Abstract: A new algorithm that constructs offsets of a planar algebraic curve by
approximating the algebraic curve with piecewise cubic PH curve is proposed. The approximation
errors are also estimated. The approximate PH curve keeps some important geometric features of
the original algebraic curve such as convexity, monotonicity and G1 continuity. Numerical
experiments show that the algorithm provides an efficient approach to approximate
parameterization of algebraic curves. The algorithm also provides a new method to calculate
rational parameter representation of the algebraic curve offsets.

Key words: computer application, offset curve, PH curve, algebraic curve