G^(0)Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves  

作　　者：Wenqing FEI Yongxia HAO 

机构地区：[1]School of Mathematical Sciences,Jiangsu University,Jiangsu 212000,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第3期408-426,共19页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11801225)。

摘　　要：The task of identifying the quintic PH curve G^(0)“closest”to a given planar Bézier curve with or without prescribed arc length is discussed here using Gauss-Legendre polygon and Gauss-Lobatto polygon respectively.By expressing the sum of squared differences between the vertices of Gauss-Legendre or Gauss-Lobatto polygon of a given Bézier and those of a PH curve,it is shown that this problem can be formulated as a constrained polynomial optimization problem in certain real variables,subject to two or three quadratic constraints,which can be efficiently solved by Lagrange multiplier method and Newton-Raphson iteration.Several computed examples are used to illustrate implementations of the optimization methodology.The results demonstrate that compared with Bézier control polygon,the method with Gauss-Legendre and Gauss-Lobatto polygon can produce the G^(0)PH curve closer to the given Bézier curve with close arc length.Moreover,good approximations with prescribed arc length can also be achieved.

关 键 词：Pythagorean-hodograph curves Gauss-Legendre polygon Gauss-Lobatto polygon constrained optimization Lagrange multiplier Newton-Raphson iteration 

分 类 号：O186.11[理学—数学]