THE ENUMERATIVE GEOMETRY OF PROJECTIVE ALGEBRAIC-SURFACES AND THE COMPLEXITY OF ASPECT GRAPHS

The aspect graph is a popular viewer-centered representation that enum erates all the topologically distinct views of an object. Building the aspect graph requires partitioning viewpoint space in view-equivalent cells by a certain number of visual event surfaces. If the object is piecewise-smooth algebraic, then all visual event surfaces are either made of lines having specified contacts with the object or made of lin es supporting the points of contacts of planes having specified contac ts with the object. In this paper, we present a general framework for studying the enumerative properties of line and plane systems. The con text is that of enumerative geometry and intersection theory. In parti cular, we give exact results for the degrees of all visual event surfa ces coming up in the construction of aspect graphs of piecewise-smooth algebraic bodies. We conclude by giving a bound on the number of topo logically distinct views of such objects.