RE: plotting with boundary conditions
- To: mathgroup at smc.vnet.net
- Subject: [mg34512] RE: [mg34482] plotting with boundary conditions
- From: "David Park" <djmp at earthlink.net>
- Date: Fri, 24 May 2002 02:42:20 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Tayade,
You will probably receive a number of replies that make a plot with ragged
edges or walls at the boundary. But with my DrawGraphics package (available
at my web site) it is possible to make a nice smooth plot with the boundary.
I am attaching a .gif image of the plot so you can see what it looks like
without using DrawGraphics. (MathGroup won't post attachments so others can
contact me for the image.)
For those who have DrawGraphics, this is what the code looks like.
Needs["DrawGraphics`DrawingMaster`"]
c[a_, b_] := 0.1*(a - 1)^2 + 0.1*(b - 1)^2 - 0.01
f[a_, b_] = a^2 - 2*c[a, b] + b^2;
This creates a 20 by 20 rectangular grid of Polygons in the ab-plane.
grid = MakePolyGrid[{20, 20}, {{0, 0}, {2, 2}}];
This trims the polygons in the grid so that only Polygons for which 0 <=
c[a,b] <= Infinity remain. Polygons that straddle the boundary are trimmed
and the others are either all in or all out.
fgrid = grid // TrimPolygons[c, {0, Infinity}];
The following plots the surface. There is a smooth missing round hold in the
middle. I used a shaded colored surface. I subdued the polygon outlines and
matched them to the color of the surface. I used neutral lighting so the
regular Mathematica lights wouldn't overwhelm the color of the surface.
plot1 =
Draw3DItems[
{SurfaceColor[Burlywood],
EdgeForm[ColorMix[Burlywood, Black][0.5]],
fgrid // RaiseTo3D[f]},
NeutralLighting[0.3, 0.5, 0],
Axes -> True,
AxesLabel -> {x, y, f},
Background -> ColorMix[CornflowerBlue, White][0.8],
BoxRatios -> {1, 1, 1},
ImageSize -> 600];
In the above I used the following DrawGraphics routines.
Draw3DItems is a shortcut for Show[Graphics[{]]...]
ColorMix will mix two colors in proportion.
RaiseTo3D raises 2D graphics items to 3D items according to the function f
on x and y.
NeutralLighting inserts Lighting options that control the saturation,
brightness and ambient lighting of the 3D lighting. You can also rotate the
lights.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> From: Tayade Rajeshwary Gunwant [mailto:rajeshwary at neo.tamu.edu]
To: mathgroup at smc.vnet.net
>
>
> Hi all,
> I need to plot a surface
> f(a,b) = a^2-2*c(a,b)+b^2; given the boundary conditions c(a,b)< ab
>
> Here c(a,b) is another function of (a,b) given by
> c(a,b) = 0.1*(a-1)^2+0.1*(b-1)^2-0.01
>
> Is there a direct command to set these boundary conditions...?? If i give
>
> f[a_, b_] := If[c[a, b] < a*b, a^2 + b^2 - 2*c[a, b],];
>
> Plot3D[f[a, b], {a, 0, 2}, {b, 0, 2}, AxesLabel -> {"a", "b", "f"},
> ViewPoint -> {2, 2, 2}]
>
> I get error messages for the values of a and b for which f(a,b)
> doesnot exist.
>
> Can anybody please tell me how i can get this plot?
>
> Thanks
> raj
>
>