Recent approaches to realistic image synthesis split the rendering process into two passes. The first pass calculates an approximate global illumination solution, the second produces an image of high quality (from a user selected view point) using the solution obtained in the first pass by applying the local illumination model to each surface point visible through each pixel. This paper presents a new method how to compute the visible surfaces as seen from a surface point - the hemisphere projection. This method allows the exact evaluation of the local illumination model and facilitates the fast and accurate computation of form factors taking occlusion into account. Using the hemisphere projection an exact local pass solution can be obtained. In addition the hemisphere projection can be used to compute an approximation of a point's local illumination to within given error bounds in significantly less time.