一类三角多项式曲线的性质及应用  

Properties and applications of a Class of trigonometric polynomial curves

作　　者：程荣[1] 潘永娟[1] 周明华[1] 

机构地区：[1]浙江工业大学理学院,杭州310023

出　　处：《计算机工程与应用》2010年第7期39-43,共5页Computer Engineering and Applications

基　　金：国家自然科学基金No.60673063;No.60673031~~

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。The B-L（Bezier-Like） curves over the trigonometric function Space Ф7=span{1,sint,cost,cos2t,sin3t,cos3t,sin4t,cos4t} and Фs =span {1, sint, cost, sin2t, eos2t, sin3t, eos3t, 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 diseussed.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.

关 键 词：三角多项式 三角基 B—L曲线曲面 

分 类 号：O29[理学—应用数学]