Geometric methods in rational interpolation theory

Geometric Interpolation by Quartic Rational Spline Motions

We discuss piecewise rational motions with first order geometric continuity. In addition we describe an interpolation scheme generating rational spline motions of degree four matching given positions which are partially complemented by associated tangent information. As the main advantage of using geometric interpolation, it makes it possible to deal successfully with the unequal distribution o...

Krylov Projection Methods for Rational Interpolation

Lagrange geometric interpolation by rational spatial cubic Bézier curves

In the paper, the Lagrange geometric interpolation by spatial rational cubic Bézier curves is studied. It is shown that under some natural conditions the solution of the interpolation problem exists and is unique. Furthermore, it is given in a simple closed form which makes it attractive for practical applications. Asymptotic analysis confirms the expected approximation order, i.e., order six. ...

Hermite Geometric Interpolation by Rational Bézier Spatial Curves

Polynomial geometric interpolation by parametric curves became one of the standard techniques for interpolation of geometric data. An obvious generalization leads to rational geometric interpolation schemes, which are a much less investigated research topic. The aim of this paper is to present a general framework for Hermite geometric interpolation by rational Bézier spatial curves. In particul...

Geometric Methods in Representation Theory

These are notes from the mini-course given by W. Schmid in June 2003 at the Brussels PQR2003 Euroschool. Both authors are very thankful to Simone Gutt for organizing the conference and her hospitality.