Final Project - Genie coming out of a Oil Lamp

Aim

Techniques implemented

• Fast subsurface scattering for the skin of the genie
• Improved photon mapping for efficient generation of caustics on the table
• Volumetric effects of the oil as a participating medium (for scattering effects, and attenuation due to the medium)
• Perlin noise: Used to generate texture for the sand that the lamp is placed on

Subsurface scattering

We followed the algorithm outlined in [1]. The steps involved are the following:

• Uniform sampling of points on the mesh: These samples were obtained using Turk's point repulsion algorithm [3] (discussed in more detail below)
• Evaluating the irradiance at each sample point: The irrradiance estimate to be stored in the cache must take into account both direct and indirect lighting.
  • Direct: For each point on the mesh, we sample incoming directions over the hemisphere and trace these rays through, taking into account direct lighting at every surface.
  • Indirect: The estimate is obtained using path tracing.
• The irradiance samples are stored in an octree. Each node stores an estimate of the total irradiance, total area and average position (weighted by irradiance) of the points below it.
• Once the octree is built, the outgoing radiance at any point can be calculated using the dipole approximation formulas.
• Note that specular reflections were ignored in the above scheme. We felt that this did not detract from the scene much as skin does not have a high component of subsurface reflections.
• For the integrator, we used the normal photon mapping integrator for objects that did not show subsurface scattering, and read the cache values for those that did.

Uniform sampling of points on the mesh (Turk's algorithm)

• Start with a random sampling of points on the mesh, where the probability of a point being in a triangle is proportional to the triangle's area.
• Apply a "relaxation procedure" to the points:
  • Each point exerts a repulsive force on the points near it. This force drops off linearly and is zero beyond a certain distance r.
  • Calculate the force on each point due to the neighboring points (rotated to come into the same plane)
  • Apply the force to each point to get the new positions.
  • If the new positions are off the mesh, one must bring them onto the mesh by always finding the edge crossed and rotating about it (this may have to be done more than once).
• The above "relaxation procedure" can be applied as many times as neccessary.
• We ran into a lot of numerical issues while implementing this algorithm, as a lot of things were dependent (if naively implemented) on the sign of a small quantity, or of the value of the division of two small numbers, which is subject to numerical errors. Programming had to be done with care to get it right and handle the edge cases correctly.

Improved photon mapping for efficient generation of caustics

• Shoot rays for caustic photons only at the specular objects:
  • Define bounding spheres for the specular objects (or regions) for which caustics are desired
  • Take a spherical projection of this bounding sphere on the sphere surrounding the various light source (we used a spherical projection because the main light source in our scene was a point light). We also experimented with spot lights and area lights, using planar projections and got relatively good results.
  • Shoot caustic photons (uniformly distributed by solid angle) in the conical region defined by the center of the light source.
• Consider only refracted rays for the caustic photons. Since we were interested in using the photon map solely for caustics, it made sense to only store those photons that were transmitted through specular surfaces (i.e. refracted). Among other things, this helped eliminate noise from low density of photons scattered in other parts (non-caustic areas) of the scene.
• There was very little indirect lighting in our scene and therefore we didnt use the photon maps for this purpose. Instead, we used an environment light to simulate an ambient source in the scene.

Volumetric effects of the oil

Texture mapping for the sand

• Given a texel (u,v), the curved nature of the dunes was modelled using an expression of the form sqrt((u-u0)^2 + (v-v0)^2) as the base image.
• This base image was then modulated using fractional Brownian motion which is based on adding a number of octaves of Perlin noise with different frequencies and amplitudes.
• The value thus obtained was used to interpolate between two appropriate shades of brown
• The texture thus generated was anti-aliased using supersampling.

Results

Genie and the Oil Lamp

Caustics: Detail

References

1. A rapid hierarchical rendering technique for translucent materials.
   Jensen, Buhler. Proc. of SIGGRAPH 2002
2. A practical model for subsurface light transport
   Jensen, Marschner, Levoy, Hanrahan. Proc. of SIGGRAPH 2001
3. Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion
   Turk. Proc of SIGGRAPH 1991