The radiosity method for the simulation of interreflection of light between diffuse surfaces is such a common image synthesis technique that its derivation is worthy of study. We here examine the radiosity method in a two dimensional, flatland world. It is shown that the radiosity method is a simple finite element method for the solution of the integral equation governing global illumination. These twodimensional studies help explain the radiosity method in general and suggest a number of improvements to existing algorithms. In particular, radiosity solutions can be improved using a priori discontinuity meshing, placing mesh boundaries on discontinuities such as shadow edges. When discontinuity meshing is used along with piecewise-linear approximations instead of the current piecewise-constant approximations, the accuracy of radiosity simulations can be greatly increased. Keywords: integral equation, adaptive mesh, finite element method, discontinuity, shadow, global illumination, di..
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