带形状参数的二次三角多项式曲线  

QUADRATIC TRIGONOMETRIC POLYNOMIAL CURVES WITH SHAPE PARAMETER

作　　者：李明珠[1] 陈丽娟[1] 

机构地区：[1]青岛理工大学理学院,青岛266033

出　　处：《高等学校计算数学学报》2013年第4期289-294,共6页Numerical Mathematics A Journal of Chinese Universities

摘　　要：B样条曲线特别是二、三次样条曲线，因其构造简单使用灵活，广泛应用到工程技术上，在CAGD和CG中占有重要的地位．但其有一定的缺点，如不能表示圆锥曲线等．非均匀有理样条虽然可以表示圆锥曲线，但有求导求积过于复杂，权因子选取不清楚等缺点．This paper presents a quadratic trigonometric polynomial curves with a shape parameter ,~. Analogous to the quadratic B-spline curves, each trigono- metric polynomial curve segment is generated by three consecutive control points. For equidistant knots, the trigonometric polynomial curves are C1 continuous, but when the shape parameter equals to 1, the curves are C3 continuous. This trigono- metric polynomial can be used to construct open and closed curves and express ellipse. From examples, the bigger λ is, the closer curves near to the control poly- gon.

关 键 词：多项式曲线 形状参数 三角 三次样条曲线 圆锥曲线 B样条曲线 工程技术 CAGD 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]