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In this paper, we introduce a real-time algorithm to render the rich visual effects of general non-height-field geometric details, known as mesostructure. Our method is based on a five-dimensional generalized displacement map (GDM) that represents the distance of solid mesostructure along any ray cast from any point within a volumetric sample. With this GDM information, we propose a technique that computes mesostructure visibility jointly in object space and texture space which enables both control of texture distortion and efficient computation of texture coordinates and shadowing. GDM can be rendered with either local or global illumination as a per-pixel process in graphics hardware to achieve real-time rendering of general mesostructure.