The bidirectional texture function (BTF) describes rough texture appearance variations due to varying illumination and viewing conditions. Such a function consists of thousands of measurements (images) per sample. Resulted BTF size excludes its direct rendering in graphical applications and some compression of these huge BTF data spaces is obviously inevitable. In this paper we present a novel fast probabilistic model-based algorithm for realistic BTF modelling allowing such an efficient compression with possibility of direct implementation inside the graphics card. The analytical step of the algorithm starts with the BTF space segmentation and range map estimation of the BTF surface followed by the spectral and spatial factorisation of selected sub-space multispectral texture images. Single monospectral bandlimited factors are independently modelled by their dedicated causal autoregressive models (CAR). During rendering the corresponding subspace images of arbitrary size are synthesis...