From a differential geometric point of view a helix segment can be con
sidered as a spatial generalization of a circular are. Thus for proble
ms of shape preservation and geometric modelling an approximate ration
al representation of a helix segment is of interest. In this paper rat
ional Bezier curves of degree 4, 5 and 6 are presented that approximat
e a helix segment. The approximants fulfill certain geometric constrai
nts. A generalized degree elevation for rational polynomials in Bezier
representation is discussed and used for the construction. (C) 1997 E
lsevier Science B.V.