I have to do some Python coding for The Lieder Project that involves Euclidean distance and variance in three-dimensional space. I'm positive that modules for these things exist out there somewhere, but I couldn't find them quickly. So I wrote the code myself. In case you also need to calculate distances between points in three-dimensional space, and/or the mean locations and standard deviation for points in three-dimensional space, here is the code for Python 3.

First, I created a class for three-dimensional objects.

``````class threedim(object):
def __init__(self, x, y, z):
self.x = x
self.y = y
self.z = z
``````

The following function measures the Euclidean distance between two points in three-dimensional space:

``````def threedimdistance(i, j):
deltaxsquared = (i.x - j.x) ** 2
deltaysquared = (i.y - j.y) ** 2
deltazsquared = (i.z - j.z) ** 2
return (deltaxsquared + deltaysquared + deltazsquared) ** 0.5
``````

To use these, declare new points in three-dimensional space:

``````lineone = threedim(1,1,1)
linetwo = threedim(1,1,0.5)
linethree = threedim(0,0,0)
linefour = threedim(0.5, 0.5, 0.5)
``````

and use threedimdistance() to measure the Euclidean distance between any two of them:

``````threedimdistance(lineone, linetwo)
``````

To find the mean position and standard deviation of a list of points in three-dimensional space, first declare the following functions:

``````def threedimmean(threedimlist):
xvalues = []
yvalues = []
zvalues = []
for point in threedimlist:
xvalues.append(point.x)
yvalues.append(point.y)
zvalues.append(point.z)
xmean = sum(xvalues)/float(len(xvalues))
ymean = sum(yvalues)/float(len(yvalues))
zmean = sum(zvalues)/float(len(zvalues))
return threedim(xmean, ymean, zmean)

def threedimSD(threedimlist):
squareddistances = []
listmean = threedimmean(threedimlist)
for point in threedimlist:
squareddistances.append(threedimdistance(point, listmean) ** 2)
return (sum(squareddistances)/float(len(squareddistances)) ** 0.5)
``````

Then create a list of points in three-dimensional space (from points already created ― see above) and call the above functions on that list:

``````listoflines = [lineone, linetwo, linethree, linefour]
threedimmean(listoflines)
threedimSD(listoflines)
``````

That's it!

Unless I missed something?