## Refraction Study

# A study that applies research in computationally controlled caustics. I experiment with a process to transform pixels into caustic images of refracted light.

LINKS | MIT Media Lab ↗︎ |

## Refraction Study

This study replicates the process of converting an image into a 3-dimensional refractive surface, developed by Yue et al.'s 2014 paper on goal-based caustics ↗︎. I adapted an improved an implementation written by Matt Ferraro ↗︎.

## Pixels To Lux

At a high level, the process involves creating a mesh that achieves a specific refracted image when illuminated. Each mesh cell directs an incoming ray of light to the appropriate position in the refracted image such that the total light energy entering the surface is conserved while the brightness values of the refracted image match the original input image as closely as possible.

## Loss Minimization

An equivalence is made between the total pixel brightness in the image and the total area of the refracted surface mesh, such that each mesh cell can be morphed to approximate the brightness of its corresponding pixel. Starting with a mesh constructed from a square grid with no variation on the z-axis, there is a loss value associated with each grid cell based on its area relative to the brightness of it's corresponding pixel. Thus the goal is to minimize the loss value.

## Poisson's Equation

The ingenuity in the Yue et al. paper is to use Poisson's equation to reframe the problem of loss minimization into a problem of pressure relaxation over time.

## Simulation

The result is a mesh in which each cell's area approximates the brightness value of its corresponding image pixel. Afterwards, Poisson's equation is used again in conjunction with Snell's law to ensure that each cell is correctly oriented to refract incoming light towards the appropriate part of the refracted image. I simulated the result in Blender using the EEVEE renderer.

I used a desktop CNC machine to mill the mesh into a piece of acrylic. I hope to explore different caustics algorithms and manufacturing strategies in the future.