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郑志浩, 汪国昭. 基于边长约束的非本原7次PH曲线识别[J]. 计算机辅助设计与图形学学报, 2019, 31(3): 378-384. DOI: 10.3724/SP.J.1089.2019.17255
引用本文: 郑志浩, 汪国昭. 基于边长约束的非本原7次PH曲线识别[J]. 计算机辅助设计与图形学学报, 2019, 31(3): 378-384. DOI: 10.3724/SP.J.1089.2019.17255
Zheng Zhihao, Wang Guozhao. Identification of Non-Prime Septic Pythagorean Hodograph Curves Based on Leg-Length Constraints[J]. Journal of Computer-Aided Design & Computer Graphics, 2019, 31(3): 378-384. DOI: 10.3724/SP.J.1089.2019.17255
Citation: Zheng Zhihao, Wang Guozhao. Identification of Non-Prime Septic Pythagorean Hodograph Curves Based on Leg-Length Constraints[J]. Journal of Computer-Aided Design & Computer Graphics, 2019, 31(3): 378-384. DOI: 10.3724/SP.J.1089.2019.17255

基于边长约束的非本原7次PH曲线识别

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

  • 摘要: 逆向工程中,已有识别PH(Pythagorean-hodograph)曲线的方法主要是由判断多项式曲线导数的模长平方是否为完全平方项来决定,这要涉及有关高次方程的重根计算,不仅求解收敛速度慢,而且极易产生舍入误差.为避免以上问题,采用几何方法,首先针对具有不同控制顶点的7次Bézier曲线控制多边形,在引入有关辅助线及辅助点的预处理下,给出该曲线能成为2类非本原PH曲线的边长约束条件;然后对结论进行详细证明;最后,以实例来阐述识别的具体步骤.结果表明,非本原PH曲线的识别,可归结为验证所对应的2组边长约束条件是否满足.

     

    Abstract: 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.

     

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