324 VI GPGPU
cordingly. However, ordering of billboards is still required, and when the order
of the billboards changes between two animation frames, visible popping still oc-
curs. This is less pronounced if there are more particles, or if they appear similar.
However, in certain circumstances—for example, in ﬁre-and-smoke scenarios, or
when shadows are cast onto the medium—particle colors and saturations may be
varied, and popping becomes more visible.
The megaparticles technique [Bahnassi and Bahnassi 06] eliminates billboard
artifacts, rendering actual spheres instead of billboards. This allows particles to
be shaded and depth-tested the same way as solid geometry. Their volumetric
nature is lost, but the eﬀect can be reintroduced in an image-space distortion and
blurring pass. The technique can render stunningly shaded dense smoke, and,
with some sorting required, even solid objects are allowed to intersect. However,
mixing of low-opacity particles and proper depth-dependent transparency are
not addressed. Megaparticles and our volumetric transparency method share the
concept of using a few complex volumetric particles rather than thousands of
The method of this chapter can be grasped both as a special case of ray
casting and a generalized case of alpha blending. From the ray-casting point of
view, what we do is assume a piecewise homogeneous medium and thus replace
costly point sampling with the evaluation of an analytic formula. Compared to
spherical billboards, our volumetric transparency method does not only clip the
volume thickness against opaque objects, but also accurately handles intersection
between particles. Mixing the two media together, it completely eliminates the
possibility of popping artifacts.
1.2 Light Transport Model
In rendering algorithms, we need to ﬁnd radiance incoming at the eye along rays
through every pixel. Transparent objects and participating media exhibit volu-
metric lighting eﬀects (see Figure 1.1): they let through some of the background
Figure 1.1. Volumetric lighting eﬀects in participating media.