The `spherical_geometry` library is a Python package for handling spherical
polygons that represent arbitrary regions of the sky.

- Python 2.7, 3.3 or 3.4
- Numpy 1.5.0 or later
- astropy 0.3 or later
- qd-library 2.3.7 or later (optional: if not available, the
bundled version will be used). To force using the system-installed
version, build with
`setup.py build --use-system-qd`.

Coordinates in world space are traditionally represented by right
ascension and declination (*ra* and *dec*), or longitude and latitude.
While these representations are convenient, they have discontinuities
at the poles, making operations on them trickier at arbitrary
locations on the sky sphere. Therefore, all internal operations of
this library are done in 3D vector space, where coordinates are
represented as (*x*, *y*, *z*) vectors. The `spherical_geometry.vector` module
contains functions to convert between (*ra*, *dec*) and (*x*, *y*,
*z*) representations.

While any (*x*, *y*, *z*) triple represents a vector and therefore a
location on the sky sphere, a distinction must be made between
normalized coordinates that fall exactly on the unit sphere, and
unnormalized coordinates which do not. A normalized coordinate is
defined as a vector whose length is 1, i.e.:

To prevent unnecessary recomputation, many methods in this library
assume that the vectors passed in are already normalized. If this is
not the case, `spherical_geometry.vector.normalize_vector` can be used to
normalize an array of vectors.

When not working in Cartesian vectors, the library allows the user to
work in either degrees or radians. All methods that require or return
an angular value have a `degrees` keyword argument. When
`degrees` is `True`, these measurements are in degrees, otherwise
they are in radians.

Warning

Due to constraints in the precision of intersection calculations, points on the sphere that are closer than along a Cartesian axis are automatically merged into a single point. This prevents intersections from being missed due to floating point rounding error. There is currently no implemented solution to deal with points that need to be closer together.

Spherical polygons are arbitrary areas on the sky sphere enclosed by
great circle arcs. They are represented by the
`SphericalPolygon` class.

The points defining the polygon are available from the
`points` property. It is a Nx3 array where
each row is an (*x*, *y*, *z*) vector, normalized. The polygon points
are explicitly closed, i.e., the first and last points are the same.

The edges of a polygon serve to separate the “inside” from the “outside” area. On a traditional 2D planar surface, the “inside” is defined as the finite area and the “outside” is the infinite area. However, since the surface of a sphere is cyclical, i.e., it wraps around on itself, the a spherical polygon actually defines two finite areas. To specify which should be considered the “inside” vs. the “outside”, the definition of the polygon also has an “inside point” which is just any point that should be considered inside of the polygon.

In the following image, the inside point (marked with the red dot) declares that the area of the polygon is the green region, and not the white region.

The inside point of the the polygon can be obtained from the
`inside` property.

If the polygon represents two disjoint areas or the polygon has holes, those areas will be connected by cut lines. The following image shows a polygon made from the union of a number of cone areas which has both a hole and a disjoint region connected by cut lines.

`SphericalPolygon` objects have 4 different constructors:

SphericalPolygon: Takes an array of (x,y,z) points, or a list of disjointSphericalPolygoninstances.SphericalPolygon.from_radec: Takes an array of (ra,dec) points and an inside point.SphericalPolygon.from_cone: Creates a polygon from a cone on the sky shere. Takes (ra,dec,radius).SphericalPolygon.from_wcs: Creates a polygon from the footprint of a FITS image using its WCS header keywords. Takes a FITS filename or aastropy.io.fits.Headerobject.

Once one has a `SphericalPolygon` object, there are a number of
operations available:

contains_point: Determines if the given point is inside the polygon.intersects_poly: Determines if one polygon intersects with another.area: Determine the area of a polygon.unionandmulti_union: Return a new polygon that is the union of two or more polygons.intersectionandmulti_intersection: Return a new polygon that is the intersection of two or more polygons.overlap: Determine how much a given polygon overlaps another.to_radec: Convert (x,y,z) points in the polygon to (ra,dec) points.draw: Plots the polygon using matplotlib’s Basemap toolkit. This feature is rather bare and intended primarily for debugging purposes.

As seen above, great circle arcs are used to define the edges of the
polygon. The `spherical_geometry.great_circle_arc` module contains a number of
functions that are useful for dealing with them.

`length`: Returns the angular distance between two points on the sphere.`intersection`: Returns the intersection point between two great circle arcs.`intersects`: Determines if two great circle arcs intersect.`intersects_point`: Determines if a point is along the great circle arc.`angle`: Calculate the angle between two great circle arcs.`midpoint`: Calculate the midpoint along a great circle arc.