Welcome to the SphericalPolygon package

The SphericalPolygon package is an archive of scientific routines for handling spherical polygons. Currently, operations on spherical polygons include:

1. Calculate the area or mass(if the area density is given)
2. Calculate the perimeter
3. Identify the centroid
4. Compute the geometrical or physical moment of inertia tensor
5. 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 pre-existing 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 NNR-MORVEL56 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
# build a spherical polygon for Antarctica Plate
polygon = Sphericalpolygon.from_file('NnrMRVL_PltBndsLatLon/an',skiprows=1) 
print(polygon)

<SphericalPolygon | ORIENTATION='Counterclockwise', NorthPoleInside=False, SouthPoleInside=True>

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 mass of the spherical polygon shell with a thickness of 100km and density of 3.1g/cm3 over the Earth.

from astropy import units as u
Re = 6371*u.km
thickness, density = 100*u.km, 3.1*u.g/u.cm**3
rho = thickness * density # area density
print(polygon.area(Re,rho))

18026399988.685192 km3 g / cm3

Calculate the perimeter

Calculate the perimeter of a spherical polygon over a unit sphere.

print(polygon.perimeter())

6.322665941435134

Calculate the compactness

print(polygon.compactness())

0.39900007344929683

Identify the centroid

Identify the centroid of a spherical polygon over a unit sphere.

print(polygon.centroid())

(-83.61081032380652, 57.80052886741478, 0.13827778179537864)

It shows that the centroid is close to the South Pole.

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

• 1.2.3 — Aug 22, 2025
  • inside_polygon is fully vectorized to handle multiple points and a single polygon efficiently.
• 1.2.2 — Mar 3, 2021
  • Add the compactness() method, which reflects the deviation of a polygon from a spherical cap.
• 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 and from_file.
• 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.

Reference

Chunxiao, Li. "Inertia Tensor for MORVEL Tectonic Plates." ASTRONOMICAL RESEARCH AND TECHNOLOGY 13.1 (2016).