Orthogonal Polynomials on Planar Cubic Curves

Geometric interpolation by planar cubic polynomial curves

The purpose of this paper is to provide sufficient geometric conditions that imply the existence of a cubic parametric polynomial curve which interpolates six points in the plane. The conditions turn out to be quite simple and depend only on certain determinants derived from the data points.

On interpolation by Planar cubic G2 pythagorean-hodograph spline curves

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is ...

On Interpolation by Planar Cubic G Pythagorean-hodograph Spline Curves

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is ...

Systems of Orthogonal Polynomials on Certain Algebraic Curves

Interpolation scheme for planar cubic G2 spline curves

In this paper a method for interpolating planar data points by cubic G splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existence of such a polynomial interpolant are derived. The obtained results are extended to the case when the de...