Find longest “straight” path between Point and Polygon

Question

Is it possible to find the longest straight distance between a Point (latitude and longitude) and a Polygon in Shapely ? I read it's possible to find the closest path, but i'm not sure about the longest.

Answer 1

Try the Hausdorff distance , which is returned by the g1.hausdorff_distance(g2) fuction:

from shapely.geometry import Polygon, Point
poly = Polygon([(-1, -1), (-2, 2), (4, 4), (4, -1), (-1, -1)])
p = Point(0, 0)
poly.hausdorff_distance(p)  # 5.656854249492381

Keep in mind, Shapely only works in Cartesian space. Your question asks about "latitude and longitude", so these distance units are in degrees. You'd need to project this into a suitable coordinate reference system (CRS) to get more conventional units of length. Furthermore, the definition of "straight path" changes depending on the choice of CRS.

Answer 2

One way is discretizing the exterior of the polygon into set of points and calculate the distance between the point and each point in this set of points:

def longest(poly, p, num):

    lr = LinearRing(poly.exterior.coords)
    dist = 0
    for i in np.linspace(0, lr.length, num):
        d = p.distance(lr.interpolate(i))
        if d > dist:
            dist = d
    return dist


poly = Polygon([(-1, -1), (-2,2), (4,4), (4, -1), (-1, -1)])
p = Point(0,0)
longest(poly, p, 20)
# out: 5.428886519426354
longest(poly, p, 100)
# out: 5.622291976018042

Of course it is not exact, but it can be a reasonable approximation for many situations.

Remark: you should not use lon/lat with shapely for distance. Shapely is based on cartesian coordinate system. Generally, you should first project your geometries (using pyproj) to be able to use shapely for measuring distance.