I recently read about a neat algorithm for determining the geometry of polyhedral scenes (an assembly of solids each of which is bounded by plane faces) in The New Turing Omnibus. The algorithm assumes that lines can only meet in a few ways, and each meeting has only a few possible labelings for the component lines. The algorithm starts by labeling the lines for one meeting and tries to make consistent labelings for its neighbors and so on. Usually, the algorithm will end up with one consistent labeling for the whole scene, with maybe a few ambiguities.
If the description is confusing, don't worry, I hope to make something soon that will make it all clear.
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