This thesis presents some advances in efficient representation of material appearance in a lighting simulation. The scope of this thesis is two-fold: an interactive shading algorithm to render measured reflectance with dynamic geometry using frequency analysis of light transport and hierarchical shading and up-sampling in deferred shading context, and a new normal distribution function for the Cook-Torrance micro-facet BRDF model, along with a new shadowing and masking function and a generalization of Schlick’s approximation of the Fresnel term. In the first part, we introduce a real-time frequency analysis of light transport framework that allows us to estimate the bandwidth and variance of the shading integrand. The bandwidth and variance are a function of frequencies in the illumination, distance traveled by light, BRDF and texture, and the geometry configuration (curvature). We use this information to under-sample the image, and also use an adaptive number of samples for shading. We devise a single-pass hierarchical shading and up-sampling scheme to assemble an image out of the sparsely shaded image pixels. We extend our interactive technique to use pre-convolved shading for real-time performance. We also take advantage of the bandwidth information to perform multi-sample anti-aliasing in deferred shading by subsampling only a small portion of image pixels whose bandwidth is smaller than 1 pixel^-1. In the second part, we propose a new distribution function for the Cook-Torrance micro-facet BRDF, based on our observations on the reflectance measurements. We isolate the distribution components of the reflectance data and directly observe that existing distribution functions are insufficient. Then we devise the Shifted Gamma Distribution (SGD) fitting more accurately to the data. We derive the shadowing and masking function from the distribution. We observe that not all materials have the Fresnel behavior expected by Schlick’s approximation. Hence, we generalize the Schlick’s approximation to more accurately fit the model to the measurements. We introduce a two-step fitting approach, that fits each RGB channel separately — accounting for wave-length dependent effects. We show that our shading model outperforms existing models and accurately represents a wider range of materials from diffuse to glossy and highly specular materials.
Material appearance : photo-realistic representation and rendering