Caustics are important visual phenomena, as well as challenging global illumination effects in computer graphics. Physically caustics can be interpreted from one of two perspectives: in terms of photons gathered on scene geometry, or in terms of a pair of caustic surfaces. These caustic surfaces

is tangent to a smooth caustic surface. The curvature of the surface at the tangent point is positive, negative, or zero. In the fourth case, the line of sight passes near a cusp. For each case we derive the map between the image and source planes. In some cases, a point source has multiple images

ABSTRACT. It is classically known that complete flat (that is, zero Gaussian curvature) surfaces in Euclidean 3-space R 3 are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface f admits