摘要
通过分析1维和2维线性插值可以推导出任意斜角直线坐标系下n维线性插值的一般计算公式以及有唯一解的条件,这一结论能够应用于三维温度场计算。可以将n维插值问题归结如下:已知n+1维空间中的n+1个点的坐标以及第n+2个点的n个坐标分量xn+2,1,x n+2,2,,xn+2,n,求解该点的第n+1个坐标分量xn+2,n+1。根据线性插值定义,第n+2个点位于前n+1个点所确定的n维超平面上。根据这一条件列写方程、求解方程可得到插值xn+2,n+1。n维插值问题有唯一解的条件是已知的n+1个点在n维空间中构成的多面体的体积不为0。推导过程在斜角直线坐标系中完成,因而结论具有较大普适性。
By analyzing 1- and 2-dimensional(2D) interpolation method, we derived anD linear interpolation formulae in oblique coordinate system and the condition that has a unique solution. The result can be applied in the calculation of 3D temperature field. The nD interpolation can be regarded as the following: Given the coordinates of n+l points in (n+1)D space and the coordinate x+2,1,xn+2,2,…,xn+2,n of the (n+2)th point, what is to solve is its (n+l)th coordinate. According to the definition of linear interpolation, the (n+2)th point locates on the nD superplane determined by the given n+1 points. Based on this, we derived the equations, and the root Xn+2,n+1 is the interpolation if existing. The root uniquely exists if and only if the volume of the hyperpolyhedron constructed by the given n+1 points is nonzero. The conclusion is of great universality due to derivating in oblique coordinate system.
出处
《中国惯性技术学报》
EI
CSCD
2007年第5期625-629,共5页
Journal of Chinese Inertial Technology
关键词
线性插值
空间
高维
斜角直线坐标
温度场
linear interpolation
space
high dimension
oblique angled rectilinear coordinate
temperature field