PH-C curve approximation of planar algebraic curves

Approximate parameterization of algebraic curve is an important topic in computer aided geometric design and graphics.PH-C curve inherits all the good quality from Bezier curve,PH curve and C curve,therefore PH-C curve approximation of algebraic curve is necessary.The algebraic curve is segmented according to convexity and monotonicity,the control polygon is constructed based on angles between two tangent lines and the line connecting two end points.A detailed algorithm is proposed to approximate algebraic curve with piecewise degree 3 PH-C curve.The approximate PH-C curve keeps some important geometric features of the original algebraic curve such as convexity、monotonicity and G1 continuity.The approximation error can be controlled by means of recursively use of the algorithm.Numerical experiments show that the algorithm provided an efficient approach to approximate parameterization of algebraic curve.