A geodesic dome (Figure 1) is constructed by splitting recursively the faces of a regular polyhedron, typically an icosaedron, and ``pushing out'' the new vertices created onto the surface of the sphere enclosing the regular solid. These actions are iterated until a predetermined resolution is reached. The viewpoints are the centres of the facets. The viewing direction from a viewpoint connects the centre of the corresponding facet with the centre of the geodesic dome.
For a coarse icosahedron-based tessellation with eighty faces, the angular resolution is about 20 degrees. The popularity of the icosaedron is due to the fact that it is the regular solid with the highest number of faces (20). Notice that no method produces a completely regular tessellation such as the facets enclose equal solid angles, are congruent and their centres are separated from the centres of neighbouring facets by equal amounts. These properties hold for the five platonic polyhedra only.
Approximate techniques offer three main advantages. First, algorithms for computing a tessellated aspect space are relatively simple and many implementations have been reported, often in applicative contexts. Second, approximate methods can be used with generic objects. Third, the designer can constrain the maximum number of views by imposing a maximum resolution on the tessellation, whereas the size of exact aspect graphs depends mostly on the object's shape. One disadvantage is that the radius of the tessellated dome must be known a priori, which implies either a fixed sensor-to-object distance or orthographic projection.
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