ABSTRACT
The theory of Tchebycheffian B-splines (cf. [10]), is based on the theory of Tchebycheffian systems (cf. [5]). Recently, the importance of these free form schemes was shown by Lempel and Seroussi (cf. [7]), who gave an explicit derivation of general spline bases over function spaces closed under differ entiation. In this paper we use a more geometric approach. Based on the normal curve of the associated function space, which was first introduced for B-splines by Seidel (cf. [11]), one can define a blossoming method and a de Casteljau algorithm for the construction of a Tchebycheffian B-spline segment (cf. [8]). First we give a brief introduction to these methods. The main part of the paper discusses symmetric Tchebycheffian splines. We present an explicit derivation of the possible spline bases and give some geometric interpretations of the achieved results.
