Cut a polygon with two lines in Shapely

Question

I am trying to cut a shapely.geometry.Polygon instance in two parts with two lines. For example, in the code below, polygon is a ring and if we cut it with line1 and line2 we should get two partial rings, one w/ 270 degrees and one with 90 degrees. Would there be a clean way to do this?

from shapely.geometry import Point, LineString, Polygon

polygon = Point(0, 0).buffer(2).difference(Point(0, 0).buffer(1))
line1 = LineString([(0, 0), (3, 3)])
line2 = LineString([(0, 0), (3, -3)])

score 15 · Accepted Answer · edited Aug 13 '20 at 09:33

15

There is a function to split one geometry by another in Shapely as of version 1.6.0 (Aug 2017), so there is no need to roll your own anymore. See the docs for: shapely.ops.split(geom, splitter)

Note that the older answers on this thread were written before the splitting function was in Shapely - they are now effectively obsolete.

edited Aug 13 '20 at 09:33

Georgy

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answered Apr 09 '19 at 11:02

Keith Ma

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score 7 · Answer 2 · answered Sep 06 '16 at 03:46

Ken Watford answered here about using buffer and difference to do the trick, w/ the drawback of losing a bit of the area. An example code below:

from shapely.geometry import Point, LineString, Polygon

polygon = Point(0, 0).buffer(2).difference(Point(0, 0).buffer(1))
line1 = LineString([(0, 0), (3, 3)])
line2 = LineString([(0, 0), (3, -3)])

line1_pol = line1.buffer(1e-3)
line2_pol = line2.buffer(1e-3)

new_polygon = polygon.difference(line1_pol).difference(line2_pol)

Works for now, and I'd be interested to see whether there is another (potentially w/o losing area) method!

I think any exact solution would require to implement the math problem behind from scratch, with significant lines of code. Specially in the general terms you are setting the problem. — eguaio, Sep 06 '16 at 11:34

Martin Thoma · Answer 3 · 2018-09-11T14:40:54.940

from shapely.ops import linemerge, unary_union, polygonize
from shapely.geometry import LineString, Polygon

# Define the Polygon and the cutting line
line = LineString([(-5, -5), (5, 5)])
polygon = Polygon([(-1, -1), (1, -1), (1, 1), (-1, 1)])


def cut_polygon_by_line(polygon, line):
    merged = linemerge([polygon.boundary, line])
    borders = unary_union(merged)
    polygons = polygonize(borders)
    return list(polygons)

def plot(shapely_objects, figure_path='fig.png'):
    from matplotlib import pyplot as plt
    import geopandas as gpd
    boundary = gpd.GeoSeries(shapely_objects)
    boundary.plot(color=['red', 'green', 'blue', 'yellow', 'yellow'])
    plt.savefig(figure_path)

result = cut_polygon_by_line(polygon, line)
print(result)
plot(result)
print(result[0].intersection(result[1]))

The result is

[<shapely.geometry.polygon.Polygon object at 0x7f50dcf46d68>, 
 <shapely.geometry.polygon.Polygon object at 0x7f50dcf46da0>]
LINESTRING (-1 -1, 1 1)

In case you have two lines, you can just add the second line in the `linemerge()` like this: `merged = linemerge([polygon.boundary, line1, line2])` — tsveti_iko, May 28 '20 at 13:01

Cut a polygon with two lines in Shapely

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