Display Of Three-Dimensional Discrete Surfaces

The currently-existing 3-D imaging technologies provide 3-D digital images of scenes in the form of 3-D arrays of numbers. In the representation of an object as a set of voxels, a boundary surface of the object is a set of faces of voxels. In spite of the large number of faces that form a boundary surface of a typical object, fast algorithms for hidden part suppression and shading of such surfaces are made possible by the simplicity of the geometry of the 3-D voxel environment. However, because of the very limited number (only three) of orientations of the faces, the shading rule based on the direction cosine of the face normals and distance of the faces from the observer sometimes produces rough display images of originally smooth surfaces. This causes an undesirable change of smoothness of the display image from one view to another in a dynamic mode of display. We propose a contextual shading scheme which assigns shading to a face based on the local shape of the surface in the neighborhood of the face. The number of computations required per face is kept to a minimum by precomputing and storing all the possible direction cosines used for shading. The new shading algorithm has speeds comparable to that of the algorithm based on three face orientations, and produces far better display images.