Colloquium Computer Science / Mathematics - Dr. Michal Bizzarri

Title:
Pythagorean varieties constructed from their normal spaces

Abstract:
Methods using varieties with Pythagorean property both in Euclidean and Minkowski spaces are often used in geometric modelling when necessary to solve the problem of rationality of offsets of planar or spatial domains. The talk will be devoted to the construction of polynomial curves and surfaces satisfying the Pythagorean property, i.e., shapes possessing a polynomial length/area element (with respect to the prescribed inner product). It is shown that the Pythagorean property of a considered variety is encoded equivalently in the tangent and as well as in the normal space. Subsequently, this approach is used for formulating a simple unified Hermite interpolation algorithm by these varieties. A main advantage of the presented method lies in the fact that it is based only on solving systems of linear equations. Whereas many interpolation methods by polynomial (Minkowski) Pythagorean hodograph curves are known and the presented algorithm can serve only as a possible alternative, the designed interpolation technique for polynomial surfaces with Pythagorean property (PN and MOS surfaces) is the first functional and complex method solving the Hermite problem.

Colloquium coordinators are Prof.dr. D. Karastoyanova (e-mail: d.karastoyanova rug.nl) and Prof.dr. M. Biehl (e-mail: M.Biehl rug.nl)