the hottest stars still obey the same relations, but the range on which these transformations remain valid is now considerably diminished: the “hot” relations now hold only for $T_{\rm eff}~\geq~11500$ K and the “cool” ones for $4750$ K $\geq~T_{\rm eff}~\geq~4000$ K. Cool stars sometimes require different relations. This is true for the ($B-b$) vs ($u-b$) as well as for both ($U-u$) colour transformations (Fig. 3a).

Comparison with observed spectra
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As a validity check, all colour transformations presented above were also derived on the basis of the mainly-observed FRV spectra. When excluding stars cooler than $4000$ K, the comparison between transformations established through Kurucz models and through FRV MS and giant star spectra is excellent, as illustrated in Fig. 3b. The latter ones are of course slightly more dispersed, but the dispersion is fully comparable to what could be expected on the basis of the transformations established in Sect. 3.2. Very small differences occur in some particular colour indices and are quite marginal: the ($B-b$) colour index discriminates between the FRV MS and giant stars, but this only happens below $5000$ K; ($V-v$) is decreased by $\sim~0.01$  mag when calculated on the FRV spectra rather than on the Kurucz spectra; 