When dealing with randomly located or clustered data, interpolation error will vary as the distance to the nearest sample or cluster of samples. The current predominant methods for interpolating non-uniform data are not guaranteed to handle this variability of error well. The non-uniformity of the error surface can easily lead to gross misinterpretations of the interpolated values by the end user.
In order to address this limitation of the existing algorithms, this paper examines a method based on the physical structure of an infinitesimally small sphere at the point of interpolation. Using this structure we are able to interpolate based on the ‘illumination’ of nearby sample points.
Our analysis shows that Microsphere Projection is a viable interpolation technique, and in some cases surpasses the abilities of existing techniques. In one dimension, Microsphere Projection proves to be as accurate as piecewise cubic spline interpolation. In two dimensions, the accuracy of Microsphere Projection seems to outperform thin-plate spline interpolation; and in three dimensions its performance is at least on par with existing techniques. In hyper dimensions it is expected that Microsphere Projection will be even more useful due to its stable extrapolation properties.