We review the theory of homogeneous splines and their relationship to special rational splines considered by J. SS anchez{Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of rational curves with rational oosets. We investigate geometric properties of these dual focal splines, and discuss...

Emotional argumentation is the result of a rational form of reasoning by the Persuader, subsequently translated into messages by applying some variants of the ‘classical’ argumentation schemes. In this paper, we discuss which may be assumed to be the relative strength of emotional vs. rational persuasion strategies and how this has been represented in a dialogic persuasion testbed.

We prove that degrees of rational solutions of an algebraic differential equation F (dw/dz,w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equation F (w′, w, z) = 0, (w′ = dw/dz) (1) where F is a polynomial in three variables. Theorem 1 For ...

In this paper, we start by introducing a novel disk rational Bézier based on parallel projection, whose properties are also discussed. Then applying weighted least squares, multiobjective optimization techniques and constrained quadratic programming, we achieve multi-degree reduction of this kind of disk rational Bézier curve. The paper also gives error estimation and shows some numerical examp...