Poisson-Based Continuous Surface Generation for Goal-Based Caustics

We present a technique for computing the shape of a transparent object that can generate user-defined caustic patterns. The surface of the object generated using our method is smooth. Thanks to this property, the resulting caustic pattern is smooth, natural, and highly detailed compared to the results btained using previous methods. Our method consists of two processes. First, we use a differential geometry approach to compute a smooth mapping between the distributions of the incident light and the light reaching the screen. Second, we utilize this mapping to compute the surface of the object. We solve Poisson's equation to compute both the mapping and the surface of the object.