Identification of Non-Prime Septic Pythagorean Hodograph Curves Based on Leg-Length Constraints

In reverse engineering,the current approach to identification of a PH(Pythagorean-hodograph)curve depends on whether or not the square of hodograph norm of the polynomial curve is factorized into a perfect square.The process involves computing root pairs of even multiplicity with respect to equations with higher order.However,methods to compute multiple roots are typically slow to converge and sensitive to rounding errors.Thus,geometric method is adopted.Firstly,some auxiliary straight lines and points are introduced to pretreat the control polygon of septic Bézier curve with distinct ordered sequence of control points,and the leg-length constraints for identifying two classes of non-prime septic PH curves are proposed.Then we give the detailed proofs for the above results.Finally,examples are given to elucidate the identifying procedures.From the example results,the identification scheme for non-prime septic PH curves is reduced to verifying that the corresponding leg-length constraints are satisfied.