凸域上温度分布的无理函数插值近似方法

Irrational function interpolation and temperature distributions approximation within convex domains

采用计算机图形学中的多边形平均值坐标,构造出以多边形顶点为插值节点的无理函数插值方法。给出了无理函数插值在实际编程计算时的计算公式,利用这些公式可以很方便地编写出无理函数插值的计算程序。对于任意的凸区域采用一个凸多边形进行逼近,利用无理函数插值对凸域上的温度分布问题进行插值近似。数值算例表明,无理函数插值能够很好地反映出温度分布的特征。

In this paper, using mean value coordinates of polygon in computer graphics, the mean value interpolation method setting vertexes of polygon as interpolating nodes is presented. The computational formulae of mean value interpolation is given. It is easy to program it by using these formulae in practical computation. Any convex domain could be approached by convex polygon, for temperature distribution within convex domain, it could be approximated by irrational function interpolation. The numerical examples indicate that the features of temperature distributions are reflected exactly by mean value interpolation.