersection and distance computations between 3D queries and sets of bounded 3D geometric objects.

— *CGAL_ipelets* [45] . Object that eases the writing of Ipe's plugins that use cgal . Plugins for several cgal 2D algorithms are provided as demo.

Also, an important extension of the 3D Spherical Kernel, for operations on circular arcs lying on a common sphere, was released in CGAL 3.5 [44] .

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.

cgal has been presented as a demo paper at ACM SIGSPATIAL GIS 2009, November 4-6 in Seattle. A course at SIGGRAPH Asia will be provided December 2009 in Yokohama, Japan, by A. Fabri and P. Alliez.

This year, two one-week cgal developers meetings have been organized: in January in Dagstuhl and in September at ETH Zürich. Sylvain Pion, Monique Teillaud, Mariette Yvinec, Samuel Hornus, Stéphane Tayeb, Manuel Caroli and Pedro Machado Manhães de Castro have participated to these meetings.

#### Standardization of Interval Arithmetic

Participant : Sylvain Pion.

In collaboration with Guillaume Melquiond (Proval project-team).

Geometric computations are very sensitive to numerical roundoff errors. There are efficient ways to solve this problem like static filters, but there is also a more general approach using a well-known tool which is interval arithmetic. Since the latter solution is more general and easier to use from a programming point of view, we are pushing for its standardization in the hope to get better support from hardware and compilers in the long term.

In the past years, we have worked on a proposal for standardization of interval arithmetic in C++. Since 2009, a new standardization effort has started as IEEE-1788 to provide a language-independent standard for interval arithmetic, similar in spirit to the IEEE-754 standard for floating-point. This standard would serve as a base for implementations in various languages such as Fortran, Matlab, C++...

This year, we have submitted a revision of a proposal for addition to the C++0x language to support basic floating-point operations with directed rounding-mode [62] , which we have presented to the C++ committee at the WG21 meetings in Summit (NJ) in March and Frankfurt in July. We think that this set of operations is as fundamental as the basic addition of floating-point variables as it is done now, and that they deserve the same special compiler support.