What is the parametric equation of cube?

Answer 1

first the parametric equation of a sphere is X=cos(a)

Y= sin(a)*cos(b)

Z=sin(a)*sin(b)

the equation of a cube is of the same type except that you have to multiply X,Y,and Z by

A=(1+tan(a-pi/2*(floor((a+pi/4)/(pi/2))))²)^(1/2)

and Y and Z by

B=(1+tan(b-pi/2*(floor((b+pi/4)/(pi/2))))²)^(1/2)

And the result should be a cube

Ps: remove Z and take b=0 and you should have the equation of a 2D square, if you want explanations i can give you some but it's a bit long...