Using corners of the map to calculate the area of whole world does not return correct result

[masterAllen]

Code Sample, a copy-pastable example if possible

from pyproj import Geod
from shapely.ops import transform, orient
from shapely.geometry import Point, Polygon

data = [
    (89.9999, 179.9999),
    (89.9999, -179.9999),
    (-89.9999, -179.9999),
    (-89.9999, 179.9999),
]
world_poly = Polygon(orient([(y, x) for (x, y) in data]))

geod = Geod(ellps="WGS84") 
area = abs(geod.geometry_area_perimeter(world_poly)[0])
print(area)

Problem description

I want to calculate the area of whole world, so i use polygon with four points which are corners of the map. But the result is 283369789.8556872 which is very small.

Expected Output

The area of whole world

Environment Information

• Output from: pyproj -v

pyproj info:
    pyproj: 3.0.1
      PROJ: 8.0.1
  data dir: /usr/share/proj
user_data_dir: /home/allen/.local/share/proj

System:
    python: 3.10.4 (main, Mar 23 2022, 23:05:40) [GCC 11.2.0]
executable: /usr/bin/python
   machine: Linux-5.17.4-arch1-1-x86_64-with-glibc2.35

Python deps:
       pip: 21.0
setuptools: 59.5.0
    Cython: 0.29.28

Installation method

• pip

[snowman2]

@cffk, apologies for bothering you again. However, I think you would be able to give a much better response to this question.

[cffk]

Plot your 4 plots on a globe instead of a map (and replace the 89.9999 by 90) and you will see that they outline a narrow lune of width 0.0002 deg. If you multiply your result by 360/0.0002 you get the full area of the earth. You got a negative result because your lune was traversed clockwise.

Better would be to bite off half the globe, e.g., with 3 points on the equator

  data = [ (0, 0), (0, 120), (0, -120) ]

and multiply this result by 2.

geometry_area_perimeter won't return more than half the area of the earth. A larger polygon will be treated as enclosing the rest of the earth in the opposite direction. This is the issue that you ran into.

[cffk]

@masterAllen Are you set now? Unless you still have questions, this issue can be closed as resolved.

[snowman2]

Thanks @cffk 👍. @masterAllen feel free to comment if you have further questions.

[masterAllen]

So sorry for late reply. I have no questions now, thank you for your help :D