Shapely Polygon centroid negative values

I am using Shapely to find the coordinates of the centroid of a polygon with all positive points. But I am getting negative values of the coordinates of the centroid.

from shapely.geometry import Polygon

poly = Polygon([[263.84, 256.29], [268.6, 253.5], [269.57, 260.44], [277.2, 253.1], [278.94, 252.69], [278.56, 260.02], [278.76, 275.95], [288.99, 269.15], [263.84, 256.29]])

centroid = poly.centroid
print(centroid.x, centroid.y)

The answer that I get is -120.68 and -311.53, which is weird! I would appreciate some inputs on this.

This polygon is invalid: it has self intersections, and most spatial operations will give wrong results for invalid input.

You can check if a geometry is valid using shapely with the is_valid geometry property (example in script below).

You can also ask shapely to make it valid using the shapely.make_valid() function. In this case this will convert the polygon to a multipolygon of 3 pieces and will result in a reasonable centroid (also example in script below).

I also checked the result of geos, the c++ library that powers shapely under the hood, directly, and this is the same.

geosop -a "POLYGON ((263.84 256.29, 268.6 253.5, 269.57 260.44, 277.2 253.1, 278.94 252.69, 278.56 260.02, 278.76 275.95, 288.99 269.15, 263.84 256.29))" centroid -f wkt
POINT (-120.6802662207054 -311.5377745805696)

Script that plots the polygon

from matplotlib import pyplot as plt
from shapely.geometry import Polygon
import shapely.plotting

poly = Polygon(
    [
        [263.84, 256.29],
        [268.6, 253.5],
        [269.57, 260.44],
        [277.2, 253.1],
        [278.94, 252.69],
        [278.56, 260.02],
        [278.76, 275.95],
        [288.99, 269.15],
        [263.84, 256.29],
    ]
)

centroid = poly.centroid
print(poly.wkt)
print(f"centroid: {centroid.x}, {centroid.y}")
print(f"poly.is_valid: {poly.is_valid}")

shapely.plotting.plot_polygon(poly)
plt.show()

poly_valid = shapely.make_valid(poly)
centroid_valid = poly_valid.centroid
print(poly_valid.wkt)
print(f"centroid_valid: {centroid_valid.x}, {centroid_valid.y}")
print(f"poly_valid.is_valid: {poly_valid.is_valid}")

shapely.plotting.plot_polygon(poly_valid)
plt.show()

Script output

POLYGON ((263.84 256.29, 268.6 253.5, 269.57 260.44, 277.2 253.1, 278.94 252.69, 278.56 260.02, 278.76 275.95, 288.99 269.15, 263.84 256.29))
centroid: -120.6802662207054 -311.5377745805696
poly.is_valid: False

MULTIPOLYGON (((269.38634635224486 259.12602441709225, 268.6 253.5, 263.84 256.29, 269.38634635224486 259.12602441709225)), ((277.2 253.1, 270.39810534205236 259.6433691729143, 278.6079766371281 263.84133914725516, 278.56 260.02, 278.94 252.69, 277.2 253.1)), ((269.38634635224486 259.12602441709225, 269.57 260.44, 270.39810534205236 259.6433691729143, 269.38634635224486 259.12602441709225)), ((278.6079766371281 263.84133914725516, 278.76 275.95, 288.99 269.15, 278.6079766371281 263.84133914725516)))
centroid_valid: 277.9350361986902 263.6861518747837
poly_valid.is_valid: True

Plot polygon (original, invalid version)

Plot multipolygon (valid version)