An efficient solid angle sampling technique using bounding volume approach

Abstract

Solid angle sampling is an important variance‐reduced technique when solving global illumination problems by Monte Carlo methods. In this paper, we present an efficient solid angle sampling technique where a paraboloidal luminaire is taken as a case study. The efficiency of our technique is due to the fact that we employ a tight bounding volume to approximate the solid angle. Our technique includes three processes. The construction process builds a bounding volume. It is a convex, frustum‐like polyhedron with a compromise between the tightness and the vertex numbers. The projection process approximates the solid angle as a convex spherical polygon on a unit hemisphere. Finally, the triangulation process triangulates the convex spherical polygon into spherical triangles for stratified sampling. We analyzed our technique in Monte Carlo direct lighting and Monte Carlo path tracing rendering algorithms. The results show that our technique provides up to 90% sampling efficiency. The significance of the proposed technique is that solid angle sampling, from being not possible for the paraboloidal luminaire, is now feasible. In addition, this technique is efficient for sampling, and it is also applicable to other types of luminaires, such as cylindrical and conic luminaires.