We present a new algorithm for radiosity, which is linear both in time and storage with the number of patches in a given scene; that is, the number of patches is increased by dividing each existing patch into smaller patches. The new algorithm is based on Integral Geometry and on the well-known algorithms for Monte Carlo particle transport. It considers the scene embedded in a field of lines, each representing the exchange between the pairs of points that result from the intersections of the line with the scene. For a given pair of points, this exchange is bidirectional. Lines are taken randomly. Both graphical and numerical results are given for the proposed algorithm, which is compared with a local Monte Carlo particle transport algorithm.
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