Application of a NURBS-based ray-tracing technique for infinitesimal-area analysis of radiant enclosures

摘要

The use of configuration factors in the analysis of radiant enclosures requires the assumption of uniform radiosity over finite areas of the enclosure surface, which is usually unrealistic and limits the solution accuracy. This can be overcome by using infinitesimal-area analysis to determine the radiosity distribution. In this method, the integral equations that govern the radiosity distribution are first derived from a suitable parametric representation of the enclosure geometry, and are then solved numerically. Recently, a generic infinitesimal-area analysis method was presented where NURBS (non-uniform rational B-spline) algorithms were used to represent the enclosure surfaces parametrically. Because of the versatility of the NURBS algorithms, this technique could be applied to treat unobstructed enclosures of arbitrary geometry. This paper extends the above method to allow analysis of enclosures that contain obstructions. This is done by adapting a ray-tracing method originally developed to render NURBS surfaces in computer graphics to the present application. It takes advantage of several favorable properties of NURBS surfaces, including the availability of the surface derivatives, to accelerate the ray-tracing process.