Re: cubic quaternion based surface

• To: mathgroup at smc.vnet.net
• Subject: [mg53481] Re: cubic quaternion based surface
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Fri, 14 Jan 2005 08:54:25 -0500 (EST)
• Organization: Uni Leipzig
• References: <cs5ap3\$3qj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

you mean
x[t_]=x0/(Sqrt[2]-t0)
y[t_]=y0/(Sqrt[2]-t0)
z[t_]=z0/(Sqrt[2]-t0)

without the SetDelayed[] because otherwise the t_ pattern
is not replaced by p in your second call of ParametricPlot3D[]

Regards
Jens

"Roger L. Bagula" <rlbtftn at netscape.net> schrieb im Newsbeitrag
news:cs5ap3\$3qj\$1 at smc.vnet.net...
> 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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