Title: Light in Power: A General and Parameter-free Algorithm for Caustic Design,
Abstract: We present in this paper a generic and parameter-free algorithm to
efficiently build a wide variety of optical components, such as mirrors or
lenses, that satisfy some light energy constraints. In all of our problems, one
is given a collimated or point light source and a desired illumination after
reflection or refraction and the goal is to design the geometry of a mirror or
lens which transports exactly the light emitted by the source onto the target.
We first propose a general framework and show that eight different optical
component design problems amount to solving a light energy conservation
equation that involves the computation of visibility diagrams. We then show
that these diagrams all have the same structure and can be obtained by
intersecting a 3D Power diagram with a planar or spherical domain. This allows
us to propose an efficient and fully generic algorithm capable to solve these
eight optical component design problems. The support of the prescribed target
illumination can be a set of directions or a set of points located at a finite
distance. Our solutions satisfy design constraints such as convexity or
concavity. We show the effectiveness of our algorithm on simulated and
fabricated examples.