APPROXIMATING A HELIX SEGMENT WITH A RATIONAL BEZIER CURVE

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.