Tech Report CS-89-50

Output-Sensitive Generation of the Perspective View of Isothetic Parallelepipeds

Franco P. Preparata, Jeffrey Scott Vitter and Mariette Yvinec

December 1989


We present a new hidden-line-elimination technique for displaying the perspective view of a scene of three-dimensional isothetic parallelepipeds (3D-rectangles). We assume that the 3D-rectangles are totally ordered based upon the dominance relation of occlusion. The perspective view is generated incrementally, starting with the closest 3D-rectangle and proceeding away from the viewpoint. Our algorithm is scene-sensitive and uses $O((n + d) \log n log log n)$ time, where $n$ is the number of 3D-rectangles and $d$ is the number of edges of the display. This improves over the heretofore best known technique. The primary data structure is an efficient alternative to dynamic fractional cascading for use with augmented segment and range trees when the universe is fixed beforehand. It supports queries in $O((\log n + k) log log n)$ time, where $k$ is the size of the output, and insertions and deletions in $O(\log n log log n)$ time, all in the worst case.

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