The radiosity method simulates the interaction of light between diffuse reflecting surfaces, thereby accurately predicting global illumination effects. One of the main problems of the original algorithm is the inability to represent correctly the shadows cast onto surfaces. Adaptive subdivision techniques were tried but the results are not good enough for general purposes. The conceptually different discontinuity meshing algorithm produces exact pictures of shadow boundaries but is computationally expensive. The newly presented adaptive discontinuity meshing method combines the speed of adaptive subdivision with the quality of the discontinuity meshing method.