Get a 3D plane through 3 points and get z of a point (x,y) on that plane

gistfile1.rb

require "matrix"

def cross( v, w )
    x = v[1]*w[2] - v[2]*w[1]
    y = v[2]*w[0] - v[0]*w[2]
    z = v[0]*w[1] - v[1]*w[0]
    Vector[x,y,z]
end

def multi_sumV( v, w )
    v[0]*w[0] + v[1]*w[1] + v[2]*w[2]
end

def planeFrom3Points(p1, p2, p3)
  v1= p3-p1
  v2= p2-p1
  crossed=cross(v1,v2)
  d=multi_sumV(crossed, p1)
  [crossed[0],crossed[1], crossed[2],d]
end

def getZfromPlane(x,y,plane)
  (plane[3]-(plane[0]*x+plane[1]*y))/plane[2]
end

p1=Vector[1,2,3]
p2=Vector[4,6,9]
p3=Vector[12,11,9]

plane=planeFrom3Points(p1, p2, p3)

#puts plane

puts getZfromPlane(12,10,plane)