A package to handle the spherical polygon
Project description
Welcome to the SphericalPolygon package
The SphericalPolygon package is an archive of scientific routines for handling spherical polygons. Currently, operations on spherical polygons include calculating area or mass(if the area density is given), geometrical or physical moment of inertia tensor, and determining whether one or more points are inside the spherical polygon.
How to Install
SphericalPolygon can be installed with pip install sphericalpolygon
.
How to use
Create a spherical polygon
Spherical polygons can be created based on a selfdefined 2d array in form of [[lat_0,lon_0],..,[lat_n,lon_n]]
with unit of degrees or a boundary file, such as Plate boundaries for NNRMORVEL56 model. The spherical polygon has a latitude range of [90,90] and a longitude range of [180,180] or [0,360].
>>> import numpy as np >>> from sphericalpolygon import create_polygon >>> boundary = np.loadtxt('NnrMRVL_PltBndsLatLon/an',skiprows=1) # boundary for Antarctica Plate >>> polygon = create_polygon(boundary) >>> print(polygon.arrangement) Counterclockwise
The results show that vertices of the spherical polygon are connected counterclockwise. For more details on attributes and methods of the polygon object, please refer to polygon?
.
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 a sphere with a radius of 6378.137km.
>>> print(polygon.area(6378.137), ' km2') 58280032.6500551 km2
Calculate the mass of the spherical polygon with an area density of 81Gt/km2 over a sphere with a radius of 6378.137km.
>>> print(polygon.area(6378.137,81), ' Gt') 4720682644.654464 Gt
Calculate the perimeter
Calculate the perimeter of a spherical polygon over a unit sphere.
>>> print(polygon.perimeter()) 6.322665894174974 >>> print(polygon.perimeter(6378.137), ' km') 40326.82927827548 km
Calculate the moment of inertia tensor
Calculate 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]
Calculate the physical moment of inertia tensor of the spherical polygon with an area density of 81Gt/km2 over a sphere with a radius of 6378.137km.
>>> print(polygon.inertia(6378.127,81)/1e12, ' Gt·Gm2') [177839.25501653 157466.66651681 48772.37278617 6830.21381414 7032.2786668 10893.9188177 ] Gt·Gm2
Points are inside the 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]
Reference
[1] 李春晓.MORVEL 构造板块的转动惯量张量(英文)[J].天文研究与技术,2016,13(01):5869.
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