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4.2.2 Path tracing
One approach to handling subsurface scattering is to directly simulate the micro-
scopic light events at the molecular level. In the Monte Carlo approach, one traces
paths of many light photons through a volumetric material and develops a prob-
abilistic model of the distribution of light energy. As a path of light enters the
material and experiences a scattering event, the ray is scattered and transmitted.
Since integrating over the entire sphere at each scattering event is too costly, ’ran-
dom’ samples are taken. If the material is isotropic (the scattering is independent
of direction), the appearance does not depend on the angle between the viewing
direction and the incoming light. If the scattering is anisotropic (dependent on
direction), the method behaves better with nonuniform sampling and respective
weighting. In general, for both cases in Monte Carlo algorithms, as the number of
random samples increases, the summation of those values converges toward the in-
tegral. This method is used frequently in computer graphics due to its convergence
rate and ease of operation.
It is typically assumed that (phase) scattering functions (the function that
describes how the light behaves at the scattering event) describe scattering of
a homogeneous distribution of particles suspended in a medium. Usually, the
particles are of equal size (or distributed in some reasonable way). Also, while the
index of refraction of both the particle and medium both influence the scattering
of light, particle size exhibits more of an effect on the phase function.
When the particles are much larger than the wavelength of light (particle diam-
eter >> (380− 700nm)), the geometric particle objects dominate the reflectance.
When the particle size approaches that of the wavelength of light, scattering events
become much more evident. In this situation, the complex theory of Mie scattering
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