局部可调的四次Catmull-Rom样条曲面及其形状优化

A locally adjustable quadric Catmull-Rom spline surface and its shape optimization

当控制顶点保持不变时,无法对三次Catmull-Rom样条曲面的形状进行局部调整。为满足实际工程对插值曲面形状设计的要求,给出了一种含局部参数的四次Catmull-Rom样条曲面,并讨论了2种对四次Catmull-Rom样条曲面形状进行优化的方案。结果表明,四次Catmull-Rom样条曲面不仅继承了三次Catmull-Rom样条曲面的插值性与连续性,而且容易利用所含的参数对曲面形状进行局部或整体调整,通过计算所含参数的最优值获得尽可能光顺和尽可能保形的四次Catmull-Rom样条曲面,为插值曲面的构造提供了方法。

The shape of the cubic Catmull-Rom spline cannot be adjusted locally when the control points remain unchanged.In order to meet the needs of the shape design of interpolation surfaces in practical engineering problems,a quadric Catmull-Rom spline surface with local parameters is presented,and two schemes for optimizing the shape of the quadric Catmull-Rom spline surface are given.The results show that the quadric Catmull-Rom spline surface not only inherits the interpolation and continuity property of the cubic Catmull-Rom spline surface,but also allow us to use the parameters contained to adjust its shape locally or globally.By determining the optimal values of the parameters,the desired smooth and shape-preserving quadric Catmull-Rom spline surface can be obtained.The proposed quadric Catmull-Rom spline surface and its shape optimization schemes provide methods for the construction of interpolation surfaces.