Can a simple spherical polygon always be triangulated? The answer depends on the definitions of "polygon" and "triangulate." Define a spherical polygon to be a simple, closed curve on a sphere S composed of a finite number of great circle arcs (also known as geodesic arcs) meeting at vertices. Can every spherical polygon be triangulated? Figure 1 shows an example of what is intended.1 The planar analog is well-known and a cornerstone of computational geometry: the interior of every planar simple polygon can be triangulated (and efficiently so). The situation for spherical polygons is not so straightforward. There are three complications.
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