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) NO European Commission DS MINDS@UW RD 29-mar-2024