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cubic quaternion based surface
*To*: mathgroup at smc.vnet.net
*Subject*: [mg53465] cubic quaternion based surface
*From*: "Roger L. Bagula" <rlbtftn at netscape.net>
*Date*: Thu, 13 Jan 2005 03:12:08 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Clear[x0,y0,z0,t,p,x,y,z]
(* four space coordinates*)
x0=Cos[t-0];
y0=Cos[t-Pi];
z0=Cos[t+2*Pi/3];
t0=Cos[t-Pi/6];
(*Clifford torus projection*)
x[t_]:=x0/(Sqrt[2]-t0)
y[t_]:=y0/(Sqrt[2]-t0)
z[t_]:=z0/(Sqrt[2]-t0)
g=ParametricPlot3D[{x[t],y[t],z[t]},{t,-Pi,Pi}]
(* this resulting surface is a projective plane of a quaternionic type*)
g2=ParametricPlot3D[{x[t]*z[p],y[t]*x[p],z[t]*y[p]},{t,-Pi,Pi},{p,-Pi,Pi},
Boxed->False,Axes->False,PlotPoints->60,PlotRange->All]
Show[g2,ViewPoint->{0.001, -0.045, 3.383}]
Show[g2,ViewPoint->{-3.360, -0.024, 0.397}]
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