Colloquium Computer Science: M. Lavicka, Ph.D. University of West Bohemia

Title: Recognizing algebraic surfaces from special class

Abstract:

In computer aided geometric design (CAGD) basic modelling surfaces, with the property being simple and widely used, are applied to construct complex models. Typical examples are ruled surfaces, rotational surfaces, canal surfaces, swept surfaces, translation surfaces, etc. Recognition of these surfaces from their equations, investigation of suitable parameterization methods and other related topics became a frequent research area in the past. In this contribution we will focus mainly on the case of surfaces of revolution and on canal surfaces, which are often used in geometric modelling, computer-aided design and technical practice (e.g. as blending surfaces smoothly joining two parts with circular ends). Our goal is to formulate a simple and efficient algorithm whose input is an implicit representation and the output is the answer whether the surface is a rotational surface or a rational canal surface. In the affirmative case we also compute a rational parameterization.

In addition, we will deal with the translation surfaces which are the shapes generated by translating one curve along another one. We focus on their properties especially useful for geometric modelling purposes and for recognition. All the results about translation surfaces can be directly applied also to minimal surfaces.

Biography:

Miroslav Lávička received the PhD degree from the Charles University in Prague in 1999. He has been an Associated Professor of Applied Mathematics at the Department of Mathematics (since 2011) and a Head of the research unit Mathematical Modelling at the European Centre of Excellence NTIS New Technologies for the Information Society (since 2016) at the University of West Bohemia in Plzeň, Czech Republic. His research interests focus mainly on various problems of geometric modelling, applied algebraic geometry and hybrid geometric computing.

Colloquium coordinators are Prof.dr. M. Aiello (e-mail : M.Aiello rug.nl ) and Prof.dr. M. Biehl (e-mail: M.Biehl rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/computerscience