Our overall goal is to extend to curved objects the definitions of the
classical geometric structures and the algorithms to compute them.
The goal is also implementation in the
CGAL Library. Historically, the CGAL
kernels provided the user mainly with linear objects (points,
line segments, lines...) and predicates on them.
Curves were present in the traits classes of certain specific packages: arrangement with a traits class for conic arcs, optimization with conics, Apollonius graph with circles.
The effort consists first of all on defining general
concepts.
The declaration is the following:

Arrangement computed with the CGAL Circular kernel and Arrangement packages, on industrial VLSI data. The zooms show the complexity of the data. (Thanks to GeometryFactory for the data and to Pierre Alliez for the picture) 
. compare on algebraic numbers and roots of polynomial systems, . solve on systems of bivariate polynomials, . critical_points on bivariate polynomials, . sign_at that computes the sign of a bivariate polynomial evaluated at roots of polynomial systems. 
Concepts for univariate and bivariate polynomials were reviewed and accepted by the CGAL editorial board.
Models for univariate polynomials, based on
the RS
software package, should be released soon in CGAL 3.6.
Other models, for both univariate and bivariate polynomials, are
expected in the future.
CGAL Packages
2D Circular kernel
3D Spherical kernel
Algebraic Kernel specifications,
in collaboration with
Eric Berberich and
Michael Hemmer
Contributors
Eric Berberich
Pedro M. M. de Castro (internship, summer 2006, now PhD student)
Frédric Cazals
Ioannis Z. Emiris
Julien Hazebrouk and Damien Leroy (project, winter 2006)
Michael Hemmer
Athanasios V. Kakargias (internship, summer 2003)
Menelaos Karavelas
Sylvain Lazard
Sébastien Loriot
Luis Peñaranda
Sylvain Pion
Ilya Suslov (internship, winter 2006)
Elias Tsigaridas
Constantinos Tsirogiannis and Julien Hazebrouk (internships, summer 2005)
Papers
Slides
Introduction to CGAL
Introduction to the curved kernel (Arcadia meeting, 2005)
CGAL news (Dagstuhl Seminar, 2005)
From triangles to curves (invited talk 
European Workshop on
Computational Geometry, Delphi, March 2729, 2006)
Design of the CGAL 3D Spherical Kernel (Dagstuhl Seminar, 2007)
Design of the Spherical Kernel
(Workshop WRSO, 2007)
Research reports

This work was partially supported by the IST Programme of the 6th Framework Programme of the EU as a STREP (FET Open Scheme) Project under Contract No IST006413 (ACS  Algorithms for Complex Shapes) This work was partially supported by the IST Programme of the EU as a Sharedcost RTD (FET Open) Project under Contract No IST200026473 (ECG  Effective Computational Geometry for Curves and Surfaces) Preliminary work was done partially within the INRIA Associate Team CALAMATA. 