The Potential Equation and Importance in Illumination Computations

An equation adjoint to the luminance equation for describing the global illumination can be formulated using the notion of a surface potential to illuminate the region of interest. This adjoint equation which we shall call as the potential equation, is fundamental to the adjoint radiosity equation used to devise the importance driven radiosity algorithm. In this paper we first briefly derive the adjoint system of integral equations and then show that the adjoint linear equations used in the above algorithm are basically discrete formulations of the same. We also show that the importance entity of the linear equations is basically the potential function integrated over a patch. Further we prove that the linear operators in the two equations are indeed transposes of each other.

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