We present a mathematical framework for enforcing energy conservation in a bidirectional reflectance distribution function (BRDF) by specifying halfway vector distributions in simple two-dimensional domains. Energy-conserving BRDFs can produce plausible rendered images with accurate reflectance behavior, especially near grazing angles. Using our framework, we create an empirical BRDF that allows easy specification of diffuse, specular, and retroreflective materials. We also present a second BRDF model that is useful for data fitting; although it does not preserve energy, it uses the same halfway vector domain as the first model. We show that this data-fitting BRDF can be used to match measured data extremely well using only a small set of parameters. We believe that this is an improvement over table-based lookups and factored versions of BRDF data.

A bidirectional reflectance distribution function (BRDF) is often expressed as a function of four real variables: two spherical coordinates in each of the the "incoming" and "outgoing" directions. However, many BRDFs reduce to functions of fewer variables. For example, isotropic reflection can be represented by a function of three variables. Some BRDF models can be reduced further. In this paper, we introduce new sets of coordinates which we use to reduce the dimensionality of several well-known analytic BRDFs as well as empirically measured BRDF data. The proposed coordinate systems are barycentric with respect to a triangular support with a direct physical interpretation. One coordinate set is based on the BRDF model proposed by Lafortune. Another set, based on a model of Ward, is associated with the "halfway" vector common in analytical BRDF formulas. Through these coordinate sets we establish lower bounds on the approximation error inherent in the models on which they are based. We present a third set of coordinates, not based on any analytical model, that performs well in approximating measured data. Finally, our proposed variables suggest novel ways of constructing and visualizing BRDFs.

A classic photographic task is the mapping of the potentially high dynamic range of real world luminances to the low dynamic range of the photographic print. This tone reproduction problem is also faced by computer graphics practitioners who map digital images to a low dynamic range print or screen. The work presented in this paper leverages the time-tested techniques of photographic practice to develop a new tone reproduction operator. In particular, we use and extend the techniques developed by Ansel Adams to deal with digital images. The resulting algorithm is simple and produces good results for a wide variety of images.

This paper presents a physically-based model of the night sky for realistic image synthesis. We model both the direct appearance of the night sky and the illumination coming from the Moon, the stars, the zodiacal light, and the atmosphere. To accurately predict the appearance of night scenes we use physically-based astronomical data, both for position and radiometry. The Moon is simulated as a geometric model illuminated by the Sun, using recently measured elevation and albedo maps, as well as a specialized BRDF. For visible stars, we include the position, magnitude, and temperature of the star, while for the Milky Way and other nebulae we use a processed photograph. Zodiacal light due to scattering in the dust covering the solar system, galactic light, and airglow due to light emission of the atmosphere are simulated from measured data. We couple these components with an accurate simulation of the atmosphere. To demonstrate our model, we show a variety of night scenes rendered with a Monte Carlo ray tracer.

We present a solution to the general problem of characterizing shadows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a spline function.Studying generalized prism-like constructions generated by the emitter and the occluder in a fourdimensional (shadow) space reveals a simpler intrinsic structure of the shadow as compared to the more complicated 2D projection onto a receiver.A closed form expression for the spline shadow irradiance function is derived by twice applying Stokes' theorem to reduce an evaluation over a 4D domain to an explicit formula involving only 2D faces on the receiver, derived from the scene geometry.This leads to a straightforward computational algorithm and an interactive implementation.Moreover, this approach can be extended to scenes involving multiple emitters and occluders, as well as curved emitters, occluders, and receivers.Spline functions are constructed from these prism-like objects.We call them generalized polyhedral splines because they extend the classical polyhedral splines to include curved boundaries and a density function.The approach can be applied to more general problems such as some of those occurring in radiosity, and other related topics.