We present an efficient G surface reconstruction scheme for complex solid models used in FE simulations. A novel technique based on low geometric degree (biquartic) polynomial interpolation is proposed to construct a smooth surface on arbitrary unstructured(irregular) rectangular meshes. A suitable parametric representation of surface as well as local control of individual rectangular patches i...

1 Radial Basis Functions 2 1.1 Multivariate Interpolation and Positive Definiteness . . . . . . 3 1.2 Stability and Scaling . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Solving Partial Differential Equations . . . . . . . . . . . . . . 7 1.4 Comparison of Strong and Weak Problems . . . . . . . . . . . 8 1.5 Collocation Techniques . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Method ...

In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarse-to-fine hie...

In this paper, we propose two adaptive interlaced-to-progressive conversion techniques in which the adequacy of the estimated motion vector is evaluated. If the motion vector is unlikely to give a good temporal motion compensated interpolation result, spatial interpolation is favored or selected to avoid temporal artifacts. In the rst proposed interlaced-to-progressive conversion technique, cal...

As known, the problem of choosing ‘‘good’’ nodes is a central one in polynomial interpolation. While the problem is essentially solved in one dimension (all good nodal sequences are asymptotically equidistributed with respect to the arc-cosine metric), in several variables it still represents a substantially open question. In this work we consider new nodal sets for bivariate polynomial interpo...

We present parallel algorithms for fast polynomial interpolation. These algorithms can be used for constructing and evaluating polynomials interpolating the function values and its derivatives of arbitrary order (Hermite interpolation). For interpolation, the parallel arithmetic complexity is 0(log2 M + log N) for large M and N, where M 1 is the order of the highest derivative information and N...

In the paper, the geometric Lagrange interpolation by quadratic parametric patches is considered. The freedom of parameterization is used to raise the number of interpolated points from the usual 6 up to 10, i.e., the number of points commonly interpolated by a cubic patch. At least asymptotically, the existence of a quadratic geometric interpolant is confirmed for data taken on a parametric su...

We show that a nested sequence of C macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H(Ω), 1 < s < r+ 3 2 , and H 0(Ω), 1 < s < σ+ 3 2 , s / ∈ Z+ 1 2 , as soon as there is a nested sequence of Lagrange interpolation sets with uniformly local and bounded basis functions, and, in case of H 0(Ω), the nodal interpolation operators ...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

The Padua points are a family of points on the square [−1, 1] given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. Interpolation polynomials and cubature formulas based on the Padua points are studied from an ideal theoretic point of view, which leads to the discovery of a compact formula for the interpolation polynomials. The L convergence of the inter...