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

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.