I. Acknowledgments, SAGA " , FP7 contract PITN-GA-2008-214584. E. Tsigaridas is partially supported by the EX- ACTA grant of the National Science Foundation of China (NSFC 60911130369) and the French National Research Agency (ANR-09-BLAN-0371-01 HPAC (ANR ANR-11-BS02-013) and an FP7 Marie Curie Career Integration Grant, GeoLMI (ANR 2011 BS03 011 06) Most of the work of G. Tzoumas was performed during his postdoc at INRIA Nancy and a smaller part during his PhD at the National and Kapodistrian University of Athens

O. Aichholzer, W. Aigner, F. Aurenhammer, T. Hackl, B. Jüttler et al., Medial axis computation for planar free???form shapes, Computer-Aided Design, vol.41, issue.5, pp.339-349, 2009.
DOI : 10.1016/j.cad.2008.08.008

H. Alt, O. Cheong, and A. Vigneron, The Voronoi Diagram of Curved Objects, Discrete & Computational Geometry, vol.34, issue.3, pp.439-453, 2005.
DOI : 10.1007/s00454-005-1192-0

F. Anton, Voronoi diagrams of semi-algebraic sets, 2004.
URL : https://hal.archives-ouvertes.fr/tel-00005932

C. Cgal, Computational Geometry Algorithms Library

D. Cox, J. Little, and D. O-'shea, Using Algebraic Geometry. Number 185 in GTM, 2005.

G. Elber and M. S. Kim, Bisector curves of planar rational curves, Computer-Aided Design, vol.30, issue.14, pp.1089-1096, 1998.
DOI : 10.1016/S0010-4485(98)00065-7

G. Elber, M. S. Kim, and H. S. Heo, The Convex Hull of Rational Plane Curves, Graphical Models, vol.63, issue.3, pp.151-162, 2001.
DOI : 10.1006/gmod.2001.0546

I. Emiris, E. Tsigaridas, and G. Tzoumas, Exact Delaunay graph of smooth convex pseudo-circles, 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling on, SPM '09, pp.211-222, 2009.
DOI : 10.1145/1629255.1629282

I. Z. Emiris and M. I. Karavelas, The predicates of the Apollonius diagram: Algorithmic analysis and implementation, Computational Geometry, vol.33, issue.1-2, pp.18-57, 2006.
DOI : 10.1016/j.comgeo.2004.02.006

I. Z. Emiris, E. P. Tsigaridas, and G. M. Tzoumas, THE PREDICATES FOR THE EXACT VORONOI DIAGRAM OF ELLIPSES UNDER THE EUCLIDIEAN METRIC, International Journal of Computational Geometry & Applications, vol.18, issue.06, pp.567-597, 2008.
DOI : 10.1142/S0218195908002763

I. Z. Emiris and G. M. Tzoumas, Exact and efficient evaluation of the InCircle predicate for parametric ellipses and smooth convex objects, Computer-Aided Design, vol.40, issue.6, pp.691-700, 2008.
DOI : 10.1016/j.cad.2008.05.001

L. Habert, Computing bitangents for ellipses, Proc. 17th Canad. Conf. Comp. Geom, pp.294-297, 2005.

I. Hanniel, R. Muthuganapathy, G. Elber, and M. S. Kim, Precise Voronoi cell extraction of free-form rational planar closed curves, Proceedings of the 2005 ACM symposium on Solid and physical modeling , SPM '05, pp.51-59, 2005.
DOI : 10.1145/1060244.1060251

M. Held, VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments, Computational Geometry, vol.18, issue.2, pp.95-123, 2001.
DOI : 10.1016/S0925-7721(01)00003-7

M. Held and S. Huber, Topology-oriented incremental computation of Voronoi diagrams of circular arcs and straight-line segments, Computer-Aided Design, vol.41, issue.5, pp.327-338, 2009.
DOI : 10.1016/j.cad.2008.08.004

M. I. Karavelas, A robust and efficient implementation for the segment Voronoi diagram, Proc. Int. Symp. Voronoi Diagrams, pp.51-62, 2004.

M. I. Karavelas and M. Yvinec, The Voronoi Diagram of Convex Objects in the Plane, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00071561

M. I. Karavelas and M. Yvinec, Voronoi diagram of convex objects in the plane, Proc. Europ. Symp. Algorithms, pp.337-348, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00071561

D. S. Kim, D. Kim, and K. Sugihara, Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry, Computer Aided Geometric Design, vol.18, issue.6, pp.563-585, 2001.
DOI : 10.1016/S0167-8396(01)00051-6

R. Klein, K. Mehlhorn, and S. Meiser, Randomized incremental construction of abstract Voronoi diagrams, Computational Geometry, vol.3, issue.3, pp.157-184, 1993.
DOI : 10.1016/0925-7721(93)90033-3
URL : http://doi.org/10.1016/0925-7721(93)90033-3

V. Ogarko and S. Luding, Data structures and algorithms for contact detection in numerical simulation of discrete particle systems, World Congress Particle Technology, vol.6, 2010.

R. Ramamurthy and R. Farouki, Voronoi diagram and medial axis algorithm for planar domains with curved boundaries ??? II: Detailed algorithm description, Journal of Computational and Applied Mathematics, vol.102, issue.2, pp.253-277, 1999.
DOI : 10.1016/S0377-0427(98)00223-4
URL : http://doi.org/10.1016/s0377-0427(98)00223-4

R. Ramamurthy and R. Farouki, Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I. Theoretical foundations, Journal of Computational and Applied Mathematics, vol.102, issue.1, pp.119-141, 1999.
DOI : 10.1016/S0377-0427(98)00211-8

M. Ramanathan and B. Gurumoorthy, Constructing medial axis transform of planar domains with curved boundaries, Computer-Aided Design, vol.35, issue.7, pp.619-632, 2003.
DOI : 10.1016/S0010-4485(02)00085-4

J. K. Seong, E. Cohen, and G. Elber, Voronoi diagram computations for planar NURBS curves, Proceedings of the 2008 ACM symposium on Solid and physical modeling , SPM '08, pp.67-77, 2008.
DOI : 10.1145/1364901.1364913

G. Tzoumas, Computational geometry for curved objects. Voronoi diagrams in the plane, 2009.

G. Tzoumas, Exact medial axis of quadratic NURBS curves, 27th Proc. Europ. Workshop Computat. Geometry, pp.91-94, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00581588