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DOI:
:2001.12(10):1569-1572

五次PH曲线的Hermite插值
陈国栋,王国瑾
(浙江大学 CAD & CG国家重点实验室,浙江杭州 310027;浙江大学数学系,浙江杭州 310027)
Hermite Interpolation by PH Quintic
CHEN Guo dong,WANG Guo jin
()
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Received:January 25, 2000    Revised:June 12, 2000
> 中文摘要: 应用复分析和曲线积分方法研究了满足Hermite插值的五次PH曲线的构造,导出了其相应的Bézier表示.所得五次PH插值曲线不但具有连续的单位切矢和有向曲率,而且其弧长函数是原参数的多项式函数,具有精确的有理Offset代数表示和优美的几何解释,可灵活处理拐点.
中文关键词: 五次PH曲线  Hermite插值  有向曲率  光顺
Abstract:Using complex analysis and curve integration, the construction of PH quintic which satisfies Hermite interpolation conditions is studied in this paper and its corresponding Bézier representation is derived. The PH quintic has continuous unit tangents and signed curvature, and its arclength function is the polynomial of its parameter. The PH quintic has offset curve that admits exact rational algebraic representation, intuitive geometrical interpretation and can flexibly deal with inflection point.
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基金项目:国家自然科学基金资助项目(69973041);国家重点基础研究发展规划973资助项目(G1998030600);浙江省自然科学基金资助项目(698025) 国家自然科学基金资助项目(69973041);国家重点基础研究发展规划973资助项目(G1998030600);浙江省自然科学基金资助项目(698025)
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陈国栋,王国瑾.五次PH曲线的Hermite插值.软件学报,2001,12(10):1569-1572

CHEN Guo dong,WANG Guo jin.Hermite Interpolation by PH Quintic.Journal of Software,2001,12(10):1569-1572