Hermite interpolation by piecewise polynomial surfaces with polynomial area element

Hermite interpolation by piecewise polynomial surfaces with polynomial area element

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 R (where they are equivalent to the PN surfaces) and in the Minkowski space R (where they provide the MOS surfaces). We show generally in real vector spaces of any dimension and any metric that the Gram determinant of a parametr...

Complete parameterization of piecewise-polynomial interpolation kernels

Every now and then, a new design of an interpolation kernel appears in the literature. While interesting results have emerged, the traditional design methodology proves laborious and is riddled with very large systems of linear equations that must be solved analytically. We propose to ease this burden by providing an explicit formula that can generate every possible piecewise-polynomial kernel ...

Hermite Interpolation Using ERBS with Trigonometric Polynomial Local Functions

Generalization of the Piecewise Polynomial Interpolation by Fractal Functions

The fractal interpolation functions defined by iterated function systems provide new methods of approximation and quantification of experimental data. The polynomial fractal functions can be considered as generalization of the piecewise polynomial interpolants. Assuming some hypotheses on the original function, a bound of the representation of the error for this kind of approximants is obtained...

Computing Moments of Piecewise Polynomial Surfaces

Combining the advantages of a low-degree polynomial surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of objects enclosed by a free-form surface. Volume, center of mass and the inertia tensor can be computed in seconds even for complex objects with 105 patches while changes due to local modification of the surface geometry can be compute...