Re: 3D graphics domain
- To: mathgroup at smc.vnet.net
- Subject: [mg55880] Re: 3D graphics domain
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Fri, 8 Apr 2005 01:37:18 -0400 (EDT)
- Organization: The University of Western Australia
- References: <d2tesa$qj2$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <d2tesa$qj2$1 at smc.vnet.net>,
Richard Bedient <rbedient at hamilton.edu> wrote:
> Graph the function
>
> f(x,y) = -64*x + 320*(x^2) - 512*(x^3) + 256*(x^4) + 20*y - 64*x*y +
> 64*(x^2)*y - 4*(y^2)
>
> over the domain:
>
> y <= 4*x*(1-x)
> y >= 4*x*(1 - 2x)
> y >= 4*(x - 1)*(1 - 2x)
David Park's solution is very nice. Just some additional comments:
[1] You can use Boole to specify the region:
<< Calculus`
ineqs[x_, y_] =
y <= 4 x (1 - x) && y >= 4 x (1 - 2 x) && y >= 4 (x - 1) (1 - 2 x)
region[x_, y_] = Boole[ineqs[x,y]]
ContourPlot[region[x, y], {x, 0, 1}, {y, -0.1, 1.1}, Contours -> {0},
PlotPoints -> 200]
[2] You can use Reduce to parameterize the region
Reduce[ineqs[x, y], y]
<<Graphics`
DisplayTogether[
FilledPlot[{4 x (1 - 2 x), 4 x (1 - x)}, {x, 0, 1/2}],
FilledPlot[{4 (x - 1) (1 - 2 x), 4 x (1 - x)}, {x, 1/2, 1}],
AspectRatio -> Automatic]
[3] Here is a 3D plot of the function:
f[x_, y_] = 256 x^4 - 512 x^3 + 64 y x^2 + 320 x^2 - 64 y x - 64 x -
4 y^2 + 20 y;
Plot3D[region[x, y] f[x, y], {x, 0, 1}, {y, -0.1, 1.1},
PlotPoints -> 300, Mesh -> False]
Cheers,
Paul
--
Paul Abbott Phone: +61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
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