Pythagorean Quadruple Parametric Equation in 3 variables

Question

I am looking for a pythagorean quadruple generator in 3 variables. I know this one with 4 variables.

$$a=2mp+2nq \\ b=2np-2mq \\ c=p^2+q^2-(n^2+m^2) \\ d=p^2+q^2+n^2+m^2 $$

Anyway to do this?

Answer 1

a=2mp b=2np c=p^2-(m^2+n^2) d=p^2+m^2+n^2

http://mathworld.wolfram.com/PythagoreanQuadruple.html