Coordinates of the closest points of two geometries in Shapely

Question

There is a polyline with a list of coordinates of the vertices = [(x1,y1), (x2,y2), (x3,y3),...] and a point(x,y). In Shapely, geometry1.distance(geometry2) returns the shortest distance between the two geometries.

>>> from shapely.geometry import LineString, Point
>>> line = LineString([(0, 0), (5, 7), (12, 6)])  # geometry2
>>> list(line.coords)
[(0.0, 0.0), (5.0, 7.0), (12.0, 6.0)]
>>> p = Point(4,8)  # geometry1
>>> list(p.coords)
[(4.0, 8.0)]
>>> p.distance(line)
1.4142135623730951

But I also need to find the coordinate of the point on the line that is closest to the point(x,y). In the example above, this is the coordinate of the point on the LineString object that is 1.4142135623730951 unit distant from Point(4,8). The method distance() should have the coordinates when calculating the distance. Is there any way to get it returned from this method?

Answer 1

The GIS term you are describing is linear referencing, and Shapely has these methods.

# Length along line that is closest to the point
print(line.project(p))

# Now combine with interpolated point on line
np = line.interpolate(line.project(p))
print(np)  # POINT (5 7)

---

An alternative method is to use nearest_points:

from shapely.ops import nearest_points
np = nearest_points(line, p)[0]
print(np)  # POINT (5 7)

which provides the same answer as the linear referencing technique does, but can determine the nearest pair of points from more complicated geometry inputs, like two polygons.