Interpolation of the MacAdam ellipses

Abstract

This paper is an attempt to provide a rigorous basis to the interpolation of the MacAdam ellipses. It starts by defining criteria used to compare the different possible interpolations. Then several interpolation strategies are compared. The main conclusion that arises from this comparison is that the ellipses should not be interpolated based on the coefficients of the matrices of the corresponding scalar products, as MacAdam suggested, but on the coefficients of their inverses. It also appears that the $uv$ parameters tend to gives better results than the $xy$ and $ab$ parameters.