Francesca Pelosi

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics,

Abstract It is shown that, depending upon the orientation of the end tangents t0,t1 relative to the end point displacement vector Δp=p1−p0, the problem of G1 Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p0,. . .,pn in R3, compatible with a G1 piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples.

Quasi-interpolation in isogeometric analysis based on generalized B-splines

Isogeometric analysis is a new method for the numerical simulation of problems governed by partial differential equations. It possesses many features in common with finite element methods (FEM) but takes some inspiration from Computer Aided Design tools. We illustrate how quasi-interpolation methods can be suitably used to set Dirichlet boundary conditions in isogeometric analysis. In particular, we focus on quasi-interpolant projectors for generalized B-splines, which have been recently proposed as a possible alternative to NURBS in isogeometric analysis.

On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of

Shape-Preserving Approximation by Space Curves

\mathbb C

Isogeometric analysis in advection-diffusion problems: Tension splines approximation

C. All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.

Quasi-interpolants with tension properties from and in CAGD

We present a new method for the construction of shape-preserving curves approximating a given set of 3D data, based on the space of “quintic like” polynomial splines with variable degrees recently introduced in [7]. These splines – which are C3 and therefore curvature and torsion continuous – possess a very simple geometric structure, which permits to easily handle the shape-constraints.

Data Approximation Using Shape-Preserving Parametric Surfaces

This paper describes a new method for the construction of C2 shape-preserving curves which approximate an ordered set of data in R3. The curves are obtained using the variable degree polynomial spline spaces recently described in [5].

Shape preserving histogram approximation

In this paper we construct multilevel representations in terms of a hierarchy of tensor-product generalized B-splines. These representations combine the positive properties of a non-rational model with the possibility of dealing with local refinements. We discuss their use in the context of isogeometric analysis.