Worst-case optimal hidden-surface removal

An O(<italic>n</italic><supscrpt>2</supscrpt>) hidden-surface removal algorithm is shown. This is an improvement over the previous best worst-case performance of O(<italic>n</italic><supscrpt>2</supscrpt> log <italic>n</italic>). It has been established that the hidden-line and hidden-surface problems have an &OHgr;(<italic>n</italic><supscrpt>2</supscrpt>) worst-case lower bound, so the algorithm is optimal. However, the algorithm is not output-size sensitive. Two corollaries to the result are (1) hidden-lines can be removed in optimal O(<italic>n</italic><supscrpt>2</supscrpt>) time, and (2) the portion of a 3-D polyhedron visible from a given interior point is constructible in optimal O(<italic>n</italic><supscrpt>2</supscrpt>) time.

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