Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (7): 39-43.DOI: 10.3778/j.issn.1002-8331.2010.07.012

• 研究、探讨 • Previous Articles     Next Articles

Properties and applications of a Class of trigonometric polynomial curves

CHENG Rong,PAN Yong-juan,ZHOU Ming-hua   

  1. College of Science,Zhejiang University of Technology,Hangzhou 310023,China
  • Received:2008-09-19 Revised:2008-12-29 Online:2010-03-01 Published:2010-03-01
  • Contact: CHENG Rong


程 荣,潘永娟,周明华   

  1. 浙江工业大学 理学院,杭州 310023
  • 通讯作者: 程 荣

Abstract: The B-L(Bézier-Like) curves over the trigonometric function space Φ7=span{1,sint,cost,cos2t,sin3t,cos3t,sin4t,cos4t}and Φ8=span{1,sint,cost,sin2t,cos2t,sin3t,cos3t,sin4t,cos4t} are constructed,the explicit expressions of the B-L curves are presented.Then some properties and applications of this kind of curves are discussed.Cardioid,elliptic curves,circular arc,ellipsoid,sphere without rational form are precisely expressing,and circular helix is approximated by the B-L curves.Examples are given to illustrate the convenience and validity in model design.

Key words: trigonometric polynomial, trigonometric basis, B-L curves and surfaces

摘要: 在三角函数空间Φ7=span{1,sint,cost,cos2t,sin3t,cos3t,sin4t,cos4t}和Φ8=span{1,sint,cost,sin2t,cos2t,sin3t,cos3t,sin4t,cos4t}中构造了B-L(Bézier-Like)曲线,并给出其显式表达式。进一步讨论了该曲线的若干性质和应用,给出了不需要有理形式的心脏线、椭圆(圆)弧等的B-L曲线精确表示,椭球(球)面的B-L曲面精确表示,以及圆柱螺线的B-L曲线逼近表示。通过实例说明在造型设计方面使用简便且有效。

关键词: 三角多项式, 三角基, B-L曲线曲面

CLC Number: