Geometric Properties of Control Polygon of Septic PH Curve

Based on the definition of PH curve and complex representation of planar curve, the sufficient and necessary conditions for septic Bézier curve are explored to possess Pythagorean Hodograph.Septic PH curves are divided into four categories on the basis of the degree of greatest common divisor of two components of their hodograph.Concerning each type of septic PH curves, their geometric properties are expressed in terms of geometric magnitudes of control polygon.Besides, in order to avoid introducing coordinate system, an order reduction method is proposed to compute the greatest common divisor of hodograph using geometric magnitudes of control polygon.