Abstract
We present a new hidden-line elemination 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 view point. Our algorithm is scene-sensitive and uses0((n +d) logn log logn) time, wheren is the number of 3D-rectangles andd 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 inO((logn +k) log logn) time, wherek is the size of the response, and insertions and deletions inO(logn log logn) time, all in the worst case.
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Communicated by C. K. Wong.
An extended abstract of this work appeared inProceedings of the 2nd Scandinavian Workshop on Algorithm Theory (SWAT '90) (edited by J. R. Gilbert and R. Karlsson), Lecture Notes in Computer Science, Volume 447, Springer-Verlag, Berlin, 1990, pp. 71–84. Franco P. Preparata's support was provided in part by NSF research grant CCR-8906419. This research was done while on the faculty of the University of Illinois and partly while visiting Ecole Normale Supérieure in Paris, France. Jeffrey S. Vitter's support was provided in part by NSF Presidential Young Investigator Award CCR-8947808 with matching funds from an IBM research contract and by NSF research grant DCR-8403613. Part of this research was done while visiting Ecole Normale Supérieure in Paris, France. Mariette Yvinec's support was provided by CNRS.
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Preparata, F.P., Vitter, J.S. & Yvinec, M. Output-sensitive generation of the perspective view of isothetic parallelepipeds. Algorithmica 8, 257–283 (1992). https://doi.org/10.1007/BF01758847
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DOI: https://doi.org/10.1007/BF01758847