A simplified technique for hidden-line elimination in terrains
In this paper we give a practical and efficient output-sensitive algorithm for constructing the display of a polyhedral terrain. It runs in O((d+n)log2n) time, where d is the size of the final display. While the asymptotic performance is the same as that of the previously best known algorithm, our implementation is simpler and more practical, because we try to take full advantage of the specific geometrical properties of the terrain. Our main data structure maintains an implicit representation of the convex hull of a set of points that can be dynamically updated in O(log2n) time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.
KeywordsConvex Hull Implicit Representation Polygonal Line Balance Tree Left Child
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- [HaS]S. Hart and M. Sharir, “Nonlinearity of Davenport-Schinzel Sequences and of a Generalized Path Compression Scheme,” Combinatorica 6(1986), 151–177.Google Scholar
- [LeP]D. T. Lee and F. P. Preparata, “Parallel Batch Planar Point Location on the CCC,” Information Processing Letters 33 (December 1989), 175–179.Google Scholar
- [OvL]M. H. Overmars and J. van Leeuwen, “Maintenance of Configurations in the Plane,” Journal of Computer and System Sciences 23(1981), 166–204.Google Scholar
- [PrS]F. P. Preparata and M. I. Shamos, Computational Geometry, Springer-Verlag, New York, 1985.Google Scholar
- [PVY]F. P. Preparata, J. S. Vitter, and M. Yvinec, “Computation of the Axial View of a Set of Isothetic Parallelepipeds,” ACM Transactions on Graphics 9 (July 1990), 278–300.Google Scholar
- [ReS]J. H. Reif and S. Sen, “An Efficient Output-Sensitive Hidden-Surface Removal Algorithm and its Parallelization,” 4th Annual ACM Symposium on Computational Geometry (June 1988), 193–200.Google Scholar