# Measuring distance from a point to a line segment in Python.

I recently had the need to calculate the distance from a point (address point) to a polyline (street segment) and wanted to avoid using any additional libraries because it was being done for an external client. Ok, I actually used arcgisscripting for reading the data but that lacked, from what I could tell, the fine-detail granularity of measuring distance between individual geometries.

But since the only spatial operations I needed were to measure the distance between two points and the distance between a point and polyline, I decided to just do it via brute force. The datasets being processed were not huge so it made this feasible.

Measuring point-to-point distance was easy enough. And while I knew I could work through the details of measuring the distance between a point and polyline, I decided NOT to re-invent the wheel if I did not have to. Google did not come up with any direct answers but I did come across this post from Paul Bourke at the University of Western Australia about measuring the distance between a point and a line segment. A polyline is just a series of line segments so I used it as the basis of my measurement–I just loop through all the consecutive vertice pairs, using the minimum distance found.

Paul did not have a python implementation included, so I went ahead and created my own from his information.

```def lineMagnitude (x1, y1, x2, y2):
lineMagnitude = math.sqrt(math.pow((x2 - x1), 2)+ math.pow((y2 - y1), 2))
return lineMagnitude

#Calc minimum distance from a point and a line segment (i.e. consecutive vertices in a polyline).
def DistancePointLine (px, py, x1, y1, x2, y2):
#http://local.wasp.uwa.edu.au/~pbourke/geometry/pointline/source.vba
LineMag = lineMagnitude(x1, y1, x2, y2)

if LineMag < 0.00000001:
DistancePointLine = 9999
return DistancePointLine

u1 = (((px - x1) * (x2 - x1)) + ((py - y1) * (y2 - y1)))
u = u1 / (LineMag * LineMag)

if (u < 0.00001) or (u > 1):
#// closest point does not fall within the line segment, take the shorter distance
#// to an endpoint
ix = lineMagnitude(px, py, x1, y1)
iy = lineMagnitude(px, py, x2, y2)
if ix &gt; iy:
DistancePointLine = iy
else:
DistancePointLine = ix
else:
# Intersecting point is on the line, use the formula
ix = x1 + u * (x2 - x1)
iy = y1 + u * (y2 - y1)
DistancePointLine = lineMagnitude(px, py, ix, iy)

return DistancePointLine
```

## 5 thoughts on “Measuring distance from a point to a line segment in Python.”

1. Line 8:

LineMag = lineMagnitude(x1, y1, x2, y2)

can be replaced by:

LineMag = math.hypot(x2-x1, y2-y1)

Thus removing the need for an additional function.

• or leave the function and just replace:

lineMagnitude = math.sqrt(math.pow((x2 – x1), 2)+ math.pow((y2 – y1), 2))

with:

lineMagnitude = math.hypot(x2 – x1,y2 – y1)

2. Subodh says:

was really helpful for me. Cheers!!

3. niu says:

there is a typo at line 22:
22 if ix > iy: