Abstract: CGAL's arrangement package is a state-of-the-art implementation
for two-dimensional subdivisions induced by a set of curves. Based on
an algebraic kernel (some details will be given), we present how
to construct and maintain arrangements of arcs of algebraic curves, that
are also unbounded. This is nowadays well supported by CGAL. We also introduce
applications or extensions of such arrangements, namely rotations of curves
and boolean set operations. Furthermore, the new design of the arrangement
package allows to consider curves embedded on parameterizable surfaces, and
we show on the example of quadrics and cyclides (a generalization of tori)
how to enable such. In the last part, we shortly cover a projection technique
to analyse an algebraic surface with the help of a special two-dimensional arrangement.

All results are based on previous work by Michael Kerber, Arno Eigenwillig
and Nicola Wolpert, and were achieved in collaboration with them and also
Pavel Emeliyanenko, Michael Hemmer, Michael Sagraloff, Kurt Mehlhorn,
Efi Fogel, Dan Halperin, and Ron Wein.

For people unfamilar with algebraic curves and surfaces, I recommend
the interactive demo  http://exacus.mpi-inf.mpg.de/cgi-bin/xalci.cgi with
its gallery http://exacus.mpi-inf.mpg.de/gallery.html, and
http://en.wikipedia.org/wiki/Algebraic_curve, and also
http://en.wikipedia.org/wiki/Algebraic_surface
and http://www.imaginary2008.de/ having very nice pictures.