Tech Report CS-92-28

A Simplified Technique for Hidded-Line Elimination in Terrains

Franco P. Preparata and Jeffrey Scott Vitter

June 1992

Abstract:

In this paper we give a practical and efficient output-sensitive algorithm for constructing the display of a polyhedral terrain. It runs in $O((d + n) log^2 n)$ time and uses $O(n alpha(n))$ space, where $d$ is 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 no rebalancing operations are required in the tree.