Re: 3D graphics domain
- To: mathgroup at smc.vnet.net
- Subject: [mg55800] Re: [mg55731] 3D graphics domain
- From: "David Park" <djmp at earthlink.net>
- Date: Wed, 6 Apr 2005 03:11:54 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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 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
- Follow-Ups:
- Re: Re: 3D graphics domain
- From: DrBob <drbob@bigfoot.com>
- Re: Re: 3D graphics domain
- From: DrBob <drbob@bigfoot.com>
- Re: Re: 3D graphics domain