Abstract
The task of identifying the quintic PH curve G0"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 effi-ciently 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 G0 PH curve closer to the given Bézier curve with close arc length.Moreover,good approximations with prescribed arc length can also be achieved.
基金项目
National Natural Science Foundation of China(11801225)
NETL
NSTL
万方数据