An efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented. The aspect graph is an approach to representing 3-D objects by a set of 2-D views, for the purpose of object recognition. In this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change. The viewing data of an object is the partition of the viewpoint space together with a representative view in each region. The algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection.>

An algorithm for computing the aspect graph for polyhedral objects is described. The aspects graph is a representation of three-dimensional objects by a set of two-dimensional 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 for the line drawing changes. It is shown 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 algorithm computes the partition together with a representative view for each region of the partition.>

J.J. Koenderink and A.J. van Doorn (1979) introduced aspect graphs as a way of representing 3-D shape for object recognition. 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. The viewing data of an object are the partition of the Gaussian sphere together with representative line drawings for each region of the partition. The authors present an algorithm for computing the viewing data of polyhedral objects. In the course of presenting the algorithm, they provide a full catalog of the visual events that occur for this type of object.>

The aspect graph is one of the approaches to representing of 3-D shape for the purposes of object recognition. In this approach, the viewing space of an object is partitioned into regions, such that in each region the topology of the line drawing of the object does not change. The viewing data of an object is the partition of the viewing space together with a representative view in each region. We present an efficient algorithm for computing the viewing data for line drawings of polyhedral objects under orthographic projection. For an object of size O(n) whose partition of size O(m), the algorithm runs O(n^4 log n + m log m) time. Using a novel data structure, we construct the set of all views in optimal O(m) time and space

J.J. Koenderink and A.J. van Doorn (1979) introduced aspect graphs as a way of representing 3-D shape for object recognition. 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. The viewing data of an object are the partition of the Gaussian sphere and representative line drawings for each region of the partition. An algorithm is presented for computing the viewing data of polyhedral objects. A full catalog of the visual events that occur for polyhedral objects is provided.>