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We describe a physically-based Monte Carlo technique for approximating bidirectional reflectance distribution functions (BRDFs) for a large class of geometries by directly simulating optical scattering. The technique is more general than previous analytical models: it removes most restrictions on surface microgeometry. Three main points are described: a new representation of the BRDF, a Monte Carlo technique to estimate the coefficients of the representation, and the means of creating a milliscale BRDF from microscale scattering events. These allow the prediction of scattering from essentially arbitrary roughness geometries. The BRDF is concisely represented by a matrix of spherical harmonic coefficients; the matrix is directly estimated from a geometric optics simulation, enforcing exact reciprocity. The method applies to roughness scales that are large with respect to the wavelength of light and small with respect to the spatial density at which the BRDF is sampled across the surface; examples include brushed metal and textiles. The method is validated by comparing with an existing scattering model and sample images are generated with a physically-based global illumination algorithm.

We present a new image-based process for measuring a surface's bidirectional reflectance rapidly, completely, and accurately. Requiring only two cameras, a light source, and a test sample of known shape, our method generates densely spaced samples covering a large domain of illumination and reflection directions. We verified our measurements both by tests of internal consistency and by comparison against measurements made with a gonioreflectometer. The resulting data show accuracy rivaling that of custom-built dedicated instruments.

A general light transfer simulation algorithm for environments composed of materials with arbitrary reflectance functions is presented. This algorithm removes the previous practical restriction to ideal specular and/or ideal diffuse environments, and supports complex physically based reflectance distributions. This is accomplished by extending previous two-pass ray-casting radiosity approaches to handle non-uniform intensity distributions, and resolving all possible energy transfers between sample points. An implementation is described based on a spherical harmonic decomposition for encoding both bidirectional reflectance distribution functions for materials, and directional intensity distributions for illuminated surfaces. The method compares favorably with experimental measurements.

We describe a physically-based Monte Carlo technique for approximating bidirectional reflectance distribution functions (BRDFs) for a large class of geometries by directly simulating optical scattering. The technique is more general than previous analytical models: it removes most restrictions on surface microgeometry. Three main points are described: a new representation of the BRDF, a Monte Carlo technique to estimate the coefficients of the representation, and the means of creating a milliscale BRDF from microscale scattering events. These allow the prediction of scattering from essentially arbitrary roughness geometries. The BRDF is concisely represented by a matrix of spherical harmonic coefficients; the matrix is directly estimated from a geometric optics simulation, enforcing exact reciprocity. The method applies to roughness scales that are large with respect to the wavelength of light and small with respect to the spatial density at which the BRDF is sampled across the surface; examples include brushed metal and textiles. The method is validated by comparing with an existing scattering model and sample images are generated with a physically-based global illumination algorithm.