Re: Re: Re: multiple 3d plots

• To: mathgroup at smc.vnet.net
• Subject: [mg56385] Re: [mg56347] Re: [mg56304] Re: multiple 3d plots
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 23 Apr 2005 01:16:18 -0400 (EDT)
• References: <200504221023.GAA18819@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

```Wow. That is gorgeous!

Bobby

On Fri, 22 Apr 2005 06:23:40 -0400 (EDT), David Park <djmp at earthlink.net> wrote:

> I had to try this with the DrawGraphics package from my web site. I will
> send you a .gif image separately so you can see the result if you don't have
> the package.
>
> This looks like much more work, but I think we get a nicer plot.
>
> First, let's solve for the intersection, which we can do in this case.
>
> Solve[x^2*y == 3*(x/y), y]
> {{y -> -(Sqrt[3]/Sqrt[x])}, {y -> Sqrt[3]/Sqrt[x]}}
>
> There are two solutions over a wider domain, so let's look at both
> solutions. We can calculate the z value for a given x by
>
> 3*(x/y) /. y -> Sqrt[3/x]
> Sqrt[3]/(1/x)^(3/2)
>
> with a similar expression for the negative solution. Then here is the plot.
>
> Needs["DrawGraphics`DrawingMaster`"]
>
> Draw3DItems[
>  {SurfaceColor[PaleGreen], EdgeForm[ColorMix[PaleGreen, Black][0.3]],
>   Draw3D[x^2*y, {x, 0, 6}, {y, -3, 3}, PlotPoints -> 20],
>
>   SurfaceColor[LightSteelBlue], EdgeForm[ColorMix[LightSteelBlue,
> Black][0.3]],
>   Draw3D[3*(x/y), {x, 0, 6}, {y, -3, -0.1}, PlotPoints -> 20],
>   Draw3D[3*(x/y), {x, 0, 6}, {y, 0.1, 3}, PlotPoints -> 20],
>
>   Red, AbsoluteThickness[2],
>   ParametricDraw3D[{x, Sqrt[3/x], Sqrt[3]/(1/x)^(3/2) + 1}, {x, 0.35, 6},
>     PlotPoints -> 20],
>   ParametricDraw3D[{x, -Sqrt[3/x], -(Sqrt[3]/(1/x)^(3/2)) + 1}, {x, 0.35,
> 6},
>    PlotPoints -> 20]},
>
>    NeutralLighting[0.3, 0.5, 0.1],
>    PlotRange -> {-40, 40},
>    BoxRatios -> {1, 1, 0.5},
>    BoxStyle -> Gray,
>    Axes -> True,
>    AxesLabel -> {x, y, ""},
>    Ticks -> {CustomTicks[Identity, {0, 6, 3, 3}],
>      CustomTicks[Identity, {-3, 3, 3, 3}], CustomTicks[Identity,
>       {-30, 30, 30, 3}]},
>    PlotLabel -> SequenceForm["Intersection of ", x^2*y," and ",3*(x/y)],
>    ViewPoint -> {2.493, -0.343, 2.262},
>    Background -> Linen,
>    ImageSize -> 450];
>
> I used two different colors for the two surfaces and NeutralLighting so the
> colors would not be overwhelmed by the regular color saturation of the
> lighting. The 3x/y surface was plotted in two parts to eliminate the 'return
> surface' at y = 0. The intersection was plotted with a thick red line and
> raised slightly so it would better display. EdgeForm was used to subdue the
> surface 'meshes' and make a different shade of the surface color.
>
> David Park
> djmp at earthlink.net
>
> From: juejung [mailto:juejung at indiana.edu]
To: mathgroup at smc.vnet.net
>
> okay, this seems to do the trick.
> but the show command doesn't use the color i specified for graph p2. any,
> idea?
>
>
> p1 = Plot3D[x^2*y, {x, 1, 2}, {y, 1, 2}];
> p2 = Plot3D[{3*x*(1/y),Hue[.4]}, {x, 1, 2}, {y, 1, 2}];
> Show[p1, p2];
>
>
>
>
>
>
>

--
DrBob at bigfoot.com

```

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