In order to develop a model for scattering we first have to understand how it works. The following figure depicts the different paths that light can take through a layer of impure calcite.

The light travelling through the crystal can be:

Forward scattering takes place when a light on the other side of the medium but not on the path of the transmitted ray get scattered and is therefore visible to the eye. Backward scattering occurs when light on the same side as the eye gets scattered by the medium and contributes to the visible light.

To capture these effects of scattering a simplified model of scattering was developed with the parameters below:

This model is similar to the one presented in the Hanrahan, Krueger paper except that it is simplified considerably and has terms that make intuitive sense.

The Henyey-Greenstein phase function is an empirical function to model anisotropic scattering. In our experiments, we used values of g that corresponded to large forward scattering. As the figure explains exp (-sigma_s d) is the probability that there is no scattering. Similarly, exp (-sigma_a d) is the probability that there is no absorption. Using similar arguments, we get the following picture:

The weights along each path present the probability that the path is taken. These weights are used by the ray tracer to weigh the relative contribution of radiance along that path.

For example the following image shows the two layers of a stalactite. This is not an actual rendering of the stalactite.

Other optimizations were also added to the ray tracer. For
example, the notion of object space intersection was eliminated and
replaced by world space intersections. This works well when there are
a large collection of triangles in world space that need to be
considered for intersection.

The following image shows stalactites and stalagmites in a scene without strong back lighting. This scene is rendered with 3 lights symmetrically distributed about the stalactite. The lights have small red, blue and green components respectively. As we can see the effects of scattering are not apparent when the stalactite is viewed from a distance.

Getting the right coefficients for the scattering is important. In this image I show the effects of using the wrong coefficients. I used the coefficients of water in this scene and produced an image that looks very much like water. This makes us believe that this scattering model will be useful in rendering icicles.

Page maintained by: Kavita Bala (kb@graphics.cornell.edu)