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数学研究及应用
数学研究及应用

王仁宏

双月刊

2095-2651

jmre@dlut.edu.cn

0411-84707392

116024

大连理工大学应用数学系

数学研究及应用/Journal Journal of mathematical research with applicationsCSCD北大核心CSTPCD
查看更多>>本刊是国家教育部主管、大连理工大学主办的数学类学术性刊物。其宗旨是推进数学研究、评论数学研究、及时报道数学理论成果与应用数学成果。主要刊载有关数学的原创性的高质量的论文、研究简报、研究通讯；国内外数学著作的评论；数学方法论、数理哲学方面的文章。还介绍某些新兴边缘学科的数学研究方法及数学新分支，反映国内外数学工作者提出的未解决问题及国内外重要数学学术研究动态。读者对象是数学工作者、大专院校数学教师、理工科研究生、数学和力学专业高年级学生、有关科技工作者以及其他数学爱好者。
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    G0 Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves

    Wenqing FEIYongxia HAO
    408-426页
    查看更多>>摘要：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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      原文链接:
    • NETL
    • NSTL
    • 万方数据