COMPUTING THE ASPECT GRAPH FOR LINE DRAWINGS OF POLYHEDRAL OBJECTS

We have developed an algorithm for computing the aspect graph for polyhedral objects. The aspect graph is a representation of 3-D objects by a set of 2-D views. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same. At the boundaries between adjacent regions are the accidental viewpoints where the structure of the line drawing changes—a visual event occurs. We show that for polyhedral objects there are two fundamental visual events: 1) the projections of an edge and a vertex coincide, and 2) the projections of three nonadjacent edges intersect at a point. The geometry of the object is reflected in the locus of the accidental viewpoints—the boundaries of the partition. The algorithm computes the partition together with a representative view for each region of the partition. In the course of presenting the algorithm, we provide a full catalog of the changes that occur in the views during each fundamental event. © 1990 IEEE