Monte Carlo Estimator for Image Creation with Symmetric Sampling of Phong BRDF Model

The paper is directed to the advanced rendering techniques for realistic image creation. We construct and offer a new Monte Carlo estimator for numerical solution of the rendering equation based on Phong BRDF (Bidirectional Reflectance Distribution Function) model. We consider the kernel of Phong rendering equation and present the Monte Carlo solution by a sum of two independent integrals, one for diffuse and one for specular part respectively. The diffuse integral equation is solved by applying Combined Uniform Separation of integration domain to achieve variance reduction. The hemispherical integration domain is symmetrically separated into 8 sub-domains of equal orthogonal spherical triangles and 8 sub-domains of equal spherical quadrangles. All spherical triangles, spherical quadrangles respectively are symmetric each to other as well as have fixed vertices and computable parameters. The symmetric sampling scheme is applied to generate the sampling points and solve the diffuse integral equation. The integration domain of specular integral equation is approximated by conical solid angle of most important region of interest. The normal vector of the conical solid angle is the direction of ideally reflected by the surface viewing vector. We show that the conical solid angle can be successfully approximated with rotation of all orthogonal spherical triangles sub-domains, constructed at solving the diffuse integral equation, being easy to reuse the sampling points.