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