Abstract: This paper presents an alternative radiosity formulation using piecewise smooth radiance functions that incorporates curved surfaces directly. Using the Galerkin integral equation technique as a mathematical foundation, surface radiance functions are approximated by polynomials. This model eliminates the need for a posteriori rendering interpolation, and allows the direct use of non-planar parametric surfaces. Convergence problems due to singularities in the radiosity kernel are analyzed and rectified, and sources of approximation error are examined. The incorporation of a shadow masking technique vastly reduces the need for meshing and associated storage space-accurate radiosity calculations can often be made with no meshing. The technique is demonstrated on traditional radiosity scenes, as well as environments with untessellated curved surfaces.