In this paper, we introduce our researches on rendering gems by computer graphics (CG). First, the principles of computer graphics and our purposes on researches on gem image generation are described. Then we show our results of researches on generation of images of brilliant cut diamond and gems with asterism. Produced images and some analysis results are given.

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Formerly, the scintillation in gemstones has been defined broadly as alternating display of refiections from the polished facets of a gemstone; it is a flashing or twinkling of light from the facet. However, for deeper consideration of the phenomenon, we should take into consideration that there are some higher radiations from facets. We define that the scintillation consists of radiation and reflection from facets, the former being the leading part. In evaluating brilliancy of diarnond, the inclinations θ (angle between optical axis and radiant ray) of a gemstone are derived from three cases (table→table, main→table, table→main; Fig.22). The changes of radiation area by the inclination of a gemstone which is based on the F-Cut I (cf. Table 2) are illustrated in Fig.23, and the changes of F- and S-values presented graphically in Fig.24. The best F-value (F'_1, F"_3) or convergent ray becomes the flash and then finally produces dispersion or fire. The twinkling can be defined as a momentary alternating display of the ray from some facets, i. e. high and low of the illumination, emanation and disappearance of the radiation, expansion and contraction of the radiation area. Of monocular and binocular vision, the latter gives higher scintillation. It can readily be conjectured that a combination of a good many facets and twinkling by a numerical image misdirects the source of the scintillation. For reference, Tolkowsky-cut and Quartz are presented graphically in Fig.25,26 and F-value. We have introduced some expressions of relation for facetting as an Appendix with Fig.28.

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In this supplement, a trial was made to improve brilliancy by additional pavilion facets corresponding to star facet. The new trial was based on F-Cut I reported in the first paper. It is expected that new pavilion main facets corresponding to the star facet will produce more brilliancies from any independent viewpoints (table→table, star→table, table→star, star→star). The secondary main facets are cutted with an angle of 41°. This trial gives an ample brilliancy, although there are some twinkles and no flash. Double main facets of the pavilion have on the whole more chances of brilliancy than the original brilliant cut. And, a loss of weight is negligible.

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