Graphics Reference
In-Depth Information
In the previous chapters, light was assumed to interact with the environment
only at object surfaces (other than the slowing of light due to refraction, which was
only relevant at intersections). Participating media were not included—radiance
along a ray was considered constant. This assumption becomes invalid in the
presence of participating media, e.g., when the environment is filled with par-
ticles such as smoke, or when refractive elements are not entirely transparent.
Participating media can affect light considerably, and were studied in optics and
general radiative transfer theory well before the advent of computer graphics. One
approach to handing participating media is to construct a mathematical expression
for its effect in a small differential volume. This is well suited to volume render-
ing, because each voxel can be treated as a differential volume.
3.2 Volume Rendering
3.2.1 Basics of Volume Rendering
The term
volume rendering
in general refers to any method for rendering vol-
ume data. To distinguish volume rendering from rendering based on object sur-
faces, the latter can be called
surface rendering
. Surface rendering computes
colors (radiance) at sample points on object surfaces, while volume rendering
computes colors at sample points throughout the entire 3D volume of the object.
The method of using a 3D rectangular grid of voxels to split up the volume de-
scribed above is one way of constructing sample points. The color of each voxel
is typically computed in a preprocessing step to speed the final rendering.
As noted above, an important aspect of volume rendering is the effect on
light as it passes through a volume. Each voxel thus has a fixed
opacity
value
in addition to an intrinsic color. The opacity, which is almost universally denoted
by
α
, is the fraction of the light that is absorbed by the voxel: when
α
=
1the
voxel is totally opaque; when
α
=
0 it is totally transparent. The term 1
−
α
is the
transparency
, the fraction of incoming light transmitted through the voxel.
The color
C
out
of light coming out of a voxel is defined by the equation
C
out
=
C
in
·
(
1
−
α
)+
C
·
α
(3.1)
where
C
in
is the incoming color (or spectral radiance) and
C
is the intrinsic color
of the voxel. The color of light passing through multiple voxels is defined recur-
sively; the light coming into a voxel is the light coming out of a previous voxel:
C
(
i
)
in
=
C
(
i
−
1
)
Out
,
C
(
i
)
out
=
C
(
i
)
in
·
(
1
−
α
i
)+
C
(
i
)
·
α
i
.
(3.2)
