Welcome to the SphericalPolygon package
The SphericalPolygon package is an archive of scientific routines for handling spherical polygons. Currently, operations on spherical polygons include:
 calculate the area or mass(if the area density is given)
 calculate the perimeter
 identify the centroid
 compute the geometrical or physical moment of inertia tensor
 determine whether one or multiple points are inside the spherical polygon
How to Install
On Linux, macOS and Windows architectures, the binary wheels can be installed using pip by executing one of the following commands:
pip install sphericalpolygon
pip install sphericalpolygon upgrade # to upgrade a preexisting installation
How to use
Create a spherical polygon
Spherical polygons can be created from a 2d array in form of [[lat_0,lon_0],..,[lat_n,lon_n]]
with unit of degrees, or from a boundary file, such as those in Plate boundaries for NNRMORVEL56 model. The spherical polygon accepts a latitude range of [90,90] and a longitude range of [180,180] or [0,360].
from sphericalpolygon import Sphericalpolygon
from astropy import units as u
# build a spherical polygon for Antarctica Plate
polygon = Sphericalpolygon.from_file('NnrMRVL_PltBndsLatLon/an',skiprows=1)
print(polygon.orientation)
Counterclockwise
Calculate the area
Calculate the area(or the solid angle) of a spherical polygon over a unit sphere.
print(polygon.area())
1.4326235943514618
Calculate the area of the spherical polygon over the Earth with an averaged radius of 6371km.
Re = 6371*u.km
print(polygon.area(Re))
58149677.38285546 km2
Calculate the mass of the spherical polygon shell with a thickness of 100km and density of 3.1g/cm3 over the Earth.
thickness, density = 100*u.km, 3.1*u.g/u.cm**3
rho = thickness * density # area density
print(polygon.area(Re,rho))
18026399988.685192 g km3 / cm3
Calculate the perimeter
Calculate the perimeter of a spherical polygon over a unit sphere.
print(polygon.perimeter())
6.322665894174733
Calculate the perimeter of a spherical polygon over the Earth.
print(polygon.perimeter(Re))
40281.70441178723 km
Calculate the compactness
print(polygon.compactness())
0.39900007941415533
Identify the centroid
Identify the centroid of a spherical polygon over a unit sphere.
print(polygon.centroid())
(<Quantity 83.61081032 deg>, <Quantity 57.80052887 deg>, 0.13827778179537997)
Identify the centroid of a spherical polygon over the Earth.
print(polygon.centroid(Re))
(<Quantity 83.61081032 deg>, <Quantity 57.80052887 deg>, <Quantity 880.96774782 km>)
It shows that the latitude of the centroid is close to the South Pole, and the centroid is located about 881km underground.
Compute the moment of inertia tensor
Compute the geometrical moment of inertia tensor of a spherical polygon over a unit sphere. The tensor is symmetrical and has six independent components. The first three components are located diagonally, corresponding to $Q_{11}$, $Q_{22}$, and $Q_{33}$; the last three components correspond to $Q_{12}$, $Q_{13}$, and $Q_{23}$.
print(polygon.inertia())
[ 1.32669154 1.17471081 0.36384484 0.05095381 0.05246122 0.08126929]
Compute the physical moment of inertia tensor of the spherical polygon shell over the Earth.
print(polygon.inertia(Re,rho))
[ 6.77582335e+17 5.99961081e+17 1.85826792e+17 2.60236820e+16
2.67935659e+16 4.15067357e+16] g km5 / cm3
Points are inside a polygon？
Determine if a single point or multiple points are inside a given spherical polygon.
single point
print(polygon.contains_points([75,152]))
False
multiple points
print(polygon.contains_points([[85,130],[35,70]]))
[True, False]
Change log

1.2.2 — Mar 3, 2021
 Add the
compactness()
method, which reflects the deviation of a polygon from a spherical cap.
 Add the

1.2.1 — Feb 23, 2021
 Replace the function create_polygon for building a spherical polygon object from a 2d array with methods
from_array
andfrom_file
.
 Replace the function create_polygon for building a spherical polygon object from a 2d array with methods

1.2.0 — Mar 20, 2020
 Add the
perimeter()
method that may calculate the perimeter of a spherical polygon.  Add the
centroid()
method that may determaine the centroid location for a spherical polygon.
 Add the
Reference
Chunxiao, Li. "Inertia Tensor for MORVEL Tectonic Plates." ASTRONOMICAL RESEARCH AND TECHNOLOGY 13.1 (2016).