centroid.rb

require 'matrix'

def centroid points
  base = points[0]
  z = (points[1] - base).cross(points[2] - base).normalize
  ds = []
  total_area = 0.0
  points.drop(1).each_cons(2) do |cons|
    a, b = cons[0] - base, cons[1] - base
    c = (base + cons[0] + cons[1])/3.0
    area = a.cross(b).magnitude/2
    ds << c * area
    total_area += area
  end
  ds.inject(:+)/total_area
end