Biography of Prof. Menelaos Karavelas

Menelaos Karavelas got his Ph.D. from the Scientific Computing and Computational Mathematics Program at Stanford University under the supervision of Leonidas Guibas. He then spent a year as a post-doc at the PRISME Project (currently GEOMETRICA) at INRIA Sophia-Antipolis. During the next year and a half he was an Assistant Professor at the Computer Science & Engineering Department of Notre Dame. Since 2005 he is an Assistant Professor at the Applied Mathematics Department at the University of Crete. Professor Karavelas' research is focused on problems in Discrete & Computational Geometry, Geometric Computing and Computer-Aided Geometric Design.

He has been working on a variety of problems, mostly involving non-punctual geometric objects including: kinetic data structures for maintaining proximity information, practical/efficient and robust algorithms for computing two-dimensional Euclidean Voronoi diagrams for disks and line segments, combinatorial complexity of Euclidean Voronoi cells and convex hulls of spheres in any fixed dimension, art gallery-like problems for polygons the edges of which are curve segments, and shape-preserving interpolation of three-dimensional point sets. His algorithms for the computation of the Euclidean Voronoi diagrams for disks and line segments are part of the Computational Geometry Algorithms Library (CGAL), for which he is a member of the Editorial Board since 2004.

Title of Talk: Delaunay triangulations and Voronoi diagrams in CGAL: 
Algorithms, Data structures and practiceThe Computational Geometry Algorithms Library (CGAL) is an open source project that provides a collection of reliable and efficient geometric algorithms and data structures. The library is written in C++ and follows the generic programming paradigm.

In this talk I am going to focus on the part of the library related to Voronoi diagrams and Delaunay triangulations. I will dive into the technical details of the algorithms involved for computing various types of Voronoi diagrams/Delaunay triangulations, including 2D/3D Delaunay triangulations and 2D Voronoi diagrams for line segments and circular disks. Moreover, I will discuss the data structures used for representing 2D and 3D triangulations. Finally, I will discuss practical issues that arise when using Delaunay triangulation and Voronoi diagrams in CGAL, and will give directions for "optimally"
using these algorithms.