Speaker: M. Lavicka
Title: GRC Parametrizations of Rational Hypersurfaces
Abstract: The contribution deals with the problems of rational parametrized hypersurfaces
which admit rational convolution (RC) generally, or in some special cases. The approach is
based on the theory of Gröbner basis of zero dimensional ideals. We lay emphasis mainly on
the study of some special parametrizations, so called GRC parametrizations, possessing an
interesting property to be accessible to receive properties of other general parametrizations if
we use a suitable reparametrization. We also aim to examine links between parametrizations
of well-known curves and surfaces (e.g. PH/PN or LN) and types of parametrizations
explored in our approach. Examples of such parametrizations and hypersurfaces are presented
and their properties are discussed.
Speaker: B. Bastl
Title: Using Gröbner bases for computation of general offsets and their self-intersections
Abstract: The undercut in 3-axis and 5-axis milling causes serious problems because of
unexpected damages of the machined surface. The motion of the cutter is planned along an
general offset surface and a self-intersection of the general offset surface indicates the
undercut during the milling. The talk introduces a special class of surfaces, called GRC
surfaces, which are given by rational parametrization and for which also the convolution
surface (i.e. also arbitrary general offset surface) with arbitrary rational surface is rational.
Groebner bases theory is usefull in identification of such surfaces. For these surfaces, the selfintersection of the general offset surface can be computed using the symbolic-numeric
algorithm based on variables elimination methods (Grobner bases, resultants) followed by
finding points of implicitly defined curve in the parametric domain of the general offset
surface.