Generation of the Photons

In order to generate the photons we have to uniformly sample the different light sources. In the case of the sphere, extending sampling procedures seen in the course:

• We locate a point x uniformly distribuited over the surface of the sphere.
• We get a direction over the projected hemisphere in that point x.

If the scene is far from the light source or we are generating caustics this is not efficient, because a large number of photons will be sent towards empty positions, hence wasting processing time. In this case, we can include the scene (or object that produces caustics) in a sphere, and draw samples uniformly distribuited over this bounding sphere (this is a simplified implementation of the projection maps).

Although this improves considerable the quality of our results, some restrictions apply:

• This is not always applicable for the global photon map, because the light is sometimes within the scene, and therefore the bounding sphere subtends a solid angle equal to the surface of the sphere.
• In the case it is possible, the power has to be scaled take into account the projected solid angle (the set of photons must carry a power proportional to the solid angle through which they are thrown). This is translated in less power for each launched photon, but the increased number of photons will yield finer grained results.
• In the caustic case it is always desirable to launch the rays using our importance sampling method to get good caustics. In this case, the solid angle of each object that produced caustic is used to:
  • Compute the number of rays that are launched against each object.
  • Compute the power of those rays.

Finally, the number of photons sent from each light has to be carefully balanced. Each light sends a number of photos proportional to the power they contribute to the scene. In general:

• The larger the light source, the more photons it sends.
• The closer to the scene, the more photons it sends.
• So far, we don't care about occlusion between pairs of light sources, but this is an interesting problem to work on.