PxrUPBP Volume Caustics

This is an experimental final-quality integrator in RenderMan. Like PxrVCM it combines bidirectional path tracing with progressive photon mapping (also known as vertex merging). In addition, it stores photon points and beams in volumes. Each of these techniques brings the ability to capture a certain range of light transport paths more efficiently than a pure forward path tracing algorithm. For surfaces, PxrUPBP computes the same results as the PxrVCM Integrator, but PxrUPBP computes better (less noisy) direct and indirect illumination in volumes -- for example crepuscular rays ("God Rays"), volume caustics, and soft indirect illumination. You may notice the controls are nearly identical to the PxrVCM Integrator.

• Photon points and beams improves the convergence of illumination in homogeneous volumes by storing some light paths as volume photon points and beams. This is combined with the techniques below and is the basis for PxrUPBP's superior performance for volume rendering.
• Bidirectional path tracing can converge faster than forward path tracing for interior scenes or scenes with significant indirect illumination. In particular, when forward path tracing can't easily find an indirect path to the dominant light source, bidirectional path tracing can help – especially if the dominant light source is "one bounce" away from illuminating the scene. It also offers the possibility of faster indirect lighting in general because bidirectional path tracing can make multiple connections between a light path and a eye path and reuse shader evaluations. (A forward path tracer has to run a shader at every bounce, and therefore cannot reuse shader evaluations.) Note that this benefit is more pronounced if your pattern evaluations are expensive; Bxdfs without pattern inputs will not benefit from this.
• Progressive photon mapping converges faster for specular-diffuse-specular lighting (reflections or refractions of caustics), especially when dealing with relatively small light sources.

These sampling techniques are combined along with direct lighting (connecting an eye vertex directly to a light source) using multiple importance sampling such that the combined algorithm is substantially more robust and converges faster across a wide range of shots than simply using any one technique by itself.

The PxrUPBP integrator in its default mode of operation enables all of these techniques, but should the need present itself, can also operate as a pure bidirectional path tracer, a pure unidirectional path tracer, or even use pure progressive photon mapping by disabling merging and/or connecting via the mergePaths and connectPaths parameters, and reducing beamsPathsRatio to 0.0%.

For direct illumination, PxrUPBP looks at the values of the numLightSamples and numBxdfSamples parameters in order to determine the number of light vs. Bxdf direct illumination samples. For lowest noise numLightSamples and numBxdfSamples should be set to the same value.

PxrUPBP fully supports multiple scattering of homogeneous volumes, including multiple overlapping homogeneous volumes and anisotropic scattering. Bidirectional path tracing, in particular, is well suited for multiple scattering in volumes. PxrUPBP improves performance by supporting a combination of volumetric photon points and beams, giving less noise in direct volume illumination and especially indirect volume illumination such as volume caustics. Inhomogeneous volumes are not yet supported.

There is an important difference to note between this integrator and PxrVCM:

• PxrUPBP introduces photon beams to improve volume rendering. This control is the beamsPathsRatio described below. By default this control is set to 5% of volume photons stored as beams.

There are several important differences to note between this integrator and PxrPathTracer:

• PxrUPBP does not explicitly support the ability to globally turn off caustic light paths (like PxrPathTracer does). However, by default your scene may render the same as if using PxrPathTracer. This is because lights control the tracing of these rays using the Trace Light Paths parameter which is off by default. You should selectively turn on this feature to produce the effects you need visually rather than having them all on which may prove costly and be more difficult to art direct. (LPEs can be used to remove caustic paths in PxrUPBP but the calculation is still performed.) 
• PxrUPBP is less forgiving for having different numLightSamples than numBxdfSamples than PxrPathTracer. These two parameters should (nearly) always be be set to the same value -- otherwise unnecessary noise can appear.
• Due to the nature of bidirectional path tracing, PxrUPBP does not expose any controls over the indirect ray sample count; all vertices generate at most one indirect ray.
• Rendering a crop window may result in a different quality render than a full frame render. This is because light paths are generated per-pixel and stored in a photon map. When rendering a smaller region, fewer photons are saved as a side-effect. In theory all the light paths could be generated but the impact on performance would begin to erode the benefit of rendering a small region of the final image.

For more information, please consult the relevant papers:

• Jaroslav Křivánek, Iliyan Georgiev, Toshiya Hachisuka, Petr Vevoda, Martin Sik, Derek Nowrouzezahrai, and Wojciech Jarosz. Unifying Points, Beams, and Paths in Volumetric Light Transport Simulation. ACM Transactions on Graphics (Proc. SIGGRAPH), 2014.
• Iliyan Georgiev, Jaroslav Křivánek, Tomáš Davidovič and Philipp Slusallek. Light Transport Simulation with Vertex Connection and Merging. ACM Transactions on Graphics (SIGGRAPH Asia 2012).
• Toshiya Hachisuka, Jacopo Pantaleoni, and Henrik Wann Jensen. A Path Space Extension for Robust Light Transport Simulation. ACM Transactions on Graphics (SIGGRAPH Asia 2012).