A fast and accurate model to compute optimal colors under a given illuminant is introduced. The model estimates the reflectance (transmittance) distributions of optimal colors, which is bandpass (Type 1) or bandstop (Type 2), at a given luminance factor with user-specified small tolerances for the bandwidth (e.g., ). The tristimulus values of the optimal colors are obtained by using trapezoidal integration of the product of color-matching functions and illuminant spectrums sampled with small wavelength steps instead of performing summation of the product values. Selecting the distribution type whether Type 1 or Type 2 is avoided in the algorithm to reduce computing cost. Some optimal color solids computed by a MATLAB program have been demonstrated.
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