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.