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multiple shape parameter
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     Uniform B-spline curves with multiple shape parameters
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Extensions of Bézier curves and Bézier surfaces over triangular domain with multiple shape parameters are presented in this paper. They include the common Bézier curves and surfaces. Their blending functions have explicit expressions and are easy to derivate and integrate. The shape of the curves and surfaces can be adjusted entirely or locally by changing the values of the shape parameters.

通过引入多个形状参数,生成Bézier曲线与三角域Bézier曲面的扩展,它们包含普通的Bézier曲线曲面为其特例.这类多项式曲线与曲面的调配函数具有显式表示,易于求导和求积.改变形状参数的值能整体或局部调控曲线与曲面的形状.

A method of generating quadratic B-spline curves with multiple shape parameters is presented, which is C1-continuous with a non-uniform knot vector, and is C2-continuous with a uniform knot vector when all shape parameters are equal to 1. Compared with the quadratic B-spline curve without shape parameters, the shape of the curve can be adjusted totally or locally and approach the given polygon from both sides. Without using multiple knots or solving system of equations,...

A method of generating quadratic B-spline curves with multiple shape parameters is presented, which is C1-continuous with a non-uniform knot vector, and is C2-continuous with a uniform knot vector when all shape parameters are equal to 1. Compared with the quadratic B-spline curve without shape parameters, the shape of the curve can be adjusted totally or locally and approach the given polygon from both sides. Without using multiple knots or solving system of equations, the curve can interpolate control points or control sides directly.

提出一种带形状参数的二次B样条曲线,这种曲线对非均匀节点为C1-连续,对于均匀节点且当所有参数都等于1时为C2-连续.与不带形状参数的二次B样条曲线相比,其形状既能整体变化又能局部变化,并且能从两侧逼近控制多边形.此外,毋需采用重节点技术或解方程组就能直接插值控制点或控制边.

Cubic non-uniform trigonometric polynomial curves with multiple shape parameters are presented in this paper.They are C~2-continuous for a non-multiple knot vector and C~3-continuous for a uniform knot vector respectively.The ellipses can also be represented by them.Taking different values of the shape parameters,one can totally or locally adjust the shapes of the curves.Trigonometric Bézier curves with multiple shape parameters are also discussed.

对于非均匀节点向量给出了一类带多个形状参数的三次三角多项式曲线,这类曲线具有三次多项式B样条的许多重要性质:对非重节点为C2-连续,对均匀节点则为C3-连续,能直接表示椭圆.根据形状参数的各种不同取值,人们既能整体、又能局部地调控这类曲线的形状.此外,还讨论了多形状参数的三角Bézier曲线的情况.

 
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