Re: Error during independent variable change parametric plot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg132383] Re: Error during independent variable change parametric plot3D
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 2 Mar 2014 21:27:34 -0500 (EST)
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• References: <20140302060512.6A98069F0@smc.vnet.net>

```v[u_, z_] := 5*z/u;
x[u_, z_] := u + v[u, z];
y[u_, z_] := u - v[u, z];

data = Table[
{x[z, v[z, u]], y[z, v[z, u]], z},
{u, 1, 3}, {z, 1, 4}];

It is not clear (to me) what you mean by "what I miss in g1" and actually
intend for g1.

As you originally defined g1

g1 = ListPlot3D[Flatten[data, 1], Mesh -> All]

If you want the data viewed as multiple data sets

g1a = ListPlot3D[data, Mesh -> All]

g2 = ParametricPlot3D[{u + v, u - v, u v/5}, {u, 1, 3}, {v, -5, 10}];

g3 = ParametricPlot3D[{x[u, z], y[u, z], z}, {u, 1, 3}, {z, 1, 4}]

Use RegionFunction option to restrict the range of g3

cons = {1 <= u <= 3, -5 <= v <= 10};

rgn = And @@
(Minimize[{#[[-1]], cons}, {u, v}][[1]] <= #[[1]] <=
Maximize[{#[[-1]], cons}, {u, v}][[1]] & /@
{x == u + v, y == u - v,
z == u*v/5})

-4 <= x <= 13 && -9 <= y <= 8 &&
-3 <= z <= 6

g3b = ParametricPlot3D[
{x[u, z], y[u, z], z},
{u, 1, 3}, {z, 1, 4},
RegionFunction ->
Function[{x, y, z, u, v}, rgn]]

Show[{g2, g3b}, PlotRange -> All]

Show[{g1, g3b}, PlotRange -> All]

Show[{g1a, g3b}, PlotRange -> All]

Bob Hanlon

On Sun, Mar 2, 2014 at 1:05 AM, Narasimham <mathma18 at gmail.com> wrote:

> v[u_,z_]:=5.* z/u;
>
> x[u_,z_]:=u+v[u,z];
>
> y[u_,z_]:=u-v[u,z];
>
> sp="end";
>
> Table[{x[z,v[z,u]],y[z,v[z,u]],z,sp},{u,1,3.,1.},{z,1.,4,1}]//RowForm
>
>
> g1=ListPlot3D[{{26.,-24.,1.},{8.25,-4.25,2.},{5.777777777777777,0.22222=
222222222276,3.},{5.5625,2.4375,4.},{51.,-49.,1.},{14.5,-10.5,2.},{8.555555=
555555554,-2.5555555555555545,3.},{7.125,0.875,4.},{76.,-74.,1.},{20.75,-16=
.75,2.},{11.333333333333332,-5.333333333333332,3.},{8.6875,-0.6875,4.}},Mes=
h->All]
>
> g2=ParametricPlot3D[{u+v,u-v,u v/5},{u,1.,3},{v,-5.,10}];
>
> Show[{g1,g2},PlotRange->All]
>
> g3=ParametricPlot3D[{x[u,z],y[u,z],z},{u,1,3},{z,1,4}];
>
> Show[{g2,g3},PlotRange->All]
>
> Show[{g1,g3},PlotRange->All]
>
w
> to delete points from g3 to include only those points within range of g2
>
> TIA
>  Narasimham
>
>

```

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