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 are swept by the foci of light rays. In this paper, we develop a novel algorithm to approximate caustic surfaces of sampled rays. Our approach locally parameterizes rays by their intersections with a pair of parallel planes. We show neighboring ray triplets are constrained to pass simultaneously through two slits, which rule the caustic surfaces. We derive a ray characteristic equation to compute the two slits, and hence, the caustic surfaces. Using the characteristic equation, we develop a GPU-based algorithm to render the caustics. Our approach produces sharp and clear caustics using much fewer ray samples than the photon mapping method and it also maintains high spatial and temporal coherency. Finally, we present a normal-ray surface representation that locally parameterizes the normals about a surface point as rays. Computing the normal ray caustic surfaces leads to a novel real-time discrete shape operator.