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MathGroup Archive 2005

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Re: cubic quaternion based surface

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53521] Re: cubic quaternion based surface
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Sat, 15 Jan 2005 21:07:49 -0500 (EST)
  • References: <cs5ap3$3qj$1@smc.vnet.net> <cs9c22$jkk$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jens-Peer Kuska wrote:

> 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}]
>>
> 
> 
> 
You're probably right.
I just put in the ":=" so I could get
the whole thing in a screen capture.
My big problem is I'd like to get Mathematica to consider i,j,k as
matrices instead of numbers.
These groups can be generalized to i^n, j^n,k^n,
but they make more sense as SU(2) type matrices.
Roger


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