Caustic Object Construction Based on Multiple Caustic Patterns

Inverse caustic problem, that is computing the geometry of a reflector and/or refractor based on a given caustic pattern, is currently not widely studied. In this paper, we propose a technique to solve the inverse caustic problem in which we compute the geometry of a semi-transparent homogeneous refractive object (caustic object) given a directional light source and a set of caustic patterns (each pattern is considered to be formed at a specified distance from the caustic object). We validate the results by using mental ray (software rendering). The novelty of our research is that we consider a set of caustic patterns whereas existing techniques only consider one caustic pattern. We employ a stochastic approach to simulate the refracted light beam paths that can approximately reconstruct the input caustic patterns. Working backward, from the computed refracted light beam paths we compute the geometry of the caustic object that can produce such light beam paths. Due to having multiple caustic patterns as the inputs, it is a challenge to reconstruct the input caustic patterns because of the differences in their shapes and intensities. We solve this problem by using a two-step optimization algorithm in which we adjust the position and size of the caustic regions in the first step and we adjust the caustic shapes in the second step. Our technique is able to construct a caustic object for a various types of input caustic patterns.