Line Drawings of Octree-Represented Objects

Abstract

The octree structure represents the space occupied by an object as a juxtaposition of cubes, where the sizes and position coordinates of the cubes are integer powers of 2 and are defined by a recursive decomposition of three-dimensional space. This makes the octree structure highly sensitive to object location and orientation, and the three-dimensional shape of the represented object obscure. It is helpful to be able to see the actual object represented by an octree, especially for visual performance evaluation of octree algorithms. Presented in this paper is a display algorithm that helps visualize the three-dimensional space represented by the octree. Given an octree, the algorithm produces a line drawing of the objects represented by the octree, using parallel projection, from any specified viewpoint with hidden lines removed. The order in which the algorithm traverses the octree has the property that if node x occludes node y, then node x is visited before node y. The algorithm produces a set of long, straight visible edge segments corresponding to the visible surface of the polyhedral object represented by the octree. Examples of some line drawing produced by the algorithm are given. The complexity of the algorithm is also discussed. © 1988, ACM. All rights reserved.