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From: SeekUp on 21 Oct 2009 06:49
I am using the following command to do a DensityPlot in grayscale. The
grayscale range is from 0-255, but I need to map my function to a grey-level
maximum of 200. How do I define a new GrayLevel with a max gray level of
200? (Or alternately change the mapping so make the max level 200?)



DensityPlot[Mod[elementphase[x, y], 2 \[Pi]], {x, -0.008, 0.008},
{y, -0.006, 0.006}, PlotRange -> All, PlotPoints -> 120, ColorFunction ->
GrayLevel, Frame -> False, ImageSize -> {{0, 800}, {0, 600}}, AspectRatio ->
600/800]



Any suggestions will be appreciated, although I'm a Mathematica newbie, so
an example of what to do rather than a broad instruction would be
invaluable.





From: Mark McClure on 22 Oct 2009 02:25
On Wed, Oct 21, 2009 at 6:27 AM, SeekUp <seek.up.girl(a)gmail.com> wrote:
> I am using the following command to do a DensityPlot in
> grayscale. The grayscale range is from 0-255, but I need
> to map my function to a grey-level maximum of 200. How do
> I define a new GrayLevel with a max gray level of 200?

I'm not quite clear what you mean when you say that the
"grayscale range is from 0-255". In fact, all arguments
to the ColorFunction will automatically be scaled to be
between 0 and 1. This is good, since that's what GrayLevel
expects. Do you want to darken your picture so that the
lightest region has shade GrayLevel[200/255]? If so, try
this:

cf[c_] = GrayLevel[200*c/255];
DensityPlot[Exp[-(x^2 + y^2)], {x, -2, 2}, {y, -2, 2},
ColorFunction -> cf]

Hope that helps,
Mark McClure

From: David Park on 22 Oct 2009 02:25
Most Mathematica color gradients go from 0 to 1 and not 0 to 255. And in
plots like DensityPlot Mathematica automatically scales the color parameter
to go from 0 to 1 over the plot. So you could use something like the
following:

A function that goes from 0 to 200:

f[x_, y_] := 200 Abs[Sin[x y]]

DensityPlot[f[x, y], {x, -\[Pi]/2, \[Pi]/2}, {y, -\[Pi]/2, \[Pi]/2},
ColorFunction -> GrayLevel
]

But if you want to key the color to the actual value of the function you can
turn off the automatic scaling with ColorFunctionScaling and use
ColorFunction with Rescale to rescale 0 to 200 to 0 to 1.

DensityPlot[f[x, y], {x, -\[Pi]/2, \[Pi]/2}, {y, -\[Pi]/2, \[Pi]/2},
ColorFunctionScaling -> False,
ColorFunction -> Function[z, GrayLevel[Rescale[z, {0, 200}, {0, 1}]]]
]


David Park
djmpark(a)comcast.net
http://home.comcast.net/~djmpark/



From: SeekUp [mailto:seek.up.girl(a)gmail.com]

I am using the following command to do a DensityPlot in grayscale. The
grayscale range is from 0-255, but I need to map my function to a grey-level

maximum of 200. How do I define a new GrayLevel with a max gray level of
200? (Or alternately change the mapping so make the max level 200?)



DensityPlot[Mod[elementphase[x, y], 2 \[Pi]], {x, -0.008, 0.008},
{y, -0.006, 0.006}, PlotRange -> All, PlotPoints -> 120, ColorFunction ->
GrayLevel, Frame -> False, ImageSize -> {{0, 800}, {0, 600}}, AspectRatio ->

600/800]



Any suggestions will be appreciated, although I'm a Mathematica newbie, so
an example of what to do rather than a broad instruction would be
invaluable.







From: Nasser M. Abbasi on 22 Oct 2009 02:40

"SeekUp" <seek.up.girl(a)gmail.com> wrote in message
news:hbmovm$k9b$1(a)smc.vnet.net...
>I am using the following command to do a DensityPlot in grayscale. The
> grayscale range is from 0-255, but I need to map my function to a
> grey-level
> maximum of 200. How do I define a new GrayLevel with a max gray level of
> 200? (Or alternately change the mapping so make the max level 200?)
>
>
>
> DensityPlot[Mod[elementphase[x, y], 2 \[Pi]], {x, -0.008, 0.008},
> {y, -0.006, 0.006}, PlotRange -> All, PlotPoints -> 120, ColorFunction ->
> GrayLevel, Frame -> False, ImageSize -> {{0, 800}, {0, 600}},
> AspectRatio ->
> 600/800]
>
>
>
> Any suggestions will be appreciated, although I'm a Mathematica newbie, so
> an example of what to do rather than a broad instruction would be
> invaluable.
>

If I understand you correctly, you want simply a linear mapping from 0-255
to 0-200 ?

If so, define a simple function to do it: This below will map "x" which is a
value between 0-255 to value which is between 0-200

Let

A = 255;
B = 0;
a = 200;
b = 0;

map[A_, B_, a_, b_, x_] := a - ((A - x)*(a - b))/(A - B)

so to map 240 write

map[A, B, a, b, 240]

So, if you have the original image and want to convert it to the new scale,
do (on the ImageData) the following

image = {{0, 240, 210}, {90, 100, 50}, {3, 213, 255}}; (*some data*)
{row, col} = Dimensions[image];
newImage = Table[map[A, B, a, b, image[[i,j]]], {i, row}, {j, col}];

N[newImage]

Out[86]= {{0., 188.23529411764707, 164.7058823529412},
{70.58823529411765, 78.43137254901961, 39.21568627450981},
{2.3529411764705883, 167.05882352941177, 200.}}

Now you can do the DensityPlot on the new scaled image?

--Nasser


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