The problem of interpolating a set-valued function with convex images is addressed by means of directed sets. A directed set will be visualised as a usually nonconvex set in R consisitng of three parts, the convex, the concave and the mixed-type part together with its normal directions. In this Banach space, a mapping resembling the Kergin map is established. The interpolating property and erro...

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0, 2π). Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to...

one of the most valuable and important application of artificial satellites in geodetic sciences is recovery of the earth's gravity field. orbits of satellites either gravimetric or nongravimetric are analyzed to improve the earth's gravity field. gravimetric satellites are launched at low altitudes to observe gravity field in more detail. grace twin satellites are the second spacecra...

We propose a general study of the convergence of a Hermite subdivision scheme H of degree d > 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme S. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of S is contractive, then S is C...

We present several Hermite-type interpolation methods for rational cubics. In case the input data come from a circular arc, the rational cubic will reproduce it. c © 2008 Elsevier Ltd. All rights reserved.

In this work, we present a method to interactively create multi-segment, curved handles between two star-shaped faces of an orientable 2-manifold mesh or to connect two 2-manifold meshes along such faces. The presented algorithm combines a very simple 2D morping algorithm with a Hermite interpolation to construct the handle. Based on the method, we have developed a user interface tool that allo...

In this article we define a new class of Pythagorean-Hodograph curves built-upon a sixdimensional mixed algebraic-trigonometric space, we show their fundamental properties and compare them with their well-known quintic polynomial counterpart. A complex representation for these curves is introduced and constructive approaches are provided to solve different application problems, such as interpol...

Construction methods are presented that generate hermite interpolation quaternion curves on SO(3). Two circular curves C 1 (t) and C 2 (t), 0 t 1, are generated that interpolate two orientations q 1 and q 2 , and have boundary angular velocities: C 0 1 (0) = ! 1 and C 0 2 (1) = ! 2 , respectively. They are smoothly blended together on SO(3) to generate a hermite quaternion curve Q(t) 2 SO(3), 0...

Article history: Available online 29 April 2010