计算机工程

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UQT-样条曲线曲面的融合及其应用

刘华勇,谢新平,李璐,张大明   

  1. (安徽建筑大学数理学院,合肥 230601)
  • 收稿日期:2014-11-24 出版日期:2016-02-15 发布日期:2016-01-29
  • 作者简介:刘华勇(1972-),男,副教授、硕士,主研方向为计算机图形学、虚拟现实;谢新平、李璐,讲师、硕士;张大明,副教授、博士。
  • 基金项目:
    国家自然科学基金资助项目(61402010);安徽省高等学校自然科学研究基金资助项目(KJ2015A328,KJ2015JD16,KJ2014A041)。

Integration and Application of UQT-spline Curves and Surfaces

LIU Huayong,XIE Xinping,LI Lu,ZHANG Daming   

  1. (School of Mathematics & Physics,Anhui Jianzhu University,Hefei 230601,China)
  • Received:2014-11-24 Online:2016-02-15 Published:2016-01-29

摘要: 在计算机辅助几何设计中,封闭曲线曲面的表示通常采用拼接的方法,但这种方法的计算相对较为复杂,且连续阶不高,为了更好地表示封闭的曲线曲面,提出一种非均匀四次三角样条(UQT-样条)曲线曲面的融合方法。构造UQT-样条基函数,讨论基于五点分段的UQT-样条曲线的性质以及曲面性质,利用曲线融合的思想,构造UQT-样条融合曲线和曲面,并研究其性质。实验结果表明,该融合的曲线曲面能较好地表示封闭的曲线曲面,且不需要添加额外的控制顶点,便于交互。

关键词: 三角样条, 融合, 连续性, 封闭的曲线曲面, 形状参数

Abstract: In computer aided geometric design,the representation of closed curves and surfaces usually uses the method of joint,but this method is relatively complex and has lower continuity.In order to better represent the closed curve and surface,the integration method of non Uniform Quartic Triangular Spline(UQT-spline) is proposed.Firstly UQT-spline basis functions are constructed and the properties of the UQT-spline curves based on five points are discussed,then the UQT-spline curves and surfaces are constructed by using the idea of blending curve.Experimental results show that the integration of curve and surface can well represent closed curves and surfaces with no additional control points,and are easy to interact.

Key words: trigonometric spline, integration, continuity, closed curve and surface, shape parameter

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