Predicting reflectance functions from complex surfaces

Abstract

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.

Image-based reconstruction of spatial appearance and geometric detail

“…In [Ramamoorthi and Hanrahan 2001] and [Gibson et al 2001] inverse rendering algorithms are proposed that reconstruct the reflection properties and the incident light field at the same time. Ramamoorthi and Hanrahan [2001] as well as Westin et al [1992] project BRDF data into a spherical harmonics basis instead of fitting an explicit reflection model.…”

A Survey of Shading and Reflectance Models

“…Instead of providing an analytical formulation, these models use an algorithmic process to compute the values of the BRDF for a couple of incoming/outcoming directions. This algorithmic evaluation can either by computed and stored (using sampled hemispheres25 or spherical harmonics 39,40 ) as a preprocessing term, or calculated directly during the rendering process 38 .…”

“…Extending an idea initially proposed by Cabral et al 39 , Westin et al 40 have presented a very general technique using a Monte-Carlo ray tracing technique to simulate local behaviour of light on surfaces with almost any kind of microscopic geometrical structure (stone, brushed metal, velvet, weaving). While Westin et al have worked mainly on multiple surface scattering created by complex microfacet configurations, Hanrahan and Krueger 38 have proposed a similar approach (using also a Monte-Carlo technique) which simulates subsurface scattering on layered surfaces (plastic, skin, pigmented or varnished materials).…”

Colour change as a result of textile transformations

“…Westin et al. [9] used a Monte Carlo technique to estimate the bidirectional reflectance distribution function (BRDF) for a great range of geometries, in particular that of fabrics. This technique was more general than several analytical models; it does not require restrictions on the microgeometry of the surface.…”

“…They proposed a realistic visualisation of the effects that the fibre surface, the refractive index of the medium and the internal reflectance had on the light path through the surface. Westin et al [9] used a Monte Carlo technique to estimate the bidirectional reflectance distribution function (BRDF) for a great range of geometries, in particular that of fabrics. This technique was more general than several analytical models; it does not require restrictions on the microgeometry of the surface.…”