There are four important angles that describe how light scatters from a surface. They are defined below in order of importance:
- Sample Rotation (enumeration label: SampleRotation)
- Angle of Incidence (enumeration label: AngleOfIncidence)
- Azimuth Scatter angles (enumeration label: ScatterAzimuth)
- Radial Scatter angles (enumeration label: ScatterRadial)
The order of the four angles is important: for every Sample Rotation, you can have data for multiple Angles of Incidence; for every Angle of Incidence, you can have data for multiple Azimuth angles; and so on.
Figure 1. The four BSDF angles important to communicating scatter data. Note that ScatterRadial and ScatterAzimuth angles are defined relative to the angle of specular reflection for BRDF. In this way, the number of values that must be reported is reduced, especially for mostly specular samples. For BTDF, ScatterRadial and ScatterAzimuth angles are defined relative to the angle of direct transmission.
The ScatterAzimuth and ScatterRadial angles are defined relative to the angle of specular reflection. In this way, the amount of data that must be reported (especially for mostly specular sources) can be greatly reduced. Radial 0° is defined at the angle of specular reflection, with increasing Radial angles extending outward. Azimuth 0° is defined by pointing from the angle of specular reflection towards the axis normal to the sample, with Azimuth angles increasing in a counter-clockwise fashion. Data from Radiant Imaging's IS-SA undergoes a rotational transformation to match this coordinate system, as the illumination axis of IS-SA is not defined at 0° Azimuth.
Figure 2. Transformation about point of specular reflection. The top image shows the original hemispherical data for a sample with an AngleOfIncidence of 30°. The bottom image shows the transformed data, centered about the point of specular reflection. Note that the data appears rotated. Azimuth 0° is defined to be along the axis of illumination for this format, but the standard Imaging Sphere coordinate system (which is used to display this transformation) defines Azimuth 0° as normal to the axis of illumination, as shown in the top image.
| Line # | Description | Values |
| # | <comments> | <Any line that starts with # is ignored as a comment> |
| 1 | Source | Measured |
| 2 | Symmetry | PlaneSymmetrical Asymmetrical Asymmetrical4D |
| 3 | SpectralContent | Monochrome XYZ |
| 4 | ScatterType | BRDF BTDF |
| 5 | SampleRotation | <number of different sample rotations> |
| 6 | <enum> | <enumeration of sample rotations> |
| 7 | AngleOfIncidence | <number of different angles of incidence> |
| 8 | <enum> | <enumeration of angles of incidence> |
| 9 | ScatterAzimuth | <number of different azimuth angles> |
| 10 | <enum> | <enumeration of azimuth angles> |
| 11 | ScatterRadial | <number of different radial angles> |
| 12 | <enum> | <enumeration of radial angles> |
| 13 | <empty line> | |
| 14 | <SpectralContent indicator> | Monochrome Tristimulus<XYZ> |
| 15 | DataBegin | <Begin Data> |
| 16+ | <enum> | <enumeration of scatter data for all angles> |
| 17 | DataEnd | <End Data> |
Table 1. Description of lines in the BSDF Data Interchange format. Changing some variable settings can affect enumeration formatting. Refer to the Formatting Notes for specific details.
Formatting Notes
Line Notes
#. Any line that starts with the # symbol is ignored as a
comment line.
1. There is currently only one option for the Source variable:
Measured
2. There are three options for the Symmetry variable:
PlaneSymmetrical, ASymmetrical, ASymmetrical4D
PlaneSymmetrical The measured data is symmetrical about
the illumination axis of the measurement,
so only 180° degrees of Azimuth data are
reported. Use this setting for isotropic
samples with plane symmetry.
ASymmetrical There is no symmetry in the measured
data; no sample rotations. All 360° of
Azimuth data is reported. Use this for
isotropic samples (only one sample
rotation).
Asymmetrical4D There is no symmetry in the measured
data; includes sample rotations. All 360°
of Azimuth data is reported. Use this for
anisotropic samples (multiple sample
rotations).
3. There are two options for the SpectralContent variable:
Monochrome, XYZ
Currently, Radiant Imaging’s IS-SA does not measure full spectral
content, but only Tristimulus data. Monochrome is the same as
Tristimulus Y (photopic).
Monochrome There will only be one group of
enumerated data between DataBegin
and DataEnd. This group is labeled by
an added line above the DataBegin line
(line 14 in Table 1).
XYZ There will be three groups of
enumerated scatter data, one for each
Tristimulus value. Each group is labeled
by an added line above the DataBegin line
(line 14 in Table 1).
4. There are two options for the ScatterType variable:
BRDF, BTDF
BRDF Reported data is in BRDF units. The
coordinate system is defined so that
Radial 0° corresponds to the angle of
specular reflection.
BTDF Reported data is in BTDF units. The
coordinate system is defined so that
Radial 0° corresponds to the angle of
direct transmission.
5-12. Value totals (lines 5, 7, 9, 11):
All value totals are expressed as positive integers (no decimal
points allowed).
There is no upper limit to the number of sample rotations or
incidence angles.
The upper limit of Azimuth angles is defined by the Symmetry
variable (180° for PlaneSymmetrical, 360° for ASymmetrical,
ASymmetrical4D).
The overall upper limit of Radial angles is 180°.
Enumeration values (lines 6, 8, 10, 12):
All enumeration values are positive.
The number of enumeration values must match the Value total
from the line above.
Enumeration values do not have to be evenly spaced. (See the
example formats in the next section; the ScatterRadial and
ScatterAzimuth enumerations are not evenly spaced.)
16. DataBegin and DataEnd statements surround each large group
of data. Before each block of scatter data for a given Angle Of
Incidence is a value for Total Integrated Scatter. That value is on
a separate line preceded by “TIS ”. The value is a fraction, such
that a value of .500 would indicate that 50% of the light is
scattered, and the remaining is absorbed or transmitted in the
case of BRDF.
Following the TIS value, Scatter data is enumerated with columns
representing the ScatterRadial values for each ScatterAzimuth
row. The rows are organized in groups. First, the ScatterAzimuth
values are reported for each AngleOfIncidence. Data for each
AngleOfIncidence, which contains various ScatterAzimuth rows, is
then reported by following rows. Data for each SampleRotation,
which contains various AngleOfIncidence groups, is then reported
by appending more rows.
The enumeration formatting of scatter data changes depending
on the settings chosen for the SpectralContent variable. If the
SpectralContent variable is set to Monochrome, the formatting
appears like Figures 3 and 4 in the next section. If the
SpectralContent variable is set to XYZ, there are two additional
DataBegin and DataEnd statement lines, with an extra label line
above each DataBegin line that labels the data group with its
associated Tristimulus value. See Figure 5 in the next section.
#Data Generated by Radiant Imaging's 'Imaging Sphere'
#6/1/2007 11:30:46 AM
#Name: Ron
#Model #: BTDF of matte sample
Source Measured
Symmetry PlaneSymmetrical
SpectralContent Monochrome
ScatterType BRDF
SampleRotation 1
0
AngleOfIncidence 6
0 10 20 30 45 60
ScatterAzimuth 5
0 30 60 90 180
ScatterRadial 15
0 1 2 3.5 5 6.7 8 13.1 ...
Monochrome
DataBegin
TIS 0.72
3.689E+00 3.575E+00 2.907E+00 ...
3.689E+00 3.585E+00 3.108E+00 ...
3.689E+00 3.585E+00 3.044E+00 ...
3.689E+00 3.511E+00 3.143E+00 ...
3.689E+00 3.313E+00 2.905E+00 ...
TIS 0.70
3.605E+00 3.491E+00 2.778E+00 ...
3.605E+00 3.444E+00 2.968E+00 ...
3.605E+00 3.444E+00 2.874E+00 ...
3.605E+00 3.316E+00 2.955E+00 ...
3.605E+00 3.206E+00 2.825E+00 ...
TIS 0.61
3.154E+00 3.059E+00 2.455E+00 ...
3.154E+00 2.924E+00 2.472E+00 ...
3.154E+00 2.924E+00 2.374E+00 ...
3.154E+00 2.768E+00 2.454E+00 ...
3.154E+00 2.892E+00 2.615E+00 ...
TIS 0.49
2.508E+00 2.453E+00 2.040E+00 ...
2.508E+00 2.341E+00 2.014E+00 ...
2.508E+00 2.341E+00 1.925E+00 ...
2.508E+00 2.203E+00 1.976E+00 ...
2.508E+00 2.311E+00 2.121E+00 ...
TIS 0.27
1.391E+00 1.362E+00 1.186E+00 ...
1.391E+00 1.351E+00 1.228E+00 ...
1.391E+00 1.351E+00 1.203E+00 ...
1.391E+00 1.324E+00 1.233E+00 ...
1.391E+00 1.323E+00 1.255E+00 ...
TIS 0.10
5.262E-01 5.333E-01 5.332E-01 ...
5.262E-01 5.295E-01 5.196E-01 ...
5.262E-01 5.295E-01 4.988E-01 ...
5.262E-01 5.122E-01 4.955E-01 ...
5.262E-01 5.070E-01 4.962E-01 ...
DataEnd
Figure 3: Example of Photopic (Monochrome) data formatting. There is only one continguous data group, and one DataBegin and DataEnd statement. This example only includes data for one sample rotation. If there are multiple sample rotations, the data group will have additional lines of data after the last data line, but before the DataEnd statement.
#Data Generated by Radiant Imaging's 'Imaging Sphere'
#6/1/2007 11:30:46 AM
#Name: Ron
#Model #: BTDF of matte sample
Source Measured
Symmetry PlaneSymmetrical
SpectralContent Monochrome
ScatterType BRDF
SampleRotation 1
0
AngleOfIncidence 6
0 10 20 30 45 60
ScatterAzimuth 5
0 30 60 90 180
ScatterRadial 15
0 1 2 3.5 5 6.7 8 13.1 ...
Monochrome
DataBegin Rad 1 Rad 2 ...
TIS 0.72
3.689E+00 Az 0 3.575E+00 2.907E+00 ...
3.689E+00 Az 30 3.585E+00 3.108E+00 ...
3.689E+00 . 3.585E+00 3.044E+00 ... Inc 0
3.689E+00 . 3.511E+00 3.143E+00 ...
3.689E+00 Az 180 3.313E+00 2.905E+00 ...
TIS 0.70
3.605E+00 3.491E+00 2.778E+00 ...
3.605E+00 3.444E+00 2.968E+00 ...
3.605E+00 3.444E+00 2.874E+00 ... Inc 10
3.605E+00 3.316E+00 2.955E+00 ...
3.605E+00 3.206E+00 2.825E+00 ...
TIS 0.61
3.154E+00 3.059E+00 2.455E+00 ...
3.154E+00 2.924E+00 2.472E+00 ...
3.154E+00 2.924E+00 2.374E+00 ... .
3.154E+00 2.768E+00 2.454E+00 ...
3.154E+00 2.892E+00 2.615E+00 ...
TIS 0.49
2.508E+00 2.453E+00 2.040E+00 ...
2.508E+00 2.341E+00 2.014E+00 ...
2.508E+00 2.341E+00 1.925E+00 ... .
2.508E+00 2.203E+00 1.976E+00 ...
2.508E+00 2.311E+00 2.121E+00 ...
TIS 0.27
1.391E+00 1.362E+00 1.186E+00 ...
1.391E+00 1.351E+00 1.228E+00 ...
1.391E+00 1.351E+00 1.203E+00 ... .
1.391E+00 1.324E+00 1.233E+00 ...
1.391E+00 1.323E+00 1.255E+00 ...
TIS 0.10
5.262E-01 5.333E-01 5.332E-01 ...
5.262E-01 5.295E-01 5.196E-01 ...
5.262E-01 5.295E-01 4.988E-01 ... Inc 60
5.262E-01 5.122E-01 4.955E-01 ...
5.262E-01 5.070E-01 4.962E-01 ...
DataEnd
Figure 4: Illustrated example of Photopic (Monochrome) data formatting. There is only one continguous data group, and one DataBegin and DataEnd statement. The figure shows graphically the placement of Incidence angle groups, Azimuth angle groups, and Radial angle columns (3 of the 15 total columns are shown). This example only includes data for one sample rotation. If there are multiple sample rotations, the data group will have additional lines of data after the last data line, but before the DataEnd statement.
#Data Generated by Radiant Imaging's 'Imaging Sphere'
#6/1/2007 11:30:46 AM
#Name: Ron
#Model #: BTDF of matte sample
Source Measured
Symmetry PlaneSymmetrical
SpectralContent XYZ
ScatterType BRDF
SampleRotation 1
0
AngleOfIncidence 6
0 10 20 30 45 60
ScatterAzimuth 5
0 30 60 90 180
ScatterRadial 15
0 1 2 3.5 5 6.7 8 13.1 ...
TristimulusX
DataBegin
TIS 0.72
3.689E+00 3.575E+00 2.907E+00 ...
3.689E+00 3.585E+00 3.108E+00 ...
3.689E+00 3.585E+00 3.044E+00 ...
3.689E+00 3.511E+00 3.143E+00 ...
3.689E+00 3.313E+00 2.905E+00 ...
TIS 0.70
3.605E+00 3.491E+00 2.778E+00 ...
3.605E+00 3.444E+00 2.968E+00 ...
3.605E+00 3.444E+00 2.874E+00 ...
3.605E+00 3.316E+00 2.955E+00 ...
3.605E+00 3.206E+00 2.825E+00 ...
TIS 0.61
3.154E+00 3.059E+00 2.455E+00 ...
3.154E+00 2.924E+00 2.472E+00 ...
3.154E+00 2.924E+00 2.374E+00 ...
3.154E+00 2.768E+00 2.454E+00 ...
3.154E+00 2.892E+00 2.615E+00 ...
TIS 0.49
2.508E+00 2.453E+00 2.040E+00 ...
2.508E+00 2.341E+00 2.014E+00 ...
2.508E+00 2.341E+00 1.925E+00 ...
2.508E+00 2.203E+00 1.976E+00 ...
2.508E+00 2.311E+00 2.121E+00 ...
TIS 0.27
1.391E+00 1.362E+00 1.186E+00 ...
1.391E+00 1.351E+00 1.228E+00 ...
1.391E+00 1.351E+00 1.203E+00 ...
1.391E+00 1.324E+00 1.233E+00 ...
1.391E+00 1.323E+00 1.255E+00 ...
TIS 0.10
5.262E-01 5.333E-01 5.332E-01 ...
5.262E-01 5.295E-01 5.196E-01 ...
5.262E-01 5.295E-01 4.988E-01 ...
5.262E-01 5.122E-01 4.955E-01 ...
5.262E-01 5.070E-01 4.962E-01 ...
DataEnd
TristimulusY
DataBegin
TIS 0.72
3.689E+00 3.575E+00 2.907E+00 ...
3.689E+00 3.585E+00 3.108E+00 ...
3.689E+00 3.585E+00 3.044E+00 ...
3.689E+00 3.511E+00 3.143E+00 ...
.
.
.
Figure 5: Example of Color (XYZ) data formatting. Note that each separate Tristimulus value has a separate DataBegin and DataEnd statement. If there are multiple sample rotations, each Tristimulus grouping will have additional lines of data after the last data line, but before the DataEnd statement.