The Mathematical Framework of Adjoint Equations for Illumination Computation

There are two basic strategies used for carrying out the illumination computation the gathering strategy in which light reaching a point from all directions is simulated and the shooting strategy in which light emitted from a point in all directions is simulated. Based on the strategy used, all the existing methods can be classi ed into two broad categories, namely gathering methods and shooting methods. The radiance equation provides the mathematical basis for the gathering methods and the potential equation provides the mathematical basis for the shooting methods. They together form an adjoint system of equations. In this paper, using the mathematical framework of the adjoint equations we review illumination computation methods, categorising them as using the gathering or shooting strategy or both. Another basis for categorisation is the basic equation solution strategy used, namely deterministic or nondeterministic.

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