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MathGroup Archive 2007

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Re: Suggestion for direct commands ParametricPlot22 and ParametricPlot33

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74552] Re: Suggestion for direct commands ParametricPlot22 and ParametricPlot33
  • From: "Narasimham" <mathma18 at hotmail.com>
  • Date: Mon, 26 Mar 2007 02:02:06 -0500 (EST)
  • References: <ett6k3$gdo$1@smc.vnet.net>

On Mar 22, 11:10 am, "Narasimham" <mathm... at hotmail.com> wrote:

 Presently in Mathematica the same ParametricPlot3D command contains
 options of 1 - and 2 -   parametered manifolds  to be embedded into 3
 - space . There  is perhaps a  need felt  in depicting
 generalized spaces, putting n-D surfaces into m-D space where
 special m=2, 3 ( R^2 and R^3)  space could be fully shown.The command
 ParametricPlot3D  could  be renamed ParametricPlot13 and
 ParametricPlot23.

 While attempting to generalize, it is noted that there are no direct
 commands  to address the options  ParametricPlot22 and
 ParametricPlot33. (n = m =2 and 3 respy.)

 For example,  ParametricPlot22[{ u + v, u v}, {u, -1, 1}, {v, -1,
 1}]  is not directly available but can be realized as a subset
command
 after setting z = 0  choosing a remote z - ViewPoint in orthogonal
 projection etc. in:

 ParametricPlot3D[{ u + v, u*v, 0}, {u, -1, 1}, {v, -1, 1}, ViewPoint -> {0,
 0, 50}, Shading -> False]

  Likewise a command may be  enabled as:

 ParametricPlot33[{ u + w, u*v, Sin[ v + w] }, {u, -1, 1}, {v, -1, 1},
 {w, -1, 1} ] for a  3-parameter manifold into 3-space.

 Regards,
 Narasimham




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