摘要
在空间Ω=span{1,t,sint,cost,sin2t,cos2t}中提出了一种新的带形状参数的三次代数三角插值样条,该样条具有许多与三次B样条类似的性质。所构造的曲线曲面无需解方程组或插入某些节点即可直接插值某些控制顶点。曲线能精确表示直线段、椭圆(圆)弧、抛物线弧以及圆柱螺旋、三角函数曲线等一些超越曲线,相应的张量积曲面能精确表示一些二次曲面和超越曲面,如球面、圆柱面和螺旋柱面等。通过改变基函数中的全局参数的取值可整体调节曲线曲面的形状,并利用奇异混合技术在三次代数三角插值样条中引入局部参数,使曲线曲面的形状能局部调节。几何造型实例表明,三次代数三角插值样条可作为几何造型的一种新的有效模型。
A new kind of cubic algebraic trigonometric interpolation splines with a shape parameter over space Ω=span {1, t, sint, cost, sint2t, cos2t} was presented. The interpolation splines have many similar properties with cubic B--splines. The curves and surfaces can interpolate directly some control points without solving system of equations or inserting some additional control points. The curves can be used to exactly represent straight line segment, circular arc, elliptic arc, parabola and some transcendental curves such as circular helix. The corresponding tensor product surfaces can also precisely represent some quadratic surfaces and transcendental surfaces, such as sphere, cylindrical surfaces and helix tube. The shape of the curves and surfaces can be modified globally through changing the values of the parameters. Furthermore, the local parameters are introduced in the splines using the singular blending technique. Examples are given to illustrate that the splines can be used as a novel efficient model for geometric design in the fields of CAGD.
出处
《计算机工程与科学》
CSCD
北大核心
2013年第5期130-135,共6页
Computer Engineering & Science
基金
湖南省教育厅资助科研项目(11C0707)
关键词
三次B样条
代数三角样条
插值
形状参数
奇异混合
cubic B-splines
algebraic-trigonometric spline
interpolation
shape parameter
singular blending
