Coordinates of the closest points of two geometries in Shapely

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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
p2 = line.interpolate(line.project(p))
print(p2)  # POINT (5 7)

An alternative method is to use nearest_points:

from shapely.ops import nearest_points
p2 = nearest_points(line, p)[0]
print(p2)  # 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.

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