Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD building wavelets numerical PDEs. In this paper, we introduce a notion of generalized (dyadic) then characterize their convergence, smoothness underlying matrix masks with or without interpolation properties....

In this paper we give new proofs of some elementary properties of the Hermite and Laguerre orthogonal polynomials. We establish Rodriguestype formulae and other properties of these special functions, using suitable operators defined on the Lie algebra of endomorphisms to the vector space of infinitely many differentiable functions.

We present an interpolation scheme for first order Hermite motion data (two positions with associated instantaneous screws specifying the tangent vector fields) that is based on a generalization of the classic biarc construction to curves on quadrics. The result is a sequence of Bennett motions. These motions possess several properties that make them particularly useful for motion interpolation...

The construction of space curves with rational rotationminimizing frames (RRMF curves) by the interpolation of G1 Hermite data, i.e., initial/final points pi and pf and frames (ti,ui,vi) and (tf ,uf ,vf ), is addressed. Noting that the RRMF quintics form a proper subset of the spatial Pythagorean–hodograph (PH) quintics, characterized by a vector constraint on their quaternion coefficients, and...

We discuss several applications of the Leja point method for univariate polynomial interpolation. First we show how more or less arbitrary interpolation points sets can be stabilized by adding some points from the Leja sequence generated beginning with the given set. We then show how the Leja point idea can be used to generate good point sets for Hermite–Lagrange polynomial interpolation. Then ...

Let be an arbitrary regular triangulation of a simply connected compact polygonal domain R 2 and let S 1 q (() denote the space of bivariate polynomial splines of degree q and smoothness 1 with respect to. We develop an algorithm for constructing point sets admissible for Lagrange interpolation by S 1 q (() if q 4. In the case q = 4 it may be necessary to slightly modify , but only if exeptiona...

A recursive algorithm for Hermite interpolation of bivariate data over triangular grids is presented. This interpolation algorithm has a dynamic programming flavor and it computes a single polynomial that interpolates the full set of data. The data we interpolate are partial derivatives and mixed partials up to some fixed order at the nodes of the grid. The interpolant is a polynomial with mini...