Calculate intersected distance across polygons between two points

I have shape files including all the coordinates (lat, long) of different polygons, for example the black, red, and green shown here. I would like to calculate the distance that the AB line across different polygons. I am using geopandas and also exploring gdal, but have not figured out any functions would allow this computation or I need implement from scratch. Thanks!

Solution

have generated some geometry. A grid over Ukraine and a diagonal line
using https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoSeries.intersection.html to find intersecting points
using https://geopy.readthedocs.io/en/stable/#module-geopy.distance to calculate distance between start point of line and intersection point

import shapely
import geopandas as gpd
import geopy.distance

world = gpd.read_file(gpd.datasets.get_path("naturalearth_lowres"))

dims = (4, 3)
a, b, c, d = world.loc[world["name"].eq("Ukraine")].total_bounds
g = 0.4
# generate some polygons and a line that cuts through some of the polygons
gdf_grid = gpd.GeoDataFrame(
    geometry=[
        shapely.geometry.box(minx + g, miny + g, maxx - g, maxy - g)
        for minx, maxx in zip(
            np.linspace(a, c, dims[0]), np.linspace(a, c, dims[0])[1:]
        )
        for miny, maxy in zip(
            np.linspace(b, d, dims[1]), np.linspace(b, d, dims[1])[1:]
        )
    ],
    crs="epsg:4326",
)

gdf_line = gpd.GeoDataFrame(
    geometry=[
        shapely.geometry.LineString(
            [shapely.geometry.Point(a, b), shapely.geometry.Point(c, d)]
        )
    ],
    crs="epsg:4326",
)

# start point of linestring, point we sill calc distance from
l_start = gdf_line.loc[0, "geometry"].coords[0]
# associate every polygon with the line being measures
df_x = gdf_grid.merge(gdf_line.rename(columns={"geometry": "line"}), how="cross")
# intersection will give a line string of the points where line intersects polygon
# from each of these points calc distance to start point
gdf_grid["distances"] = df_x.intersection(gpd.GeoSeries(df_x["line"])).apply(
    lambda g: [round(geopy.distance.geodesic(l_start, p).km, 2) for p in g.coords]
)

# visualize ....
m = gdf_grid.explore(height=200, width=400)
gdf_line.explore(m=m, color="red")

data frames

The line does not pass through some of the polygons, hence no distances.

	distances	geometry
0	[120.44, 658.42]	POLYGON ((27.68400190604637 45.69330801043112, 27.68400190604637 48.41419129088147, 22.48560835133485 48.41419129088147, 22.48560835133485 45.69330801043112, 27.68400190604637 45.69330801043112))
1	[]	POLYGON ((27.68400190604637 49.21419129088147, 27.68400190604637 51.9350745713318, 22.48560835133485 51.9350745713318, 22.48560835133485 49.21419129088147, 27.68400190604637 49.21419129088147))
2	[752.25, 937.0]	POLYGON ((33.68239546075789 45.69330801043112, 33.68239546075789 48.41419129088147, 28.48400190604637 48.41419129088147, 28.48400190604637 45.69330801043112, 33.68239546075789 45.69330801043112))
3	[1176.08, 1360.15]	POLYGON ((33.68239546075789 49.21419129088147, 33.68239546075789 51.9350745713318, 28.48400190604637 51.9350745713318, 28.48400190604637 49.21419129088147, 33.68239546075789 49.21419129088147))
4	[]	POLYGON ((39.68078901546941 45.69330801043112, 39.68078901546941 48.41419129088147, 34.48239546075789 48.41419129088147, 34.48239546075789 45.69330801043112, 39.68078901546941 45.69330801043112))
5	[1453.4, 1985.1]	POLYGON ((39.68078901546941 49.21419129088147, 39.68078901546941 51.9350745713318, 34.48239546075789 51.9350745713318, 34.48239546075789 49.21419129088147, 39.68078901546941 49.21419129088147))

	geometry
0	LINESTRING (22.08560835133486 45.29330801043113, 40.08078901546941 52.3350745713318)

visualisation

Two distances which relate to the two points line intersects polygons that is being hovered over

multiple lines, irregular polygons

scope of question has been extended: What if the polygon shapes are irregular and share boundaries? How do I check which intersect line belong to which polygon?
countries boundaries are irregular and shared. Used countries as polygons instead
have created 3 lines (horizontal, vertical and diagonal). Use exactly same approach, looping through lines and adding distances as columns to polygons geo data frame

gdf_poly = world.loc[(world["continent"]=="Europe") & (~world["iso_a3"].isin(["-99","RUS"]))].copy().reset_index(drop=True)
a,b,c,d = gdf_poly.total_bounds

gdf_line = gpd.GeoDataFrame(
    data={"line": ["diagonal", "vertical", "horizontal"]},
    geometry=[
        shapely.geometry.LineString([(a, b), (c, d)]),
        shapely.geometry.LineString([((a + c) / 2, b), ((a + c) / 2, d)]),
        shapely.geometry.LineString([(a, (b + d) / 2), (c, (b + d) / 2)]),
    ],
    crs="epsg:4326",
)

# multiple lines,  put distances into columns
for _, r in gdf_line.iterrows():
    l_start = r["geometry"].coords[0]

    gdf_poly[r["line"]] = gdf_poly.intersection(
        gpd.GeoSeries([r["geometry"]] * len(gdf_poly), crs=gdf_line.crs)
    ).apply(
        lambda g: [
            round(geopy.distance.geodesic(l_start, p).km, 2)
            for gg in ([g] if isinstance(g, shapely.geometry.LineString) else g.geoms)
            for p in gg.coords
        ]
    )

m = gdf_poly.explore(height=400, width=800)
gdf_line.explore(m=m, color="red")

Germany intersects vertical four times, so their are four distances for vertical