Break a shapely Linestring at multiple points
<p>This code below was modified from the one I found <a href="http://stackoverflow.com/questions/21407233/get-the-vertices-on-a-linestring-either-side-of-a-point/21419035#21419035">here</a> which splits a shapely Linestring into two segments at a point defined along the line. I have also checked other questions but they don't address my query directly. However I will like to extend it to split the line into multiple segments (at multiple points), all my attempts to do that so far has failed. How can it be modified to split the string into any given number of segments or at multiple points say ((4,5),(9,18) and (6,5)). </p>

<pre><code>input: 

line = LineString([(1,2),(8,7),(4,5),(2,4),(4,7),(8,5),(9,18),(1,2),(12,7),(4,5),(6,5),(4,9)])
       breakPoint = Point(2,4)

from shapely.geometry import Point,LineString

def make_line_segment(line_string, breakPoint):
    geoLoc = line_string.coords
    j = None
    for i in range(len(geoLoc) - 1):
        if LineString(geoLoc[i:i + 2]).intersects(breakPoint):
           j = i
           break
    assert j is not None
    # Make sure to always include the point in the first group
    if Point(geoLoc[j + 1:j + 2]).equals(breakPoint):
        return geoLoc[:j + 2], geoLoc[j + 1:]
    else:
        return geoLoc[:j + 1], geoLoc[j:]

line1,line2 = make_line_segment(line,breakPoint)
line1 = LineString(line1)
line2 = LineString(line2)
print line1, line2

output: `LINESTRING (1 2, 8 7, 4 5, 2 4) LINESTRING (2 4, 4 7, 8 5, 9 18, 1 2, 12 7, 4 5, 6 5, 4 9)`
</code></pre>

<p>The <code>projection</code> and <code>interpolate</code> lineString methods are usually handy for this kind of operations.</p>

<pre><code>from shapely.geometry import Point, LineString

def cut(line, distance):
    # Cuts a line in two at a distance from its starting point
    # This is taken from shapely manual
    if distance &lt;= 0.0 or distance &gt;= line.length:
        return [LineString(line)]
    coords = list(line.coords)
    for i, p in enumerate(coords):
        pd = line.project(Point(p))
        if pd == distance:
            return [
                LineString(coords[:i+1]),
                LineString(coords[i:])]
        if pd &gt; distance:
            cp = line.interpolate(distance)
            return [
                LineString(coords[:i] + [(cp.x, cp.y)]),
                LineString([(cp.x, cp.y)] + coords[i:])]

def split_line_with_points(line, points):
    """Splits a line string in several segments considering a list of points.

    The points used to cut the line are assumed to be in the line string 
    and given in the order of appearance they have in the line string.

    &gt;&gt;&gt; line = LineString( [(1,2), (8,7), (4,5), (2,4), (4,7), (8,5), (9,18), 
    ...        (1,2),(12,7),(4,5),(6,5),(4,9)] )
    &gt;&gt;&gt; points = [Point(2,4), Point(9,18), Point(6,5)]
    &gt;&gt;&gt; [str(s) for s in split_line_with_points(line, points)]
    ['LINESTRING (1 2, 8 7, 4 5, 2 4)', 'LINESTRING (2 4, 4 7, 8 5, 9 18)', 'LINESTRING (9 18, 1 2, 12 7, 4 5, 6 5)', 'LINESTRING (6 5, 4 9)']

    """
    segments = []
    current_line = line
    for p in points:
        d = current_line.project(p)
        seg, current_line = cut(current_line, d)
        segments.append(seg)
    segments.append(current_line)
    return segments

if __name__ == "__main__":
    import doctest
    doctest.testmod()
</code></pre>

python shapely