# `pygeos.linear`¶

`pygeos.linear.``line_interpolate_point`(line, distance, normalize=False)

Returns a point interpolated at given distance on a line.

Parameters

line : Geometry or array_like

distance : float or array_like

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

normalize : bool

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

Examples

```>>> line = Geometry("LINESTRING(0 2, 0 10)")
>>> line_interpolate_point(line, 2)
<pygeos.Geometry POINT (0 4)>
>>> line_interpolate_point(line, 100)
<pygeos.Geometry POINT (0 10)>
>>> line_interpolate_point(line, -2)
<pygeos.Geometry POINT (0 8)>
>>> line_interpolate_point(line, [0.25, -0.25], normalize=True).tolist()
[<pygeos.Geometry POINT (0 4)>, <pygeos.Geometry POINT (0 8)>]
>>> line_interpolate_point(Geometry("LINESTRING EMPTY"), 1)
<pygeos.Geometry POINT EMPTY>
```
`pygeos.linear.``line_locate_point`(line, other, normalize=False)

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

line : Geometry or array_like

point : Geometry or array_like

normalize : bool

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

Examples

```>>> line = Geometry("LINESTRING(0 2, 0 10)")
>>> line_locate_point(line, Geometry("POINT(4 4)"))
2.0
>>> line_locate_point(line, Geometry("POINT(4 4)"), normalize=True)
0.25
>>> line_locate_point(line, Geometry("POINT(0 18)"))
8.0
>>> line_locate_point(Geometry("LINESTRING EMPTY"), Geometry("POINT(4 4)"))
nan
```
`pygeos.linear.``line_merge`(line)

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

Parameters

line : Geometry or array_like

Examples

```>>> line_merge(Geometry("MULTILINESTRING((0 2, 0 10), (0 10, 5 10))"))
<pygeos.Geometry LINESTRING (0 2, 0 10, 5 10)>
>>> line_merge(Geometry("MULTILINESTRING((0 2, 0 10), (0 11, 5 10))"))
<pygeos.Geometry MULTILINESTRING ((0 2, 0 10), (0 11, 5 10))>
>>> line_merge(Geometry("LINESTRING EMPTY"))
<pygeos.Geometry GEOMETRYCOLLECTION EMPTY>
```
`pygeos.linear.``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

a : Geometry or array_like

b : Geometry or array_like

Examples

```>>> geom1 = Geometry("LINESTRING (0 0, 1 0, 1 1, 0 1, 0 0)")
>>> geom2 = Geometry("LINESTRING (1 0, 2 0, 2 1, 1 1, 1 0)")
>>> shared_paths(geom1, geom2)
<pygeos.Geometry GEOMETRYCOLLECTION (MULTILINESTRING EMPTY, MULTILINESTRING ((1 0, 1 1)))>
```