BRDF importance sampling for polygonal lights

With the advent of real-time ray tracing, there is an increasing interest in GPU-friendly importance sampling techniques. We present such methods to sample convex polygonal lights approximately proportional to diffuse and specular BRDFs times the cosine term. For diffuse surfaces, we sample the polygons proportional to projected solid angle. Our algorithm partitions the polygon suitably and employs inverse function sampling for each part. Inversion of the distribution function is challenging. Using algebraic geometry, we develop a special iterative procedure and an initialization scheme. Together, they achieve high accuracy in all possible situations with only two iterations. Our implementation is numerically stable and fast. For specular BRDFs, this method enables us to sample the polygon proportional to a linearly transformed cosine. We combine these diffuse and specular sampling strategies through novel variants of optimal multiple importance sampling. Our techniques render direct lighting from Lambertian polygonal lights with almost no variance outside of penumbrae and support shadows and textured emission. Additionally, we propose an algorithm for solid angle sampling of polygons. It is faster and more stable than existing methods.