A Simplified Technique for Hidden-Line Elimination in Terrains

F. P. Preparata and J. S. Vitter. ``A Simplified Technique for Hidden-Line Elimination in Terrains,'' International Journal of Computational Geometry & Applications, 3(2), 1993, 167-181. A shortened version appears in Proceedings of the 1992 Symposium on Theoretical Aspects of Computer Science (STACS '92), Paris, France, February 1992, published in Lecture Notes in Computer Science, 577, Springer-Verlag, Berlin, 135-146.

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In this paper we give a practical and efficient output-sensitive algorithm for constructing the display of a polyhedral terrain. It runs in $O((d + n)\log^2 n)$ time and uses $O(n \alpha(n))$ space, where dis the size of the final display, and $\alpha(n)$ is a (very slowly growing) functional inverse of Ackermann's function. Our implementation is especially simple and practical, because we try to take full advantage of the specific geometrical properties of the terrain. The asymptotic speed of our algorithm has been improved upon theoretically by other authors, but at the cost of higher space usage and/or high overhead and complicated code. Our main data structure maintains an implicit representation of the convex hull of a set of points that can be dynamically updated in $O(\log^2 n)$ time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.

Keywords: display, hidden-line elimination, polyhedral terrain, output-sensitive, convex hull.