Viewing Transformations of Voxel-Based Objects Via Linear Octrees

This article gives three viewing-transformation algorithms for displaying on a screen 3D pictures represented by linear octrees. All the procedures take advantage of the recursive labeling used to identify the successive decomposition of an object into octants. The first algorithm performs transformations directly on the linear octree, while the second and third algorithms determine the 3D border of the given object first and then project onto the screen the surface voxels thus found. All the algorithms perform the viewing transformations in O(RN) time, where R is the resolution of the picture and N is the number of elements in the linear octree. One of the algorithms provides views of the object at different layers of gray level, while another allows internal views.