Related papers: Polyhedral Splines for Analysis
In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…
In this article, we study the dimension of the spline space of di-degree $(d,d)$ with the highest order of smoothness over a hierarchical T-mesh $\mathscr T$ using the smoothing cofactor-conformality method. Firstly, we obtain a dimensional…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
Within the linearized three-dimensional theory of polymer gels, we consider a sequence of problems formulated on a family of cylindrical domains whose height tends to zero. We assume that the fluid pressure is controlled at the top and…
Nonlinear approximation from regular piecewise polynomials (splines) of degree $<k$ supported on rings in $\R^2$ is studied. By definition a ring is a set in $\R^2$ obtained by subtracting a compact convex set with polygonal boundary from…
Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…
The `linear orbit' of a plane curve of degree d is its orbit in the projective space of dimension d(d+3)/2 parametrizing such curves under the natural action of PGL(3). In this paper we compute the degree of the closure of the linear orbits…
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…
In this paper we present the construction of a skeletal diagram category, which we call the square with bands category. This category extends the Temperley-Lieb (TL) category, where morphisms now include diagrams of embedded curves on…
We generalise the fold map for the wedge sum and use this to give a loop space decomposition of topological spaces with a high degree of symmetry. This is applied to polyhedral products to give a loop space decomposition of polyhedral…
A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears that many (but not all) of them can be relaxed to smooth minimal…
We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius…
For a finite planar graph, it associates with some metric spaces, called (regular) spherical polyhedral surfaces, by replacing faces with regular spherical polygons in the unit sphere and gluing them edge-to-edge. We consider the class of…
In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial…
Multivariate B-splines and Non-uniform rational B-splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical B-splines (THB-splines) provide a solution for this. THB-splines organize the parameter space…
We develop a systematic study about the spectrality of measures supported on piecewise smooth curves by studying the support of the tempered distributions arising from the tiling equation of some singular spectral measures. In doing so, we…
We consider the problem of B\'{e}zier curves/surfaces subdivision using blossoms. We propose closed-form formulae for blossoms evaluation, as needed for the calculation of control points. This approach leads to direct and efficient way to…