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.