to the image above, ABCM is an external boundary of a planar region with a hole FGHJ. The cut ED connects the hole with the exterior and is traversed twice in the resulting weakly simple polygonal representation. In an alternative and more general definition of weakly simple polygons, they are the limits of sequences of simple polygons of the same combinatorial type, with the convergence under the Fréchet distance. This formalizes the notion that such a polygon allows segments to touch but not to cross. However, this type of weakly simple polygon does not need to form the boundary of a region, as its "interior" can be empty. For example, referring to the image above, the polygonal chain ABCBA is a weakly simple polygon according to this definition: it may be viewed as the limit of "squeezing" of the polygon ABCFGHA. Computational problems In computational geometry, several important computational tasks involve inputs in the form of a simple polygon; in each of these problems, the distinction between the interior and exterior is crucial in the problem definition. Point in polygon testing involves determining, for a simple polygon P and a query point q, whether q lies interior to P. Simple formulae are known for computing polygon area; that is, the area of the interior of the polygon. Polygon partition is a set of primitive units (e.g. squares), which do not overlap and whose union equals the polygon. A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example: a partition with a smallest number of units or with units of smallest total side-length. A special case of polygon partition is Polygon triangulation: dividing a simple polygon into triangles. Although convex polygons are easy to triangulate, triangulating a general simple polygon is more difficult because we have to avoid adding edges that cross outside the polygon. Nevertheless, Bernard Chazelle showed in 1991 that any simple polygon with n vertices can be triangulated in Θ(n) time, which is optimal. The same algorithm may also be used for determining whether a closed polygonal chain forms a simple polygon. Another special case is the art gallery problem, which can be equivalently reformulated as a partition into a minimum number of star-shaped polygons. Boolean operations on polygons: Various Boolean operations on the sets of points defined by polygonal regions. The convex hull of a simple polygon may