Approximating a helix segment with a rational Bézier curve Original Research Article

From a differential geometric point of view a helix segment can be considered as a spatial generalization of a circular arc. Thus for problems of shape preservation and geometric modelling an approximate rational representation of a helix segment is of interest. In this paper rational Bézier curves of degree 4, 5 and 6 are presented that approximate a helix segment. The approximants fulfill certain geometric constraints. A generalized degree elevation for rational polynomials in Bézier representation is discussed and used for the construction.