Related papers: Curve network interpolation by $C^1$ quadratic B-s…
We introduce a spatial graph and hypergraph model that smoothly interpolates between a graph with purely pairwise edges and a graph where all connections are in large hyperedges. The key component is a spatial clustering resolution…
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of Dupin cyclides, each…
A New Error Bound for shifted surface spline interpolation is presented. This error bound probably is the most powerful one up to now.
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…
The space of $C^1$ cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a space there is no B-spline basis available, which is a…
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
Given a surface S in P^3 and a collection of general points on it, how many surfaces of a given degree intersect S in a curve with prescribed multiplicities at the points? We formulate two natural conjectures which would answer this…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…
We consider surface area approximations by Lagrange and Crouzeix--Raviart interpolations on triangulations. For Lagrange interpolation, we give an alternative proof for Young's classical result that claims the areas of inscribed polygonal…
We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
A number of basic image processing tasks, such as any geometric transformation require interpolation at subpixel image values. In this work we utilize the multidimensional coordinate Hermite spline interpolation defined on non-equal spaced,…
When $a\ge2$, we show that a general pointed curve never interpolates through the expected number of points in the Hirzebruch surface $\mathcal{H}_a$, with one exception. In the exceptional case, the number of such interpolating maps is…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.