Re: Help!

• To: mathgroup at smc.vnet.net
• Subject: [mg132552] Re: Help!
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 11 Apr 2014 02:09:09 -0400 (EDT)
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• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
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• References: <20140410070757.C6C146A0F@smc.vnet.net>

```It is not clear to me what you want, but here are several views of the
intersection.

SetOptions[ContourPlot3D,
PlotPoints -> 100,
PlotRange -> Automatic,
Boxed -> False,
Axes -> False,
ImageSize -> 300];

param = {x, a, b} /.
Solve[{x^3 + x a + b == 0, a + 3 x^2 == 0},
{a, b}][[1]]

{x, -3*x^2, 2*x^3}

pp = ParametricPlot3D[
param,
{x, -3.2, 3.2},
PlotPoints -> 100,
PlotStyle ->
Directive[Red, AbsoluteThickness[4]]];

{{cp1 = ContourPlot3D[
x^3 + x a + b == 0,
{x, -3.2, 3.2},
{a, -3.2, 3.2},
{b, -3.2, 3.2},
MeshFunctions ->
{Function[{x, a, b},
a + 3 x^2]},
Mesh -> {{0}},
MeshStyle -> Thick],
cp2 = ContourPlot3D[
a + 3 x^2 == 0,
{x, -3.2, 3.2},
{a, -3.2, 3.2},
{b, -3.2, 3.2},
MeshFunctions ->
{Function[{x, a, b},
x^3 + x a + b]},
Mesh -> {{0}},
MeshStyle -> Thick]},
{Show[cp3 = ContourPlot3D[
x^3 + x a + b == 0,
{x, -3.2, 3.2},
{a, -3.2, 3.2},
{b, -3.2, 3.2},
Mesh -> None,
RegionFunction ->
Function[{x, a, b},
a + 3 x^2 < 0]], pp],
Show[cp4 = ContourPlot3D[
a + 3 x^2 == 0,
{x, -3.2, 3.2},
{a, -3.2, 3.2},
{b, -3.2, 3.2},
Mesh -> None,
RegionFunction ->
Function[{x, a, b},
x^3 + x a + b < 0]], pp]},
{Show[cp1, cp2, pp],
Show[cp3, cp4, pp]}} //
Grid

Bob Hanlon

On Thu, Apr 10, 2014 at 3:07 AM, =E6=9E=97=E9=9A=BD <jlin at ynao.ac.cn> wrote:

>
> Could anybody teach me how to shade the region surrounded by the curve
> plotted by the code below? The curve is determined by the intersection of
> two 3D curves, x^3 + x a + b == 0, and a + 3 x^2==0.
>
> Thanks a lot!
>
> Jun
>
>
>
> ContourPlot3D[
>   x^3 + x a + b == 0, {x, -3.2, 3.2}, {a, -3.2, 3.2}, {b, -3.2, 3.2},
>   MeshFunctions -> {Function[{x, a, b}, a + 3 x^2]}, Mesh -> {{0}},
>   ContourStyle -> None, PlotPoints -> 100, Boxed -> False,
>   Axes -> False] /. {x_Real, a_Real, b_Real} -> {3.1, a, b}
>
>
>
>
>
>

```

• References:
• Help!
• From: 林隽 <jlin@ynao.ac.cn>
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