Related papers: High quality local interpolation by composite para…
The aim of this paper is a construction of quartic parametric polynomial interpolants of a circular arc, where two boundary points of a circular arc are interpolated. For every unit circular arc of inner angle not greater than $\pi$ we find…
In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate $C^1$ quadratic splines on…
A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals.…
In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered. The splines interpolate points, the corresponding tangent planes and normal curvature forms at domain vertices and approximate tangent…
Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of…
How good is a triangulation as an approximation of a smooth curved surface or manifold? We provide bounds on the {\em interpolation error}, the error in the position of the surface, and the {\em normal error}, the error in the normal…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…
Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both approaches leads to splines defined over mixed triangle and…
A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…
Traditional approaches to interpolate/extrapolate frames in a video sequence require accurate pixel correspondences between images, e.g., using optical flow. Their results stem on the accuracy of optical flow estimation, and could generate…
This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
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 presented that results in $G^1$ limit curves, reproduces conic…
We propose a framework that connects the spatial symmetries of a metasurface to its material parameter tensors and its scattering matrix. This provides a simple yet effective way to effortlessly determine properties of a metasurface…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space $\mathbb R^3$ (where they are equivalent to the PN surfaces) and in the…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…