Cosine lobes for interactive direct lighting in dynamic scenes

摘要

Cosine functions have been widely used for representing Bidirectional Reflection Distribution Functions (BRDF) such as Lambert, Phong and Lafortune models. They are well suited to represent both high and low frequency signals. However, they are difficult to use with visibility and incident radiance. In most systems, the rendering equation terms are thus estimated using various methods. Several interactive rendering systems rather rely on the projection of each term onto orthonormal basis functions such as spherical harmonics or wavelets. These methods are easier to handle since the integration becomes a dot product. However, these functions are also subject to several drawbacks. For instance the number of coefficients is high for the representation of high frequency phenomena; the pre-computation time required for projecting each term of the rendering equation cannot be neglected. This paper demonstrates that cosine lobes can be generalized to visibility and incoming radiance with several advantages. First, cosine lobes do not form an orthonormal basis of functions and the number of parameters remains naturally adapted to the signal. This is very interesting for complex and high frequency functions: glossy BRDF or small light sources for instance. We also use this property for reducing the number of parameters as the computation goes along. Second, Lambert, Phong and Lafortune BRDF models are already used in many rendering systems. Since they already rely on this representation, no transformation into other types of model is necessary. This paper shows how it is possible to rapidly integrate the product of cosine lobes. As a demonstration of our methodology, we propose an interactive rendering system for direct lighting, including soft shadows and spatially varying materials.