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.
Beccari C.V., Gonsor D.E., Neamtu M. (2014). RAGS: Rational geometric splines for surfaces of arbitrary topology. COMPUTER AIDED GEOMETRIC DESIGN, 31, 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.
