Re: Re: 3D graphics domain
- To: mathgroup at smc.vnet.net
- Subject: [mg55825] Re: [mg55800] Re: [mg55731] 3D graphics domain
- From: DrBob <drbob at bigfoot.com>
- Date: Thu, 7 Apr 2005 05:10:04 -0400 (EDT)
- References: <200504060711.DAA13640@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
That's beautiful! IteratorSubstitution still puzzles me, though. I need a second grade example to get me started, I think. Bobby On Wed, 6 Apr 2005 03:11:54 -0400 (EDT), David Park <djmp at earthlink.net> wrote: > > Here is a solution that those who have DrawGraphics can try out. > > Needs["DrawGraphics`DrawingMaster`"] > > 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 > > The region that Dick wants is the triagular region between the three curves. > (We communicated on this.) > > Draw2D[{Black, Draw[4 x (1 - x), {x, 0, 1}], > Red, Draw[4 x (1 - 2 x), {x, 0, 1}], > Blue, Draw[4 (x - 1) (1 - 2 x), {x, 0, 1}]}, > Frame -> True, > ImageSize -> 400]; > > domain1 = IteratorSubstitution[{y, f[x, y]}, {y, 4x(1 - 2x), 4 x(1 - x)}, w] > > domain2 = > IteratorSubstitution[{y, f[x, y]}, {y, 4 (x - 1) (1 - 2 x), 4 x (1 - x)}, > w] > > Here I used Sequence to paste in the y and z arguments (instead of cutting > and pasting). I used EdgeForm and ColorMix (from DrawGraphics) to subdue the > 'mesh' colors and make them a shade of the surface color. I used two > different surface colors for the two regions. I used the DrawGraphics > options command NeutralLighting to specify a less saturated set of lights so > they don't overwhelm the surface colors. > > plot1 = > Draw3DItems[ > {SurfaceColor[Cadet], EdgeForm[ColorMix[Cadet, Black][0.5]], > ParametricDraw3D[{x, Sequence @@ First[domain1]} // Evaluate, {x, 0, > 0.5}, {w, 0, 1}, PlotPoints -> {21, 21}], > SurfaceColor[LightCoral], EdgeForm[ColorMix[LightCoral, > Black][0.5]], > ParametricDraw3D[{x, Sequence @@ First[domain2]} // Evaluate, {x, > 0.5, > 1}, {w, 0, 1}, PlotPoints -> {21, 21}]}, > NeutralLighting[0.3, 0.7, 0.0], > PlotRange -> {Automatic, Automatic, Automatic}, > Axes -> True, > AxesLabel -> {x, y, f}, > BoxRatios -> {1, 1, 1}, > BoxStyle -> Gray, > Background -> Linen, > ViewPoint -> {1.300, -2.400, 2.000}, > ImageSize -> 600]; > > SpinShow[plot1] > SelectionMove[EvaluationNotebook[], All, GeneratedCell] > FrontEndTokenExecute["OpenCloseGroup"]; Pause[0.5]; > FrontEndExecute[{FrontEnd`SelectionAnimate[200, AnimationDisplayTime -> 0.1, > AnimationDirection -> Forward]}] > > Use the up and down arrow keys to view one frame at a time. > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > > > From: Richard Bedient [mailto:rbedient at hamilton.edu] To: mathgroup at smc.vnet.net > To: mathgroup at smc.vnet.net > > Thanks to Bob and Dan for helping me get this far. Again, I've exhausted > my Mathematica knowledge along with anything I can find in the Help > files. I now need to take the function they found for me and graph it > in 3D over a restricted domain. Here's the problem: > > 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) > > Thanks for any help. > > Dick > > > > > > -- DrBob at bigfoot.com
- References:
- Re: 3D graphics domain
- From: "David Park" <djmp@earthlink.net>
- Re: 3D graphics domain