A simplified technique for hidden-line elimination in terrains

Abstract

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)log² n) 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(log² n) time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.

Support was provided in part by National Science Foundation grant CCR-8906419.

Support was provided in part by a National Science Foundation Presidential Young Investigator Award CCR-9047466 with matching funds from IBM Corporation, by National Science Foundation grant CCR-9007851, by the U.S. Army Research Office under grant DAAL03-91-G-0035, and by the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-91-J-4052, ARPA order 8225.