SHAPELY_DISTANCE

Computes the minimum Cartesian distance between two geometries provided in WKT format.

The distance corresponds to the minimum point-to-point separation:

d(A,B) = \min_{a\in A,\, b\in B} \lVert a-b \rVert_2

Intersecting or overlapping geometries yield a distance of 0.

Excel Usage

=SHAPELY_DISTANCE(geom_one, geom_two)

geom_one (str, required): First geometry (WKT).
geom_two (str, required): Second geometry (WKT).

Returns (float): Minimum distance.

Example 1: Distance between two points

Inputs:

geom_one	geom_two
POINT (0 0)	POINT (3 4)

Excel formula:

=SHAPELY_DISTANCE("POINT (0 0)", "POINT (3 4)")

Expected output:

5

Example 2: Distance between point and line

Inputs:

geom_one	geom_two
POINT (0 0)	LINESTRING (10 0, 10 10)

Excel formula:

=SHAPELY_DISTANCE("POINT (0 0)", "LINESTRING (10 0, 10 10)")

Expected output:

10

Example 3: Distance between overlapping polygons

Inputs:

geom_one	geom_two
POLYGON ((0 0, 2 0, 2 2, 0 2, 0 0))	POLYGON ((1 1, 3 1, 3 3, 1 3, 1 1))

Excel formula:

=SHAPELY_DISTANCE("POLYGON ((0 0, 2 0, 2 2, 0 2, 0 0))", "POLYGON ((1 1, 3 1, 3 3, 1 3, 1 1))")

Expected output:

0

Example 4: Distance between parallel lines

Inputs:

geom_one	geom_two
LINESTRING (0 0, 4 0)	LINESTRING (0 3, 4 3)

Excel formula:

=SHAPELY_DISTANCE("LINESTRING (0 0, 4 0)", "LINESTRING (0 3, 4 3)")

Expected output:

3

Python Code

from shapely import wkt

def shapely_distance(geom_one, geom_two):
    """
    Calculate the minimum distance between two geometries.

    See: https://shapely.readthedocs.io/en/stable/reference/shapely.distance.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        geom_one (str): First geometry (WKT).
        geom_two (str): Second geometry (WKT).

    Returns:
        float: Minimum distance.
    """
    try:
        if not geom_one or not geom_two:
            return "Error: Both geometries must be provided"

        g_one = wkt.loads(geom_one)
        g_two = wkt.loads(geom_two)

        return float(g_one.distance(g_two))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

geom_one *

First geometry (WKT).

geom_two *

Second geometry (WKT).