Re: Re: multiple 3d plots

• To: mathgroup at smc.vnet.net
• Subject: [mg56347] Re: [mg56304] Re: multiple 3d plots
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 22 Apr 2005 06:23:40 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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

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];

```

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