38 citations · 111 across the 15 of their papers we have counts for
17 papers
Trivariate Splines on Fans of Hyperplane Arrangements and Koszul Homology
Carles Checa, Michael DiPasquale, Pablo Mazón +5
We study the space of splines where denotes a smoothness distribution and is the fan of a central hyperplan…
Time-optimal neural feedback control of nilpotent systems as a binary classification problem
Sara Bicego, Samuel Gue, Dante Kalise +1
A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, wh…
A general formulation of reweighted least squares fitting
Carlotta Giannelli, Sofia Imperatore, Lisa Maria Kreusser +3
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be ex…
Multivariate polynomial splines on generalized oranges
Maritza Sirvent, Tatyana Sorokina, Nelly Villamizar +1
We consider spaces of multivariate splines defined on a particular type of simplicial partitions that we call (generalized) oranges. Such partitions are composed of a finite number…
An algebraic framework for geometrically continuous splines
Angelos Mantzaflaris, Bernard Mourrain, Nelly Villamizar +1
Geometrically continuous splines are piecewise polynomial functions defined on a collection of patches which are stitched together through transition maps. They are called -…
Algebraic Methods for Supersmooth Spline Spaces
Deepesh Toshniwal, Nelly Villamizar
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of appli…
Completeness characterization of Type-I box splines
Nelly Villamizar, Angelos Mantzaflaris, Bert Jüttler
We present a completeness characterization of box splines on three-directional triangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties. Fo…
A lower bound for the dimension of tetrahedral splines in large degree
Michael DiPasquale, Nelly Villamizar
We derive a formula which is a lower bound on the dimension of trivariate splines on a tetrahedral partition which are continuously differentiable of order in large enough degr…
A lower bound for splines on tetrahedral vertex stars
Michael DiPasquale, Nelly Villamizar
A tetrahedral complex all of whose tetrahedra meet at a common vertex is called a \textit{vertex star}. Vertex stars are a natural generalization of planar triangulations, and unde…
Dimension of polynomial splines of mixed smoothness on T-meshes
Deepesh Toshniwal, Nelly Villamizar
In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges…
-smooth splines on quad meshes with 4-split macro-patch elements
Ahmed Blidia, Bernard Mourrain, Nelly Villamizar
We analyze the space of differentiable functions on a quad-mesh $\cM$, which are composed of 4-split spline macro-patch elements on each quadrangular face. We describe explicit tra…
Varieties of apolar subschemes of toric surfaces
Matteo Gallet, Kristian Ranestad, Nelly Villamizar
Powersum varieties, also called varieties of sums of powers, have provided examples of interesting relations between varieties since their first appearance in the 19th century. One…
Geometrically continuous splines for surfaces of arbitrary topology
Bernard Mourrain, Raimundas Vidunas, Nelly Villamizar
We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational tran…
Planar Linkages Following a Prescribed Motion
Matteo Gallet, Christoph Koutschan, Zijia Li +3
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also…
Bounds on the dimension of trivariate spline spaces: A homological approach
Bernard Mourrain, Nelly Villamizar
We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lo…
Degenerations of real irrational toric varieties
Elisa Postinghel, Frank Sottile, Nelly Villamizar
An irrational toric variety X is an analytic subset of the simplex associated to a finite configuration of real vectors. The positive torus acts on X by translation, and we conside…
Homological techniques for the analysis of the dimension of triangular spline spaces
Bernard Mourrain, Nelly Villamizar
The spline space attached to a subdivided domain of is the vector space of functions of class which are polynomials of degree on each piece…