Analysis of planar light fields from homogeneous convex curved surfaces under distant illumination

We consider the flatland or 2D properties of the light field generated when a homogeneous convex curved surface reflects a distant illumination field. Besides being of considerable theoretical interest, this problem has applications in computer vision and graphics—for instance, in determining lighting and bidirectional reflectance distribution functions (BRDFs), in rendering environment maps, and in image-based rendering. We demonstrate that the integral for the reflected light transforms to a simple product of coefficients in Fourier space. Thus, the operation of rendering can be viewed in simple signal processing terms as a filtering operation that convolves the incident illumination with the BRDF. This analysis leads to a number of interesting observations for computer graphics, computer vision, and visual perception.