A reflectance function occurring in practice is usually smooth. The square of its derivative, integrated over the entire visual range, is defined as a measure of its smoothness. The problem (to determine for given tristimulus values under a given illuminant the smoothest reflectance function in this sense) has 16 types of solution, each valid in a certain domain of the object color solid. The four simplest solutions, which are also those of most practical importance, are studied in this paper, together with their domains of validity. A simple algorithm for their generation is described.
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C. van Trigt (1990) studied this question.
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