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# Flat Land Reflection

##### By SGI Fellows Hector Chahuara, Anna Krokhine, and Elshadai Tegegn

During the third week of SGI, under the guidance of Associate Professor Paul Kry, we worked on Revisiting Computational Caustics. The team returned to this project by EPFL, exploring ideas in differentiable rendering and alternative solutions for optimal transport.

The shape of a mirror can be designed such that the reflection of sunlight on the surface forms a desired image on an adjacent wall.

The project’s starting point was designing a simple flat land that isn’t completely flat as a reflective surface. By changing the reflective land’s surface from flat to something that resembles a zigzag, by a little amount each time, we were able to notice it impacts the reflected rays a lot more and disperses them all around the surface.

We first designed the light source with the light rays (color red), and the reflective surface (color green), and the final surface (color light blue) we wanted to project our light rays. Then our simulation began by varying the reflective surface with the function by $$t$$; for $$t$$ from 0 to 0.005 with 100 line spaces.

$$f(x) = \sin(8x)\cdot t$$, for $$x$$: -1 to 1.3 with 100 linespaces

Since we multiply the function by $$t=0$$ at the first iteration, the reflective surface is a flatland. But as t increases, through every iteration, the reflective becomes more like a $$\sin x$$ function, giving us light rays that are spread across the final surface.