Seminars

Tueday April 12th, Byron 106

Dual representation of curves and surfaces

Zybnek Sir

In our talk we focus on several constructions of polynomial and rational curves and surfaces with rational offsets.
We introduce a system of elementary rational pseudoconvex shapes possessing rational offsets. These elementary shapes correspond to some simple support functions defined over circle (in the curve case) or sphere (in the surface case). By adding the support functions we obtain the Minkowski sum of the elementary shapes. Exploiting this setup we suggest methods for simultaneous rational approximation of offsets of a given shape and for computing (approximate) Minkowski sums of given objects.  We also describe our recent construction of rational spatial PH curves using the envelope of their osculating planes.