集逼近插值于一体的分段三次多项式曲线曲面  

Piecewise cubic polynomial curve and surface combining approximation and interpolation into one

作　　者：严兰兰[1,2] 韩旭里[2] 应正卫[1] 

机构地区：[1]东华理工大学理学院,南昌330013 [2]中南大学数学与统计学院,长沙410083

出　　处：《计算机应用研究》2015年第8期2529-2532,2537,共5页Application Research of Computers

基　　金：国家自然科学基金资助项目(11261003;11271376;60970097);江西省教育厅科技项目(GJJ14493)

摘　　要：为了用一种模型实现逼近与插值的统一,在多项式函数空间上构造了含两组参数的混合函数,并由之定义了基于四点分段的多项式曲线和相应的张量积曲面。当参数取特殊值时,新曲线曲面成为三次均匀B样条曲线曲面。除了继承B样条方法的局部性、自动光滑性等优点之外,新曲线曲面还具有局部形状可调性。限制混合函数中参数的取值范围,可以使新曲线曲面位于控制顶点的凸包内;让混合函数中的一组参数取特定值,可以使新曲线曲面自动插值除边界点以外的控制顶点,且插值曲线曲面的形状依然局部可调,并给出了一些曲线曲面图例。In order to use one model to realize the unification of the approximation and interpolation, this paper constructed a kind of blending function which contained two groups of parameters in the polynomial function space. Based on the blending function, it defined a kind of polynomial curve on four-point piecewise scheme and the corresponding tensor product surface. When taking special parameters, the new curve and surface became the cubic uniform B-spline curve and surface. In addition to the locality and automatic smoothness, the new curve and surface also had local shape adjustability. Limiting the value range of the parameters of the blending function, the new curve and surface could be located within the convex hull of the control points. Letting one set of the parameters take a specific value, the new curve and surface could pass through the control points except the boundary points. The shape of the interpolation curve and surface is still local adjustable. It gave some curves and surfaces illustrations.

关 键 词：B样条曲线曲面 逼近与插值 分段组合 形状参数 连续性 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]