Radiosity A method for computing global illumination Donald P. Greenberg, Michael F. Cohen, and Kenneth E. Torrance Cornell University, Program of Computer Graphics, 120 Rand Hall, Ithaca, NY 14853, USA The radiosity method for computing the interreflection of light within diffuse envi- ronments is described. The development of the method for realistic image synthesis over the past three years is outlined. A short discussion of the underlying theory and implementation is followed by a real life example which illustrates the power and accuracy of the radiosity method and points out the different results from ray tracing procedures. Current and future de- velopments of the radiosity method are outlined. Key words: Radiosity - Reflectance mod- els - Interreflection - Diffuse he following brief article reviews the radio- sity approach and explains the fundamen- tal algorithms used to generate images of diffuse environments. The work is not new, but may help to clarify the difference between ray- tracing and radiosity in attempting to simulate global illumination effects. Light reflecting off of a surface depends upon the reflecting surface's properties (reflective, trans- missive, and absorptive) and the composition and direction of the incident light. In computer graph- ics, the reflected light historically has been artifi- cially subdivided into three categories, ambient, diffuse, and specular reflections. Early models made no attempt to simulate the in- terreflections from object to object or the shadow- ing within an environment, and modeled the ambi- ent light as a constant term (Phong 1973). This approach resulted in images which were obviously computer generated, since the global illumination effects, resulting from the interreflections and sha- dowing, have significant effect on the lighting of a scene. In 1979, Whitted (1980) presented his classic paper on ray-tracing, producing images of excellent quali- ty. The method produced the most realistic pictures to data, creating enormous interest in the tech- nique. However, the ray-tracing procedure is lim- ited and can only model intra-environment reflec- tions in the specular direction. In addition, since lights are modeled as points in space, the shadows cast always exhibit sharp boundaries. Although improvements in sampling procedures, as well as more comprehensive reflection models have been made, the basic restrictions still exist (Hall 1986). Furthermore, the ray-tracing procedures are view- dependent, and the entire process must be repeated for every different view. By contrast, the radiosity method determines the global illumination of the environment indepen- dent of the viewer position. At the SIGGRAPH convention of 1984, Goral et al. (1984) first introduced this new approach to computer graphics. The new procedure, derived from methods used in thermal engineering, has a fundamental energy equilibrium basis, and correct- ly models the interaction of light between reflecting surfaces (Sparrow and Cess 1978). Goral's paper was restricted to simple, convex envi- ronments consisting only of diffusely reflecting sur- faces. However, the procedure demonstrated the significance of this approach by accurately simulat- ing the effects of diffuse area light sources as well as the "color bleeding" effects which are caused by diffuse reflections. ,4 The Visual Computer (1986) 2:291-297 L~ | 9 Springer-Verlag 1986The following year, two papers were presented which extended the radiosity method to occluded environments containing hidden surfaces and shad- ows. Cohen (1985) introduced a general procedure, the "hemi-cube", for computing the relationship be- tween discrete surfaces within occluded environ- ments. The "hemi-cube" technique was an efficient algorithm, similar in nature to the projection of visible surfaces, and was applicable to scenes of any complexity. Nishita and Nakamae (1985) also presented a paper which extended the radiosity method to complex environments. Shadows and occlusion ef- fects were computed by using a shadow algorithm restricted to convex polyhedra. In both presentations, because light sources were modeled as finite areas, subtle shadowing effects such as penumbrae were obtained, significantly im- proving the quality of the images. In addition, the previously arbitrary ambient term was replaced by an accurate representation of the global illumina- tion which arises from complex intra-environment reflections. To provide an explanation of the radiosity proce- dure, the following section describes the fundamen- tal algorithms. Radiosity Theory The radiosity method describes an equilibrium en- ergy balance within an enclosure. The essential fea- tures are presented below. It is assumed that all emission and reflection processes are ideally dif- fuse. The light leaving a surface (its radiosity) consists of self-emitted light and reflected or transmitted incident light. The amount of light arriving at a surface requires a complete specification of the geo- metric relationships among all reflecting and trans- mitting surfaces, as well as the light leaving every other surface. This relationship is given by: N Bi=Ei+pi ~, B3F q for i=ltoN (1) j=l Radiosity (B): The total rate of energy leaving a surface. Sum of emitted and reflected energy. (energy/unit time time/unit area) Emission (E): The rate of energy (light) emitted from a surface. (energy/unit time/unit area) Reflectivity (p): The fraction of incident light which is reflected back into the environment. (unitless) Form-factor (F): The fraction of the energy leaving one surface which lands on another surface. (unit- less) N = the number of discrete surfaces of "patches". This equation states that the amount of energy (or light) leaving a particular surface is equal to the self-emitted light plus the reflected light. The re- flected light is equal to the light leaving every other surface multiplied by both the fraction of that light which reaches the surface in question, and the re- flectivity of the receiving surface. The sum of the reflected light from a given surface plus the light emitted directly from the surface is termed its ra- diosity (Fig. 1). If the environment is