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The paper is devoted to the derivation of a bidirectional distribution function for crystals, which specifies all outgoing rays for a ray coming to the boundary of two transparent crystalline media with different optical properties, i.e., a particular mineral, directions of optical axes if they exist, and other features. A local model of interaction based on the notion of polarized light ray is introduced, which is specified by a geometric ray, its polarization state, light intensity, and so on. The computational algorithm that is suggested allows computing the directions and other properties of all (up to four) outgoing rays. In this paper, isotropic, uniaxial, and biaxial crystals are processed in a similar manner. The correctness of the model is validated by comparison of photos of real uniaxial crystals with corresponding computed images. The case of biaxial crystals is validated by testing the effect of conical refraction. Specifications of a series of tests devoted to rendering of optically different objects is presented also.