Rational Surfaces with Rational Offsets and Their Applications to<br/><br/>Blending Constructions

Thursday, May 31, 2007 - 10:30am - 11:20am
EE/CS 3-180
Rimvydas Krasauskas (Vilnius State University)
A surface offsetting operation in CAGD (Computer Aided Geometric Design)
involves sophisticated approximation techniques, since an offset of a general
rational surface is not rational. On the other hand, a class of rational
surfaces with rational offsets (PN-surfaces) includes main primitive surfaces
in CAGD: i.e. natural quadrics (sphere, circular cylinders and cones), torus,
and also their generalizations: Dupin cyclides and rational canal surfaces.
Therefore, it is important to understand what geometric modeling constructions
are possible if only PN-surfaces are used, and what is their lowest
parametrization degree. We follow Laguerre geometric approach to the theory of
PN-surfaces and use a universal rational parametrization of the Blaschke
cylinder. This allows us to generate new low degree analytic solutions for
PN-surface blendings between the following pairs: plane/natural quadric, two
natural quadrics and natural quadric/Dupin cyclide. Applications will be
illustrated by recent implementations in a commercial CAD software package.