Abstract

Understanding irradiance/illuminance is important in many fields including machine vision, image processing, and computer graphics. In this paper we present a general method for calculating the illuminance at a point due to an arbitrary spatial arrangement of uniform, diffusely-emitting sources whose surfaces comprise arbitrarily-shaped planar polygons. The calculation is based on a hemisphere projection method that had been considered suitable for obtaining qualitative, but not quantitative, understanding.¹ By approximating sources as planar polygons, exact solution is achieved. This approximation is not restrictive in practice because surfaces can be tesselated into polygons that are arbitrary with respect to number and shape. The calculation handles cases that can be difficult using other methods: sources that occlude each other and points that lie on edges where sources meet. The hemisphere projection method has use in designing illumination systems for machine vision, in calculating illumination for model-based image processing algorithms such as "shape-from-shading," and in calculating radiosity form factors for computer graphic simulation of scenes with interreflection between objects. We also present the conditions under which the method can be extended to planar polygon sources with non-uniform, non-Lambertian emission.

© 1990 Optical Society of America