Current radiosity methods rely on the calculation of geometric factors, known as form-factors, which describe energy exchange between pairs of surfaces in the environment. The most computationally efficient method for form-factor generation is a numerical technique known as the hemi-cube algorithm. Use of the hemi-cube is based on assumptions about the geometry of the surfaces involved. First, this paper examines the types of errors and visual artifacts that result when these assumptions are violated. Second, the paper shows that these errors occur more frequently in progressive refinement radiosity than in the originally proposed full matrix radiosity solution. Next, a new analytical technique for determining form-factors that is immune to the errors of the hemi-cube algorithm is introduced. Finally, a hybrid progressive refinement method that invokes the new technique to correctly compute form-factors when hemi-cube assumptions are violated is presented.