Hiroshi Sakuta 
Oct.22,1997
This method is based on the 2 dimensional bilinear interpolation, and the reference points are selected by Aitken's algorithm. Select three reference points are
and the objective point is
A couple of 1st order independent vectors which are introduced
can make arbitrary vectors on the plane.
The objective vector 
is defined as following,
Here, the projections of 
, 
and on X-Y plane are
defined as
,
and
, where
To solve this equation about 
and 
,
the scalar products of
with 
and 
are made.
As the numerical treatment, the truncation error should be
considered in and calculation.
The condition, in which the truncation error affects the overflow of floating point calculation, is the dominator is nearly equal to 0.
Then
is the angle between and .
This means the selected points 
, 
and 
are
almost on a line, 
or 
.
The algorithm of its implementation should be avoided
this condition and select another point as reference.
Finally,
will give the interpolated value.