In this paper, we discuss an interpolation method which can be used to create a look up table to map tristimulus values to BRDF parameters. For a given tristimulus value, we interpolate the XYZ lattice formed by eight primaries and secondaries that were printed and measured, and their corresponding optimised BRDF parameters. The BRDF parameters are obtained by careful optimisation of the Ward model and Cook Torrance model with the BRDF measurements of these primaries. The interpolated BRDF parameters of nine test samples from the same printed samples were then evaluated against the optimised BRDF parameters and their reference BRDF measurements. The results show that, this simple and efficient interpolation method produces consistent BRDF parameters that preserves the diffuse colour of the input sample.
Two methods to transform primary chromaticities and white point into primary tristimulus values are examined and compared. One method appears in numerous places in the literature; we refer to this as the "familiar" method, and provide a novel interpretation of it. The second is much less well-known and is referred to as the "unfamiliar" method. Necessary and sufficient conditions for computing primary tristimulus values from their chromaticities are identified; in brief, the triangle in the (x, y) chromaticity diagram must have non-zero area. The computational burdens for the methods were compared; the familiar method required slightly more arithmetical operations. Two problems with the familiar method were identified: high potential for rounding error and the inability to contend with a non-luminous primary. The unfamiliar method is less prone to rounding error, and is able to contend with primaries on the alychne. It is recommended that the unfamiliar method be preferred.