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曲面隐式化新进展 被引量：7

Recent advances on surface implicitization
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摘要 给定曲线/曲面的参数方程求其隐式方程,称为曲线/曲面的隐式化.隐式化是经典代数几何消元理论中的研究问题,同时在现代计算数学与计算机应用的交叉学科分支——计算机辅助几何设计中有重要应用.本文在回顾曲线与曲面隐式化的经典方法的基础上,重点介绍近十几年发展起来的基于动曲线/曲面与μ基理论的隐式化方法的相关进展. The procedure of converting the parametric equation of a curve or a surface into the implicit equation is called implicitization.Implicitization is a classic elimination problem in algebraic geometry and has found important applications in computer aided geometric design an inter-discipline in computer science and scientific computing.The classic methods for implicitization were reviewed first,and then the state of the art techniques in curve and surface implicitization were surveryed,especially the recent advances of the moving curves/surfaces method andμ basis method developed in the last decade.
作者 陈发来
机构地区 中国科学技术大学数学院
出处 《中国科学技术大学学报》 CAS CSCD 北大核心 2014年第5期345-361,共17页 JUSTC
基金 国家重点基础研究发展(973)计划(2011CB302400) 国家自然科学基金重点项目(11031007)资助
关键词 参数曲线 参数曲面 隐式化 结式 GROEBNER基 吴方法 动曲线 曲面 μ基 parametric curve parametric surface implicitization resultant Groebner basis Wu＇s method moving curves/surfaces μ-basis
分类号 TB115 [理学—应用数学]
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参考文献48

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同被引文献37

  • 1康宝生,石茂,张景峤.有理Bézier曲线的降阶[J].软件学报,2004,15(10):1522-1527. 被引量：18
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  • 7LIU Ligang, WANG Guojin. Recusive formulae for hermite polynomial approximations to rational Bezier curves [C]// Proceedings of Geometric Modeling and Processing 2000 : Theory and Applications. Hong Kong: IEEE Computer Society Press, Los Alamitos, 2000: 190-197.
  • 8CHEN Jie, WANG Guojin. Hybrid polynomial ap- proximation to higher derivatives of rational curves [J]. Journal of Computational and Applied Mathemat- ics, 2011, 235(17):4925-4936.
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  • 10AHN Y J. Using Jacobi polynomials for degree reduc- tion of B6zier curves with Ck-constraints[J]. Comput- er Aided Geometric Design, 2003, 20(7):423-434.

引证文献7

二级引证文献14

中国科学技术大学学报
2014年 第5期

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