Abstract: Methods for exact computation of irradiance and form factors associated with polygonal objects have ultimately relied on a formula for a differential area to polygon form factor attributed to Lambert. This paper presents an alternative, an analytical expression based on vertex behavior rather than the edges of the polygon. Using this formulation, irradiance values in a scene consisting of patrially occluded uniformly emitting polygons can be computed exactly by examining only the set of apparent vertices visible from the point of evaluation without explicit reconstruction of polygon contours. This leads to a fast, low-overhead algorithm for exact illumination computation that involves no explicit polygon clipping and is applicable to direct lighting and to radiosity gathering across surfaces or at isolated points.