Cosine lobes for interactive direct lighting in dynamic scenes

Many rendering systems rely on spherical harmonics or wavelets that provide a mean to solve the rendering equation using scalar products. In addition, these basis of functions may represent hemispherical lighting, visibility and reflectance with a small number of coefficients. However, their use requires the projection of each term of the rendering equation, which is computationally intensive at run-time (for instance with dynamic environments), and limits practically the number of basis functions used at the expense of precision. In this paper, we show how cosine lobes can also be used for representing each term of the rendering equation, without the drawbacks usually existing in the above basis of functions. Cosine lobe representations (such as Lambert, Phong or Lafortune models) have already been used intensively by many authors for their advantage of intuitively and compactly representing reflectance functions. Using this representation also for visibility and lighting, we explain how the rendering equation can be efficiently solved. As an application, we propose an interactive rendering system for direct lighting, naturally including soft shadows and spatially varying materials.