What's the best way to calculate a 3D (or n-D) centroid?

Question

As part of a project at work I have to calculate the centroid of a set of points in 3D space. Right now I'm doing it in a way that seems simple but naive -- by taking the average of each set of points, as in: centroid = average(x), average(y), average(z) where `x`, `y` and `z` are arrays of floating-point numbers. I seem to recall that there is a way to get a more accurate centroid, but I haven't found a simple algorithm for doing so. Anyone have any ideas or suggestions? I'm using Python for this, but I can adapt examples from other languages.

Answer 1

You need to work with trig. Using points (2,-5,7) and (3,4,5) the formula is:

d​=((3−2)^2+(4−(−5))^2+(5−7)^2​=1+81+4​)^.5

1 + 81 + 4 =86​. □​​