Graphics Reference
In-Depth Information
Reflectance
Trasmittance
Thinnner
1
1
++++
++++
Monte Carlo
Multipole
Dipole
Monte Carlo
Multipole
Dipole
0.1
T
0.1
0.01
0.01
0.001
0.001
R
1e -04
1e -04
1e -05
1e -05
1e -06
1e -06
1e -07
1e -07
0
5
10
15
20
0
5
10
15
20
r
(mm)
r
(mm)
Reflectance
Trasmittance
1
1
++++
++++
Monte Carlo
Multipole
Dipole
Monte Carlo
Multipole
Dipole
0.1
0.1
T
0.01
0.01
0.001
0.001
++
+
+
R
+
1e -04
1e -04
1e -05
1e -05
1e -06
1e -06
1e -07
1e -07
0
5
10
15
20
0
5
10
15
20
r
(mm)
r
(mm)
Reflectance
Trasmittance
1
1
++++
Monte Carlo
Multipole
Dipole
++++
Monte Carlo
Multipole
Dipole
0.1
0.1
T
0.01
0.01
0.001
0.001
R
1e -04
1e -04
++++
+++
++
+
+++
+++++
1e -05
1e -05
1e -06
1e -06
1e -07
1e -07
Thicker
0
5
10
15
20
0
5
10
15
20
r
(mm)
Figure 4.18
Verification of the multipole model for a slab. Each graph contains plots of the reflectance
or transmittance profile computed from the multipole model, approximated by the dipole
model, and computed using a Monte Carlo simulation. The thickness of the slab increases
from top to bottom. (From [Donner and Jensen 05] c
r
(mm)
2005 ACM, Inc. Included here by
permission.)
of the sources just as in the dipole model (Equation (4.13)). For a thin slab, the
ratio of the radiant exitance at the bottom surface to the incident flux is the diffuse
transmittance profile T
for slabs
of widths varying from 2 to 20 times the length of one mean free path. Each plot
also contains the corresponding dipole approximation and a Monte Carlo simu-
lation of the multiple scattering inside the slab. These plots show a good match
between the multipole approximation and the Monte Carlo simulation, although
the approximation is better for thicker slabs. In contrast, the dipole reflectance
matches the simulation poorly when the slab is thin, and the dipole transmittance
does not match well for any thickness.
Figure 4.19 shows images of a back-lit parchment rendered using (left to right)
the dipole model, the multipole model, and a Monte Carlo simulation. The visible
(
r
)
. Figure 4.18 contains plots of
R
(
r
)
and
T
(
r
)
