Platforms based on OpenGL ES 2.0 such as mobile devices and WebGL have recently being used to render 3D volumetric models. However, the texture storage limitations of these platforms cause that only low-resolution models can be visualized. This paper describes a novel technique that overcomes these limitations and allows us to render detailed high resolution volumes on these platforms. Additionally, we propose a software architecture that permits existing volume rendering techniques to be adapted to mobile devices and WebGL. A set of experiments has been carried out to assess the performance of the proposed architecture on these platforms with different volumes of increasing resolution. Results prove that our proposal is feasible, robust and achieves visualization of very large volumes on constrained platforms.