Computing global illumination by finite element techniques usually generates a piecewise constant approximation of the radiosity distribution on surfaces. Directly displaying such scenes generates artefacts due to discretization errors.We propose to remedy this drawback by considering the piecewise constant output to be samples of a (piecewise) smooth function in object space and reconstruct this function by applying a binary subdivision scheme. We design custom taylored subdivision schemes with quadratic precision for the efficient refinement of cell- or pixeltype data. The technique naturally allows to reconstruct functions from non-uniform samples which result from adaptive binary splitting of the original domain (quadtree). This type of output is produced, e.g., by hierarchical radiosity algorithms. The result of the subdivision process can be mapped as a texture on the respective surface patch which allows to exploit graphics hardware for considerably accelerating the display.