Computer Graphic Rendering of Material Surfaces
Virtual Light Meter
While it is important to be able to accurately depict the full BRDF of a material, there is also much merit in the ability to characterize a material with appearance attributes such as glossiness or haziness. To this end, people in the appearance industry have sought to develop and standardize a number of simple measurements and corresponding measuring devices which easily and objectively quantify the reflection properties of a surface. The result is a number of one-dimensional scales of appearance, such as gloss and haze, and inexpensive appearance measurement devices, such as glossmeters.
The standard specular gloss measurement defined by the American Society for Testing and Materials (ASTM) in ASTM method D523 measures the magnitude of light reflected in a small solid solid angle about the specular direction. ASTM method E430 specifies that haze is a measure of the fraction of light reflected in the off-specular direction to that reflected in the specular direction. These well defined measurements result in a single numerical value describing particular appearance attributes of the measured surface. An analogous measurement may be performed on the BRDF of a surface through computer simulation of the measurement protocol. In this way, a simulated glossmeter or hazemeter can be used to determine the gloss or haze of any arbitrary BRDF.
A computer program was developed which applies the measurement protocol of many of these standardized appearance tools (eg., glossmeters and hazemeters) to BRDFs. This new virtual light meter is essentially a customized integration tool, using numerical quadrature of the specified BRDF model over an adaptively subdivided source and receptor aperture (see Figure 5 below) to compute the final standard appearance value. In addition to being able to calculate the current standards, the virtual light meter can be customized for other measurements. The customizable parameters include the size and locations of the source and receptor apertures, the specular angle, the surface orientation, and the reflection model.
Figure 5: (left) Subdivision of light meter apertures using the 60 degree specular gloss specifications. The source and receptor apertures are oriented in directions and , 60 degrees down from the surface normal, N, in the plane of incidence. (right) Flux passing through receptor aperture due to one source aperture subdivision. Aperture sizes are not to scale.
Standard gloss and haze values are directly dependent upon the measured flux reflected off the surface and passing through the receptor aperture. The integration of this flux begins by subdividing the source aperture. For each sample point on the source, the receptor aperture is subdivided. Based on the initial results of the integration, the receptor aperture is adaptively subdivided until the discretely computed flux is within some specified tolerance. Figure 5 above shows an example of the flux due to one subdivided source element passing through the receptor. After this flux is determined, the next source sample point is chosen and the process is repeated. The source aperture continues to be subdivided until a specified tolerance is achieved. Figures 6 and 7 are two renderings of tiles with BRDF model parameters selected so as to achieve specific gloss and haze values.
Figure 6: Rendered tiles using BRDF models with parameters set so as to produce 20 degree specular gloss values 80, 60, 40, and 20. Figure 7: Rendered tiles using BRDF models with parameters set so as to produce 2 degree haze values 10, 60, 110, and 160.