Square

Jesse Kearns

Defining the functions

x[u_,v_]:=u^2-v^2

y[u_,v_]:=2u v

z[u_,v_]:=u

w[u_,v_]:=v

umin=-1;

umax=1;

vmin=-1;

vmax=1;

Projecting the shadow

a = 0;

b = 0;

d = 0;

Manipulate[ParametricPlot3D[{x[u,v]Cos[a]Cos[b]Cos[c]-Sin[a]y[u,v]-Sin[b]z[u,v]-Sin[c]w[u,v],
y[u,v]Cos[a]Cos[d] Cos[e]+Sin[a]x[u,v]-Sin[d]z[u,v]-Sin[e]w[u,v],
z[u,v]Cos[b]Cos[d]Cos[f]+Sin[b]x[u,v]+Sin[d]y[u,v]-Sin[f]w[u,v]},
{u,umin,umax},{v,vmin,vmax}],
{{c,0, "XW Plane"},0,2Pi},{{e,0, "YW Plane"},0,2Pi},{{f,0, "ZW Plane"},0,2Pi}]