A construction of spline spaces suitable for representing smooth parametric surfaces of arbitrary topological genus and arbitrary order of continuity is proposed. The obtained splines are a direct generalization of bivariate polynomial splines on planar partitions. They are defined as composite functions consisting of rational functions and are parametrized by a single parameter domain, which is a piecewise planar surface, such as a triangulation of a cloud of 3D points. The idea of the construction is to utilize linear rational transformations (or transition maps) to endow the piecewise planar surface with a particular ∞-differentiable structure appropriate for defining rational splines.
RAGS: Rational geometric splines for surfaces of arbitrary topology / Beccari C.V.; Gonsor D.E.; Neamtu M.. - In: COMPUTER AIDED GEOMETRIC DESIGN. - ISSN 0167-8396. - STAMPA. - 31:(2014), pp. 97-110. [10.1016/j.cagd.2013.11.004]
RAGS: Rational geometric splines for surfaces of arbitrary topology
BECCARI, CAROLINA VITTORIA;
2014
Abstract
A construction of spline spaces suitable for representing smooth parametric surfaces of arbitrary topological genus and arbitrary order of continuity is proposed. The obtained splines are a direct generalization of bivariate polynomial splines on planar partitions. They are defined as composite functions consisting of rational functions and are parametrized by a single parameter domain, which is a piecewise planar surface, such as a triangulation of a cloud of 3D points. The idea of the construction is to utilize linear rational transformations (or transition maps) to endow the piecewise planar surface with a particular ∞-differentiable structure appropriate for defining rational splines.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.