The loci in CIE space of colors with a given difference from a standard are calculated from the Adams-Nickerson equation. The calculation is carried out by means of a point-by-point transformation from an intermediate chromatic value space to CIE space. Digital computers are used for the entire calculation and transformation. The calculated quasi-ellipsoids may be compared with those observed by Brown and MacAdam. For routine decision work, an approximation involving the intersection of three right cylinders based on projections of the original ellipsoid is employed.
ASCER OPLER and M. D. YEAMAN, "Calculation of CIE Coordinates of Color Tolerance Ellipsoids," J. Opt. Soc. Am. 47, 253-253 (1957)