首页|G0 Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves
G0 Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves
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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.
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