Editing Photon mapping (section)

===Rendering (2nd pass)===

In this step of the algorithm, the photon map created in the first pass is used to estimate the radiance of every pixel of the output image.  For each pixel, the scene is ray traced until the closest surface of intersection is found.

At this point, the [[rendering equation]] is used to calculate the surface radiance leaving the point of intersection in the direction of the ray that struck it.  To facilitate efficiency, the equation is decomposed into four separate factors: direct illumination, specular reflection, caustics, and soft indirect illumination.

For an accurate estimate of direct illumination, a ray is traced from the point of intersection to each light source.  As long as a ray does not intersect another object, the light source is used to calculate the direct illumination.  For an approximate estimate of indirect illumination, the photon map is used to calculate the radiance contribution.

Specular reflection can be, in most cases, calculated using ray tracing procedures (as it handles reflections well).

The contribution to the surface radiance from caustics is calculated using the caustics photon map directly.  The number of photons in this map must be sufficiently large, as the map is the only source for caustics information in the scene.

For soft indirect illumination, radiance is calculated using the photon map directly.  This contribution, however, does not need to be as accurate as the caustics contribution and thus uses the global photon map.

====Calculating radiance using the photon map====

In order to calculate surface radiance at an intersection point, one of the cached photon maps is used.  The steps are:

# Gather the N nearest photons using the nearest neighbor search function on the photon map.
# Let S be the sphere that contains these N photons.
# For each photon, divide the amount of flux (real photons) that the photon represents by the area of S and multiply by the [[Bidirectional reflectance distribution function|BRDF]] applied to that photon.
# The sum of those results for each photon represents total surface radiance returned by the surface intersection in the direction of the ray that struck it.