RT info:eu-repo/semantics/article
T1 Computing all parametric solutions for blending parametric surfaces
A1 Pérez Díaz, Sonia
A1 Sendra Pons, Juan Rafael
K1 Matemáticas
K1 Mathematics
AB In this paper we prove that, for a given set of parametric primary surfaces and parametric clipping curves, all parametric blending solutions can be expressed as the addition of a particular parametric solution and a generic linear combination of the basis of a free module of rank 3. As a consequence, we present an algorithm that outputs a generic expression for all the parametric solutions for the blending problem. In addition, we also prove that the set of all polynomial parametric solutions (i.e. solutions that have polynomial parametrizations) for a parametric blending problem can also be expressed in terms of the basis of a free module of rank 3, and we prove an algorithmic criterion to decide whether there exist parametric polynomial solutions. As a consequence we also present an algorithm that decides the existence of polynomial solutions, and that outputs (if this type of solution exists) a generic expression for all polynomial parametric solutions for the problem.
PB Elsevier
SN 0747-7171
YR 2003
FD 2003-12
LK http://hdl.handle.net/10017/49618
UL http://hdl.handle.net/10017/49618
LA eng
NO Publicado en OA (open archive)
DS MINDS@UW
RD 02-abr-2023