Reconstructing Visible Regions from Visible Segments

An algorithm is presented for reconstructing visible regions from visible edge segments in object space. This has applications in hidden surface algorithms operating on polyhedral scenes and in cartography. A special case of reconstruction can be formulated as a graph problem: "Determine the faces of a straight-edge planar graph given in terms of its edges." This is accomplished in O(n log n) time using linear space for a graph with n edges, and is worst-case optimal. The graph may have separate components but the components must not contain each other. The general problem of reconstruction is then solved by applying our algorithm to each component in the containment relation. CR categories: 1.3.5, 1.3.7, F.2.2.