一类新的有理四次样条曲线的形状控制  

SHAPE CONTROL OF A NEW RATIONAL BIQUADRATIC INTERPOLATION SPLINE

作　　者：李莉[1] 唐月红[1] 钱伟密[1] 刘琳[1] 

机构地区：[1]南京航空航天大学数学系,南京211106

出　　处：《南京大学学报（数学半年刊）》2012年第2期226-236,共11页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：本文基于Cauchy—Vandermonde函数组构造了一类带控制参数包含极点的（4，2）^1阶加权有理插值样条．以它为逼近工具可以很方便地通过选取参数调整其曲线形状，比较多项式样条和其它的有理样条具有更灵活、有效、还能刻划被插函数的奇性等固有特性．特别地权系数的引入，增加了曲线形状控制中约束不等式的可解性．当权系数λ=0，λ=1时，它退化成已有（4，2）^1阶有理插值样条的重要曲线类．进一步研究了约束插值问题，推导出了这种曲线约束于给定折线、分段二次曲线之上，之下或之间的充分条件，由此，通过对参数和权系数的不等式约束，实现对有理插值样条曲线的区域控制，数值例子验证了方法的可行性和有效性．In the paper, based on the Cauchy-Vandermonde functions, a kind of control parameters and extreme points weighted rational interpolating spline of order （4, 2）^1 is constructed.As a tool of approximation, we can easily modify the curve shape by choosing parameters,and it is more flexible and effective than the polynomial spline and other rational splines, further,it can also depict singularity and other inherent characteristics of the function being interpolated. Particularly, introduction of weight coefficient parameters increases solvability of constrained inequalities in curve shape control. When the weight coefficient parameters λ = 0 and λ = 1, it degenerates into the existing important rational inter- polating spline curves of order （4, 2）^1. Then the paper studies the constraint interpolation problem, and the sufficient condition for the interpolating curves to be above, below or between the given broken lines or piecewise quadratic curves are derived respectively.Thus, by constraint inequalities with parameters and weight coeigficient parameters, it realize aero control of rational interpolating spline curve. The numerical examples vertify the feasibility and validity of the method

关 键 词：计算几何 有理样条 约束插值 权系数 

分 类 号：O174.41[理学—数学]