Virtual Gonioreflectometry

Guy Mann

A gonioreflectometer measures the reflectance properties of a material. It is a physical method which bounces light off of the surface of a sample and detects the light which reflects off the sample. The hardware required for this is at once prohibitively expensive and requires a physical sample of the material which is not always feasible for computer generated objects. The physical setup of the gonioreflectometer consists of a light source, an object being measured and a detector. To perform the measurement a defined amount of light is emitted at the object. Light interacts with the surface and is measured after its interaction with the object. BRDF is determined from the amount and wavelengths of light detected after the interaction.

The goal of virtual gonioreflectometry is to simulate the reflectance properties of materials without a physical sample by using geometric approximation at the milli- and micro- scale. Sub-scale information is used to simulate the BRDF of a material by creating geometry at a small scale to mimic the understood behavior of the light which interacts with the material which is being modeled. So with sub-scale geometry the light interaction with the small scale geometry is measured and then this information is used as the BRDF for the next larger scale. This simulates the interactions of gonioreflectometry; for a given geometry.

In virtual gonioreflectometry all the pieces of the physical setup have analogies. Light is distributed using a Monte Carlo Raytracing approximation. Objects are represented with polygons in the usual way. The detector is analogous to the method in which the BRDF which is created is stored. The two methods I discuss for measuring and storing the reflected light information from the geometry are Capture Spheres and Spherical Harmonics.

Before we go into detail the methods for capturing and storing the reflectance data a more detailed explanation of the overall process of gonioreflectometry. If we say we can store the information of light reflectance which is gained from a set of geometry then all we require to create a BRDF for an object is an understanding of the geometry of its material. With a model of the material we can measure learn the reflectance properties of the materials geometry. Then we can apply these reflectance properties to the object scale geometry as its material properties or BRDF. A good example of this is a model of a velvet chair [6]. The object’s material was defined by the output BRDF of a model of cylinders. A square patch of cylinders was created which bent at various angles. This model represented the velvet material and can be referred to as the micro-geometry of the object. Once the reflectance of the micro-geometry was measured this information was applied to the object and a picture was created which looked very much like a velvet chair. Using this technique, we can create arbitrarily complex BRDFs by modelling the surface microgeometry and then passing it to the virtual gonioreflectometer.

Now that we understand what is done with the BRDF once it has been captured we can go into some depth on how we obtain this BRDF from the micro-geometry. Spherical Harmonics uses the polar coordinate system to create a function which defines the direction of all possible rays of light exitant from the geometry for any incident ray. Reflectance information from the micro-geometry is stored by using a spherical harmonic function to define the approximate ray scattering. The second method is called a capture sphere. Capture spheres define a tree, representing facets of a geodesic sphere, which store the ray scattering information from the micro-geometry. Each facet of the sphere is used as a bin to store the ratio of the exitant to incident flux density, also known as the spectral flux density. The geodesic spheres are created dynamically and its facets subdivide when needed

. The subdivision of the facets of the capture sphere is based on the root mean squared deviation at each wavelength for the spectral flux density of each possible sub-facet of a facet. This means that when a packet is tested for subdivision it is broken up into its 4 possible sub-facets and each of these is tested for its spectral flux density, meaning how much light is reflecting off the geometry and passing through that facet of the geodesic. If the root mean squared deviation is above a small tolerance then the facet is subdivided. This allows the capture sphere to store a great deal of information about the locations at which the light will reflect from the surface material defined by the micro-geometry.

References

1.Westin S. H., J.R. Arvo, K.E. Torrance, “Predicting Reflectance Functions from Complex Surfaces”, Proc. ACM SIGGRAPH 1992

2.Gondek J.S., Meyer, G.W., and Newman J.G, “Wavelength Dependent Reflectance Functions”, Proc. ACM SIGGRAPH 1994

3.Cabral B. et al, “Bidirectional Reflection Functions from Surface Bump Maps”, Proc. ACM SIGGRAPH 1987, pp 273-281

4.Meyer G W et al, “A Computer Graphics System for Rendering Gonio-Apparent Colors”, Proc. AIC Congress 2001

5.Cornell University Program of Computer Graphics, Cornell Gonioreflectometer, [Online], Available: http://www.graphics.cornell.edu/research/measure/gonio.html [February 2003]

6.Imager Computer Graphics Laboratory, The Main Image Gallery, [Online] Available: http://www.cs.ubc.ca/nest/imager/contributions/bobl/imagergallery/main/top.html, [February 2003]