The radial basis function interpolant is known to be the best approximation to a set of scattered data when the error is measured in the native space norm. The approximate moving least squares method, on the other hand, was recently proposed as an efficient approximation method that avoids the solution of the system of linear equations associated with the radial basis function interpolant. In t...

Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...

Este artigo tem como objetivo apresentar resultados do uso de uma unidade ensino dos conteúdos projeção ortogonal, amparado na teoria aprendizagem significativa e nos aspectos sequenciais para elaboração potencialmente significativa. Dados foram coletados com cinco alunos turma primeiro semestre um curso técnico em Edificações, no desenvolvimento 10 atividades. Por meio análise qualitativa, ten...

Smolyak’s sparse grid construction is commonly used in a setting involving quadrature of a function of a multidimensional argument over a product region. However, the method can be applied in a straightforward way to the interpolation problem as well. In this discussion, we outline a procedure that begins with a family of interpolants defined on a family of nested tensor product grids, and demo...

Interpolation is a form of function approximation in which the approximating function (interpolant) and the underlying function must agree at a finite number of points. In some cases additional restrictions may be imposed on the interpolant. For example its first derivative evaluated at a finite number of points may have to agree with that of the underlying function. Other examples include addi...

We present an algorithm for the efficient and accurate computation of geodesic distance fields on triangle meshes. We generalize the algorithm originally proposed by Surazhsky et al. [1]. While the original algorithm is able to compute geodesic distances to isolated points on the mesh only, our generalization can handle arbitrary, possibly open, polygons on the mesh to define the zero set of th...

Abstract— A smooth curve interpolation is very significant in computer graphics or in data visualization. In the present paper -piecewise rational cubic spline function with tension parameter is considered which produces a monotonic interplant to a given monotonic data set. The parameters in the description of the spline curve can be used to modify the shape of the curve, locally and globally. ...

Visualization depends among other things on the interpolant used in generating images. One way to assess this is to construct case tables for Marching Cubes that represent the chosen interpolant accuracy. Instead, we show how to construct the interpolants induced by Marching Cases for comparison and assessment, how to extend this approach to Marching Squares, Cubes and Hypercubes, and how to co...

4. Hermite Interpolants . . , . . . . . . . . . . . . . 104 4.1. The Co nine parameter interpolant ...... 104 4.2. C’ quintic interpolants .............. 104 4.3. The general case ................... 106 5. Split Triangle Interpolants . . . . . . . . . 107 5.1. The C’ Clough-Tocher interpolant . . _ . . 108 5.2. Limitations of the Clough-Tocher split . 110 5.3. The C’ Powell-Sabin interpolants ...