# Linestring operations#

line_interpolate_point(line, distance, normalized=False, **kwargs)#

Returns a point interpolated at given distance on a line.

Parameters
lineGeometry or array_like

For multilinestrings or geometrycollections, the first geometry is taken and the rest is ignored. This function raises a TypeError for non-linear geometries. For empty linear geometries, empty points are returned.

distancefloat or array_like

Negative values measure distance from the end of the line. Out-of-range values will be clipped to the line endings.

normalizedbool, default False

If True, the distance is a fraction of the total line length instead of the absolute distance.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString, Point
>>> line = LineString([(0, 2), (0, 10)])
>>> line_interpolate_point(line, 2)
<POINT (0 4)>
>>> line_interpolate_point(line, 100)
<POINT (0 10)>
>>> line_interpolate_point(line, -2)
<POINT (0 8)>
>>> line_interpolate_point(line, [0.25, -0.25], normalized=True).tolist()
[<POINT (0 4)>, <POINT (0 8)>]
>>> line_interpolate_point(LineString(), 1)
<POINT EMPTY>
```
line_locate_point(line, other, normalized=False, **kwargs)#

Returns the distance to the line origin of given point.

If given point does not intersect with the line, the point will first be projected onto the line after which the distance is taken.

Parameters
lineGeometry or array_like
pointGeometry or array_like
normalizedbool, default False

If True, the distance is a fraction of the total line length instead of the absolute distance.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString, Point
>>> line = LineString([(0, 2), (0, 10)])
>>> point = Point(4, 4)
>>> line_locate_point(line, point)
2.0
>>> line_locate_point(line, point, normalized=True)
0.25
>>> line_locate_point(line, Point(0, 18))
8.0
>>> line_locate_point(LineString(), point)
nan
```
line_merge(line, **kwargs)#

Returns (multi)linestrings formed by combining the lines in a multilinestrings.

Parameters
lineGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import MultiLineString
>>> line_merge(MultiLineString([[(0, 2), (0, 10)], [(0, 10), (5, 10)]]))
<LINESTRING (0 2, 0 10, 5 10)>
>>> line_merge(MultiLineString([[(0, 2), (0, 10)], [(0, 11), (5, 10)]]))
<MULTILINESTRING ((0 2, 0 10), (0 11, 5 10))>
>>> line_merge(MultiLineString())
<GEOMETRYCOLLECTION EMPTY>
```
shared_paths(a, b, **kwargs)#

Returns the shared paths between geom1 and geom2.

Both geometries should be linestrings or arrays of linestrings. A geometrycollection or array of geometrycollections is returned with two elements in each geometrycollection. The first element is a multilinestring containing shared paths with the same direction for both inputs. The second element is a multilinestring containing shared paths with the opposite direction for the two inputs.

Parameters
aGeometry or array_like
bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString
>>> line1 = LineString([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])
>>> line2 = LineString([(1, 0), (2, 0), (2, 1), (1, 1), (1, 0)])
>>> shared_paths(line1, line2).wkt
'GEOMETRYCOLLECTION (MULTILINESTRING EMPTY, MULTILINESTRING ((1 0, 1 1)))'
>>> line3 = LineString([(1, 1), (0, 1)])
>>> shared_paths(line1, line3).wkt
'GEOMETRYCOLLECTION (MULTILINESTRING ((1 1, 0 1)), MULTILINESTRING EMPTY)'
```
shortest_line(a, b, **kwargs)#

Returns the shortest line between two geometries.

The resulting line consists of two points, representing the nearest points between the geometry pair. The line always starts in the first geometry a and ends in he second geometry b. The endpoints of the line will not necessarily be existing vertices of the input geometries a and b, but can also be a point along a line segment.

Parameters
aGeometry or array_like
bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`prepare`
improve performance by preparing `a` (the first argument) (for GEOS>=3.9)
```>>> from shapely import LineString