by Dmitry Anisimov (università della svizzera italiana, Lugano)
Astract: Nowadays, there exists a lot of different types of generalized barycentric coordinates. First, introduced by famous German mathematician and theoretical astronomer August Ferdinand Mobius in 1827, they have become widely used last decade due to their simple construction and variety of applications. However, Mobius was studying these coordinates only in the context of a triangle, and that is why his original coordinates are called triangular barycentric coordinates. These particular functions have applications in many different areas including computer graphics, geometry processing, finite element method, topology optimization, and similar. But due to a variety of different problems, which came into focus in recent years, the interest in a generalization of triangular barycentric coordinates to arbitrary polytopes has appeared, and a lot of interesting constructions saw the light. In this talk I will give a short overview of the current state within this topic and discuss some of the most famous types of generalized barycentric coordinates, their properties, and applications.
Bio: Dmitry is currently a Ph.D. student in the area of generalized barycentric interpolation at the Università della Svizzera italiana in Lugano (Switzerland), faculty of Informatics, advised by professor Kai Hormann.
