The study of common classes of diffuse emitters, such as planar convex polygons, reveals several interesting properties of the functions of illumination these emitters cast on receiver surfaces. Some properties, such as the position of the maximum and the curvature are of particular interest for sampling and reconstruction of illumination across receivers. A computationally efficient approach is presented that identifies these properties, and uses them to select samples of illumination. In addition these properties are used to determine upper bounds on the error due to linear and quadratic interpolants. These bounds are then used to adaptively subdivide the nonuniform sampling grid, resulting in accurate reconstruction. Results show that the method reduces the error compared to uniform approaches, and produces more consistent animated sequences.