The paper presents a technique for construction of C interpolating rational Bézier spline curves by means of blending rational quadric Bézier curves. A class of polynomials which satisfy special boundary conditions is used for blending. Properties of the polynomials are considered. The constructed spline curves have local shape control that make them useful in such geometric applications as rea...

Abstract Bezier curves are indispensable for geometric modelling and computer graphics. They have numerous favourable properties provide the user with intuitive tools editing shape of a parametric polynomial curve. Even more control flexibility can be achieved by associating parameter each point considering rational curves, which comes additional advantage being able to represent all conic sect...

In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure o...

This paper presents a method to selectively elevate the degree of an S-Patch of arbitrary dimension. We consider not only S-Patches with 2D domains but 3D and higher-dimensional domains as well, of which volumetric cage deformations are a subset. We show how to selectively insert control points of a higher degree patch into a lower degree patch while maintaining the polynomial reproduction orde...