  In this paper, we propose SpongeCake: a layered BSDF model where each layer
is a volumetric scattering medium, defined using microflake or other phase
functions. We omit any reflecting and refracting interfaces between the layers.
The first advantage of this formulation is that an exact and analytic solution
for single scattering, regardless of the number of volumetric layers, can be
derived. We propose to approximate multiple scattering by an additional
single-scattering lobe with modified parameters and a Lambertian lobe. We use a
parameter mapping neural network to find the parameters of the newly added
lobes to closely approximate the multiple scattering effect. Despite the
absence of layer interfaces, we demonstrate that many common material effects
can be achieved with layers of SGGX microflake and other volumes with
appropriate parameters. A normal mapping effect can also be achieved through
mapping of microflake orientations, which avoids artifacts common in standard
normal maps. Thanks to the analytical formulation, our model is very fast to
evaluate and sample. Through various parameter settings, our model is able to
handle many types of materials, like plastics, wood, cloth, etc., opening a
number of practical applications.
