Colloquium Computer Science - Prof. Kai Hormann University of Svizzera Italiana

Title: Generalized Barycentric Coordinates

Abstract:
     Interpolating given discrete data with continuous functions in
one or more variables is a fundamental problem in diverse fields of
sciences and engineering. Barycentric coordinates, which were
introduced by Möbius in 1827, still provide perhaps the most
convenient way to linearly interpolate data prescribed at the vertices
of an n-dimensional simplex. While barycentric coordinates are unique
for simplices, they can be generalized in several ways to arbitrary
polygons and polytopes in higher dimensions, and over the past few
years, a number of recipes for such generalized barycentric
coordinates have been developed. As they are usually given in closed
form and can be evaluated efficiently, they have many useful
applications, e.g. in computer graphics, computer aided geometric
design, and image processing.

Bio:
     Kai Hormann is a full professor in the Faculty of Informatics at
the Università della Svizzera italiana (USI) in Lugano. He received a
Diploma in Mathematics in 1997 and a Ph.D. in Computer Science in
2002, both from the University of Erlangen-Nürnberg. Before moving to
Lugano in 2009, he worked as a postdoctoral research fellow at Caltech
in Pasadena and the CNR in Pisa, and as an assistant professor at
Clausthal University of Technology. He was a visiting BMS substitute
professor at Freie Universität Berlin during the winter term 2007/2008
and a visiting professor at NTU Singapore in 2018.

His research interests are focussed on the mathematical foundations of
geometry processing algorithms as well as their applications in
computer graphics and related fields. In particular, he is working on
generalized barycentric coordinates, subdivision of curves and
surfaces, barycentric rational interpolation, and dynamic geometry
processing.