Design and Optimization of Orthogonally Intersecting Planar Surfaces

Computational Design Modelling 2012 (Proceedings of the Design Modelling Symposium 2011)

Abstract

We present a new algorithm for computational caustic design. Our algorithm solves for the shape of a transparent object such that the re- fracted light paints a desired caustic image on a receiver screen. We introduce an optimal transport formulation to establish a correspon- dence between the input geometry and the unknown target shape. A subsequent 3D optimization based on an adaptive discretization scheme then finds the target surface from the correspondence map. Our approach supports piecewise smooth surfaces and non-bijective mappings, which eliminates a number of shortcomings of previous methods. This leads to a significantly richer space of caustic images, including smooth transitions, singularities of infinite light density, and completely black areas. We demonstrate the effectiveness of our approach with several simulated and fabricated examples.