PhD defenses at the Faculty of Informatics

Analysis and New Constructions of Generalized Barycentric Coordinates in 2D

You are cordially invited to attend the PhD Dissertation Defense of Dmitry ANISIMOV on Tuesday, May 23rd 2017 at 10h30 in room A34 (Red building)



Different coordinate systems allow to uniquely determine the position of a geometric element in space. In this dissertation, we consider a coordinate system that lets us determine the position of a two-dimensional point in the plane with respect to an arbitrary simple polygon. Coordinates of this system are called generalized barycentric coordinates in 2D and are widely used in computer graphics and computational mechanics.

There exist many coordinate functions that satisfy all the basic properties of barycentric coordinates, but they differ by a number of other properties. We provide an extensive comparison of these coordinate functions, perform a theoretical analysis of some well-known closed-form coordinates as well as show how to achieve their numerically stable implementation, and finally present a few novel constructions with favourable properties.


Dissertation Committee:

  • Kai Hormann, Università della Svizzera italiana, Switzerland (Research Advisor)
  • Matthias Hauswirth, Università della Svizzera italiana, Switzerland (Internal Member)
  • Evanthia Papadopoulou, Università della Svizzera italiana, Switzerland (Internal Member)
  • Michael S. Floater, University of Oslo, Sweden (External Member)
  • Pierre Alliez, Inria Sophia-Antipolis, France (External Member)