Abstract: In view of the wide usage of the orthogonal basis such as Legendre basis in the
algebra polynomial space, the applications of the quasi-Legendre basis in inversion and offsetting
approximations are given in this paper. Inversion approximation is constructed by using the
blending of polynomial and hyperbolic functions, and the experimental results show that the
approximation method is effective. An approach to approximate the offset curves of the H-Bézier
curve based on the ideal approximation for the normal curve is presented. The algebraic
approximation algorithms which can obtain the control points of the approximation curves directly
are simple and more precise.

Key words: H-Bézier basis, quasi-Legendre basis, inverse function, offset curve