Generating Reflectance Curves from sRGB Triplets

I present several algorithms for generating a reflectance curve from a specified sRGB triplet, written for a general audience. Although there are an infinite number of reflectance curves that can give rise to the specific color sensation associated with an sRGB triplet, the algorithms presented here are designed to generate reflectance curves that are similar to those found with naturally occurring colored objects. My hypothesis is that the reflectance curve with the least sum of slope squared (or in the continuous case, the integral of the squared first derivative) will do this. After presenting the algorithms, I examine the quality of the computed reflectance curves compared to thousands of documented reflectance curves measured from paints and pigments available commercially or in nature. Being able to generate reflectance curves from three-dimensional color information is useful in computer graphics, particularly when modeling color transformations that are wavelength specific.