       Suggestion for direct commands ParametricPlot22 and ParametricPlot33

• To: mathgroup at smc.vnet.net
• Subject: [mg74455] Suggestion for direct commands ParametricPlot22 and ParametricPlot33
• From: "Narasimham" <mathma18 at hotmail.com>
• Date: Thu, 22 Mar 2007 01:07:49 -0500 (EST)

```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
ParametricPlot3Dshould 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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