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an attempt at solid modeling with Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109813] an attempt at solid modeling with Mathematica
  • From: Narasimham <mathma18 at hotmail.com>
  • Date: Wed, 19 May 2010 07:01:15 -0400 (EDT)

a=1;
base=ParametricPlot3D[{ a Cos[u], a Sin[u], u},{u,0, 2 Pi}]
var1=ParametricPlot3D[{ a Cos[u+v], a Sin[u+v], u},{u,0, 2 Pi},{v,0,2 Pi}]
var2=ParametricPlot3D[{ u Cos[v], u  Sin[v], u},{u,0, 2 Pi},{v,0,2 Pi}]
var3=ParametricPlot3D[{ u Cos[v], u  Sin[v], v},{u,0, 2 Pi},{v,0,2 Pi}]
ThreeParaInto3D[u_,v_,w_]={ u Cos[v+w], u  Sin[v+w], v} ;
(*  we could, so to say, say that ParametricPlot3D1, ParametricPlot3D2
commands are available already as above, but not the next/extended
ParametricPlot3D3 *)

ParametricPlot3D3_[{u_,v_,w_} ,{u,0, 2 Pi},{v,0,2 Pi},{w,0, 2 Pi}]:=ParametricPlot3D[[ThreeParaInto3D[u,v,w], {u,0, 2 Pi},{v,0,2 Pi}],{w,0, 2 Pi}]
ParametricPlot3D3[ThreeParaInto3D[u,v,w], {u,0, 2 Pi},{v,0,2 Pi},{w,0, 2 Pi}]

The above does not work,  how to write the macro ?

TIA
Regards
Narasimham


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