# Exploring Difficult Manifolds for Light Transport

To produce photorealistic pictures, we seek all paths connecting light source and camera, after multiple bounces on the scene geometry.Explicitly finding all paths is difficult, especially with multiple refractive interfaces. Manifold Exploration is the idea that the set of good paths forms a manifold in path space, and once we have a point on this manifold, we can explore path space while staying on it.

Manifold exploration is great for exploring difficult paths, but we have to find a point on the manifold first. With two specular interfaces (especially refractive), this becomes difficult. Our goal in this project is to extend manifold exploration to these difficult cases.

For example, the volume caustics in this amber sphere are caused by single scattering: light enters the sphere, is refracted at the interface, is scattered exactly once inside the material, and leaves the material, being refracted again at the interface. The two refractions make this example case difficult for existing algorithms such as BDPT and Photon Mapping.

The picture on the left (Our algorithm) is the reference: it finds all possible paths by fast exploration, for each camera ray and each triangle.

Although this is an extreme case, having two specular interfaces is quite frequent: it happens with droplets on a surface, or a cupboard with a glass door. These situations, apparently simple, make most light simulation algorithms fail. The goal is to find the difficult manifolds and explore them.