There are two basic models for representing the visibility space, the viewsphere and 3D space. A viewsphere is a unit sphere centred around the object. Each point of the sphere defines a unit vector or viewing direction, connecting the point with the centre of the sphere. This direction is used usually to obtain an orthographic projection of the object: the unit sphere does not carry information about the object-viewer distance, necessary to compute perspective projections. Visual events are curves or points on the viewsphere. In the 3D model, each point in space is considered as a possible viewpoint. The visual events can be points, lines or surfaces in space.

In most practical applications approximate models are adopted, whereby only a finite number of viewpoints is considered. A popular technique makes use of a geodesic dome or quasi-uniform tessellation to obtain a uniform distribution of viewpoints around an object. A typical way to build such a tessellation is to split recursively the facets of a regular polyhedron (e.g. an icosaedron) until a given resolution is reached. The centres of the facets of the resulting polyhedron define a discrete quasi-uniform grid giving the set of all possible viewpoints.

Figure 1:   A geodesic dome

Views are represented usually as line drawings in exact aspect graphs, and the features adopted to compute view equivalence are therefore edges, vertices and junctions. Surfaces are considered commonly as the sole features, in approximate methods, especially in applicative contexts when based on ray-tracing.