A collection of utility functions for geographical regions:

• area(shape): returns the geographical area of a shape, as a percentage of the planet's surface area.
• bounds(shape): returns the bounding quadrangle of a shape (which is, itself, a shape). (This is useful because most functions are much faster for a quadrangle than they are for a polygon.)
• overlaps(shape1,shape2): returns a boolean representing whether or not two shapes overlap each other. (That is, whether they have at least a point in common.)
• contains(shape1,shape2): returns a boolean representing whether or not a shape completely contains another. (That is, whether all points of shape2 are also in shape1.)

A shape is an Array of number pairs, representing the latitude and longitude of a point on a planet's surface. The length of the array affects the how the library interprets the shape:

• An array of length 2 is a point (in the Euclidean sense).
• An array of length 4 is a quadrangle bounded by the latitudes and longitudes of two points. The latitude and longitude of the first point are assumed to be less than the latitude and longitude of the second.
• An array of length 6 or more is a polygon bounded the points in order. No particular winding order is assumed, though it is assumed that the polygon is closed: that is, that the first and last points are connected by an edge. (Said another way, one does not need to manually "close" a polygon by specifying the first point at both the beginning and end of the polygon.)