Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On transfinite interpolations with respect to convex domains
 Computer aided geometric design : CAGD 28 (2011), Nr.2, S.135149 ISSN: 01678396 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer SCAI () 
Abstract
We propose an approach for constructing a transfinite interpolation where the domain of definition is a convex polytope. For multifaceted domains which are not of tensor product type, it is difficult to directly generalize the usual approach of transfinite interpolation which blends opposite faces and which then substracts that by a mixed term. Therefore, we suggest a short formula which uses topologic entities of the convex domain. Our formula uses some projection operator onto the faces of the polytope. Both representations (Vsetting and Hsetting) of a polytope are used. We show also that the transfinite interpolation is stable under affine transformations. As a supplement to the theoretical demonstrations, we show some interesting practical illustrations.