SAN FRANCISCO JULY 22-26 Volume 19, Number 3,1985 THE HEHI-CUBE A RADIOSITY SOLUTION FOR COMPLEX EI4VIROI~II4EI~ITS Hichael F. Cohen and Donald P. G~eenber 8 Cornell University Ithaca, N. ¥. 14853 ABSTRACT This paper presents a comprehensive method to calculate object to object diffuse reflections within complex environments containing hidden surfaces and shadows. In essence, each object in the environment is treated as a secondary light source. The method provides an accurate representation of the "diffuse" and "ambient" terms found in typical image synthesis algorithms. The phenomena of "color bleeding" from one surface to another, shading within shadow envelopes, and penumbras along shadow boundaries are accurately reproduced. Additional advantages result because computations are independent of viewer position. This a11ows the efficient rendering of multiple views of the same scene for dynamic sequences. Light sources can be modulated and object reflectivities can be changed, with minimal extra computation. The procedures extend the radiosity method beyond the bounds previously imposed. CR Categories and Subject Descriptors: 1.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism; 1.3.3 [Computer Graphics]: Picture/Image Generation General Terms: Algorithms Additional Keywords and Phrases: Radiosity, diffuse reflections, hidden surface, form-factors, depth buffer. INTRODUCTION The representation of a realistic image of both actual and imagined scenes has been the goal of artists and scholars for centuries. The invention of the camera allowed the photographer to mechanically record the light passing through a lens and focused onto a piece of film, thus producing a realistic image. Today, within the field of computer graphics, one aspect of current Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission, © 1985 ACM 0-89791-166-0/85/007/0031 $00.75 research has been the attempt to produce realistic images of non-existent scenes. This is accomplished by simulating the distribution of light energy given a geometric and physical description of the environment. One major difficulty has been the correct simulation of the global illumination effects. Light leaving an object surface originates from the surface by direct emission, as from a light source, or by the reflection or transmission of incident light. The incident light on a surface can arrive directly from a light source (along a direct line of sight) or indirectly by generally complex intermediate reflections and transmissions from other surfaces within the environment. Previously these secondary light "sources" have been ignored in computer graphics image generation algorithms. The summation of these sources have usually been approximated by an added constant term, referred to as the ambient component. [9] Some aspect of the global illumination has been achieved by the addition of a specular component found in ray tracing algorithms [13]. In essence, rays are traced only in the mirror reflection or transmission directions, point sampling the environment at the specific surface intersections. Ray tracing with 31@ S l G G R A P H '85 cones [1] or distributed ray tracing [2] extends this procedure by gathering light from more than one point per ray, but can not accurately model the global environmental lighting effects. The majority of surfaces in a real environment are "diffuse" reflectors, i.e., an incident beam of light is reflected or scattered in all directions within the entire hemisphere above the reflecting surface. A special case of diffuse reflection is the so-called "ideal" diffuse or "Lambertian" reflection. In this case, the incident light is reflected from a surface with equal intensity in all directions. Ideal diffuse reflection is assumed in this paper. Specular reflections, from mirror-]ike surfaces, which account for a much smaller proportion of the reflected light energy, are not considered. Thermal engineers have previously developed methods to determine the exchange of radiant energy between surfaces. [10] [11] Methods have been developed to determine the energy exchange within enclosures. The application of one such method, known as the radiosity method to computer graphics, was outlined in a paper by Goral. [5] This paper extends the use of the radiosity method, to a broader class of problems. In particular, complex environments with occluded surfaces are allowed. In addition, very efficient procedures to render an image from the radiosity data are discussed and illustrated with examples. RADIOSITY The radiosity method describes an equilibrium energy balance within an enclosure. The essential features are summarized here for completeness. [5] It is assumed that all emission and reflection processes are ideal diffuse. Thus, after reflection from a surface, the past history or direction of a ray is lost. 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 geometric relationships among all reflecting and transmitting surfaces, as well as the light leaving every other surface. This relationship is given by: Radiosity i = env Radiosity (B): The total rate of energy leaving a surface. Sum of emitted and reflected energy. (energy/unit 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