2 citations · 6 across the 13 of their papers we have counts for
18 papers
Construction and evaluation of PH curves in exponential-polynomial spaces
Lucia Romani, Alberto Viscardi
In the past few decades polynomial curves with Pythagorean Hodograph (for short PH curves) have received considerable attention due to their usefulness in various CAD/CAM areas, ma…
Annihilation Operators for Exponential Spaces in Subdivision
Costanza Conti, Sergio Lopez-Urena, Lucia Romani
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to…
Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes
Luca Gemignani, Lucia Romani, Alberto Viscardi
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate in…
Dual Univariate Interpolatory Subdivision of Every Arity: Algebraic Characterization and Construction
Lucia Romani, Alberto Viscardi
A new class of univariate stationary interpolatory subdivision schemes of dual type is presented. As opposed to classical primal interpolatory schemes, these new schemes have masks…
Convergence analysis of corner cutting algorithms refining points and refining nets of functions
Costanza Conti, Nira Dyn, Lucia Romani
In this paper we give an elementary proof of the convergence of corner cutting algorithms refining points, in case the corner cutting weights are taken from the rather general clas…
Optimal Hölder-Zygmund exponent of semi-regular refinable functions
Maria Charina, Costanza Conti, Lucia Romani +2
The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. Ho…
Anisotropic, interpolatory subdivision and multigrid
Maria Charina, Marco Donatelli, Lucia Romani +1
In this paper, we present a family of multivariate grid transfer operators appropriate for anisotropic multigrid methods. Our grid transfer operators are derived from a new family…
Convergence and normal continuity analysis of non-stationary subdivision schemes near extraordinary vertices and faces
Costanza Conti, Marco Donatelli, Lucia Romani +1
Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue.…
A practical method for computing with piecewise Chebyshevian splines
Carolina Vittoria Beccari, Giulio Casciola, Lucia Romani
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces…
Pythagorean-Hodograph B-Spline Curves
Gudrun Albrecht, Carolina Vittoria Beccari, Jean-Charles Canonne +1
We introduce the new class of planar Pythagorean-Hodograph (PH) B-Spline curves. They can be seen as a generalization of the well-known class of planar Pythagorean-Hodograph (PH) B…
Multigrid methods: grid transfer operators and subdivision schemes
Maria Charina, Marco Donatelli, Lucia Romani +1
The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer…
Ellipse-preserving Hermite interpolation and subdivision
Costanza Conti, Lucia Romani, Michael Unser
We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint i…
Approximation order and approximate sum rules in subdivision
Costanza Conti, Lucia Romani, Jungho Yoon
Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a statio…
Exponential Splines and Pseudo-Splines: Generation versus reproduction of exponential polynomials
Costanza Conti, Luca Gemignani, Lucia Romani
Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also c…
Reproduction of Exponential Polynomials by Multivariate Non-stationary Subdivision Schemes with a General Dilation Matrix
Maria Charina, Costanza Conti, Lucia Romani
We study scalar multivariate non-stationary subdivision schemes with a general dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials…
Polynomial Reproduction of Multivariate Scalar Subdivision Schemes with General Dilation
Maria Charina, Lucia Romani
In this paper we study scalar multivariate subdivision schemes with general integer expanding dilation matrix. Our main result yields simple algebraic conditions on the symbols of…
On the reproduction properties of non-stationary subdivision schemes
Costanza Conti, Lucia Romani
We present an accurate investigation of the algebraic conditions that the symbols of a convergent, univariate, binary, non-stationary subdivision scheme should fulfill in order to…
Convexity preserving interpolatory subdivision with conic precision
Gudrun Albrecht, Lucia Romani
The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm is pr…