# zbMATH — the first resource for mathematics

Radiosity and realistic image synthesis. (English) Zbl 0814.68138
Boston: Academic Press Professional (ISBN 0-12-178270-0). XV, 381 p. (1993).
This book is structured as follows. The first step is to derive a mathematical model of global illumination. This derivation is undertaken in Chapter 2, working from basic transport theory to the rendering equation, and finally making the assumptions that lead to the radiosity equation.
In Chapter 3, the basic principles of finite element approximation are used to cast the radiosity equation into a discrete form that is amenable to numerical solution. In particular, the original radiosity function is approximated by a sum of weighted basis functions. These basis functions are in turn defined by a mesh or discretization of the surfaces in the environment.
The finite element formulation of the radiosity integral equation produces a system of linear equations that must be solved for the weights of the basis functions. The coefficients of this linear system are formed by integrals over portions of the surfaces in the environment. These integrals can be solved using both analytic and numerical methods. Chapter 4 describes a variety of algorithms that have been developed for this purpose.
Techniques for solving the matrix equation once it has been formulated are described in Chapter 5. We examine a number of linear equation solvers and discuss their applicability to the system of equations resulting from the radiosity problem.
Chapters 6, 7 and 8 cover the general problem of subdividing the surfaces of the model into the elements upon which the finite element approximation is based. The accuracy and the efficiency of the solution are strongly dependent on this subdivision. Basic subdivision strategies are described in Chapter 6. The use of hierarchical methods that incorporate subdivision into the solution process itself and accelerate the matrix solution is described in Chapter 7. Chapter 8 covers the basic mechanics of meshing.
Once a solution has been obtained, the final step is to produce an image, which is discussed in Chapter 9. This is less straightforward than it might seem, due to the limitations of display devices and the demands of visual perception. In Chapter 10 techniques for extending the basic radiosity method are described. These provide methods to handle more general global illumination models, including general light sources, glossy and mirror reflection, and participating media. Chapter 11 concludes this book with a discussion of applications that are already taking advantage of this technology. We also discuss current trends in the development of radiosity methods.

##### MSC:
 68U10 Computing methodologies for image processing 68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science