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Question about ColorFunction
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Jee Lou
May 23, 2012, 3:30:22 AM5/23/12
to
Anyone explain to me how ColorFunction works? Why Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[Sin[#1 + #2]] &)] and Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)] return different color distributions?
Bob Hanlon
May 24, 2012, 3:33:07 AM5/24/12
to
"With the usual default setting ColorFunctionScaling->True, all
arguments supplied to func are scaled to lie in the range 0 to 1."
In your first example, #1 and #2 are each scaled before being fed to
Sin[#1 + #2]] & so the argument of the Sin is in the interval {0, 2}.
In your second example, the argument of Hue[#3] & is in the interval
{0, 1}. The plots would be identical if you used ColorFunctionScaling
-> False in each.
Bob Hanlon
arguments supplied to func are scaled to lie in the range 0 to 1."
In your first example, #1 and #2 are each scaled before being fed to
Sin[#1 + #2]] & so the argument of the Sin is in the interval {0, 2}.
In your second example, the argument of Hue[#3] & is in the interval
{0, 1}. The plots would be identical if you used ColorFunctionScaling
-> False in each.
Bob Hanlon
JiHui Lou
May 24, 2012, 3:34:08 AM5/24/12
to
Thx for replying.
But when option ColorFunctionScaling->False is added in both, the plots are
still different if u check them carefully...
As you remind me, "With the usual default setting
ColorFunctionScaling->True, all arguments supplied to func are scaled to
lie in the range 0 to 1." is helpful and inspiring. As a result, I have
tried Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction ->
(Hue[Sin[Pi (#1 + #2)]] &)] to get the same plot as Plot3D[Sin[x + y], {x,
0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)] produce, but unfortunately
they are still different.
So would u be so kind to help me find a way to make the same plot
as Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)]
without using ColorFunction form Hue[#3]& but with other form including #1
and #2 ?
Thx a lot!
*=C2=A5=BC=AA=BB=D4 *=BE=B4=C9=CF From Jee Lou
*Jee Lou* *Student, Major: Physics, Zhejiang Normal University, Jinhua,
P.R.China*
Bob Hanlon
May 24, 2012, 3:34:38 AM5/24/12
to
On my system the two plots on the bottom row of the Grid below look the
same.
$Version
"8.0 for Mac OS X x86 (64-bit) (October 5, 2011)"
With[{is = ImageSize -> 300,
cfs = ColorFunctionScaling -> False},
Grid[{
{Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3},
ColorFunction -> (Hue[Sin[#1 + #2]] &), is],
Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3},
ColorFunction -> (Hue[#3] &), is]},
{Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3},
ColorFunction -> (Hue[Sin[#1 + #2]] &), cfs, is],
Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3},
ColorFunction -> (Hue[#3] &), cfs, is]}}]]
I recommend that you use Rescale to understand how the scaling affects the
output
data = Prepend[Flatten[Table[{
x, y, z = Sin[x + y],
xs = Rescale[x, {0, 3}],
ys = Rescale[y, {0, 3}],
Sin[Pi (xs + ys)],
Rescale[z, {-1, 1}]},
{x, 0, 3, .75}, {y, 0, 3, 0.75}], 1],
{"x", "y", "z=Sin[x+y]", "xs", "ys",
"Sin[Pi(xs+ys)]", "zs"}] // Grid
Bob Hanlon
On Wed, May 23, 2012 at 9:56 AM, JiHui Lou <ywdr...@gmail.com> wrote:
> Thx for replying.
> But when option ColorFunctionScaling->False is added in both, the plots
> are still different if u check them carefully...
> As you remind me, "With the usual default setting
> ColorFunctionScaling->True, all arguments supplied to func are scaled to
> lie in the range 0 to 1." is helpful and inspiring. As a result, I have
> tried Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction ->
,
> 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)] produce, but unfortunatel=
y
> they are still different.
> So would u be so kind to help me find a way to make the same plot
> as Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)]
> without using ColorFunction form Hue[#3]& but with other form including #=
> they are still different.
> So would u be so kind to help me find a way to make the same plot
> as Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)]
1
> and #2 ?
> Thx a lot!
>
>
>
>
>
>
>
> *=C2=A5=BC=AA=BB=D4 *=BE=B4=C9=CF From Jee Lou
>
>
> *Jee Lou* *Student, Major: Physics, Zhejiang Normal University, Jinhua,
> P.R.China*
>
> Tel: (+86) 15958451501 | Email: ywdr...@gmail.com
> and #2 ?
> Thx a lot!
>
>
>
>
>
>
>
> *=C2=A5=BC=AA=BB=D4 *=BE=B4=C9=CF From Jee Lou
>
>
> *Jee Lou* *Student, Major: Physics, Zhejiang Normal University, Jinhua,
> P.R.China*
>
> Contact me: [image: Google Talk] ywdr...@gmail.com [image: MSN]
> yw...@live.cn [image: QQ] yw...@qq.com
> Reach me by the followings: [image: Facebook]<http://www.facebook.com/y=
wdr1987>
> [image: Twitter] <https://twitter.com/#!/ywdr1987> [image: Google Plus=
]<https://plus.google.com/101548232068182998139/about>
> [image: Blog RSS] <http://xiaochoublog.appspot.com/feed> [image:
> Blogger] <http://ywdr.blogspot.com/> [image: Google Reader]<https://www.=
google.com/reader/shared/ywdr1987>
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> YouTube] <http://youtube.com/user/ywdr1987> [image: Orkut]<http://www.or=
kut.com/Main#Profile?uid=10216865585918422690>
>
>
>
>
>
> On Wed, May 23, 2012 at 9:23 PM, Bob Hanlon <hanlo...@gmail.com> wrote:
>
>> "With the usual default setting ColorFunctionScaling->True, all
>> arguments supplied to func are scaled to lie in the range 0 to 1."
>>
>> In your first example, #1 and #2 are each scaled before being fed to
>> Sin[#1 + #2]] & so the argument of the Sin is in the interval {0, 2}.
>> In your second example, the argument of Hue[#3] & is in the interval
>> {0, 1}. The plots would be identical if you used ColorFunctionScaling
>> -> False in each.
>>
>>
>> Bob Hanlon
>>
>>
>> On Wed, May 23, 2012 at 3:29 AM, Jee Lou <ywdr...@gmail.com> wrote:
>> > Anyone explain to me how ColorFunction works? Why Plot3D[Sin[x + y],
>> {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[Sin[#1 + #2]] &)] and
>> Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)]
>> return different color distributions?
>> >
>>
>
>
--
>
>
>
>
> On Wed, May 23, 2012 at 9:23 PM, Bob Hanlon <hanlo...@gmail.com> wrote:
>
>> "With the usual default setting ColorFunctionScaling->True, all
>> arguments supplied to func are scaled to lie in the range 0 to 1."
>>
>> In your first example, #1 and #2 are each scaled before being fed to
>> Sin[#1 + #2]] & so the argument of the Sin is in the interval {0, 2}.
>> In your second example, the argument of Hue[#3] & is in the interval
>> {0, 1}. The plots would be identical if you used ColorFunctionScaling
>> -> False in each.
>>
>>
>> Bob Hanlon
>>
>>
>> On Wed, May 23, 2012 at 3:29 AM, Jee Lou <ywdr...@gmail.com> wrote:
>> > Anyone explain to me how ColorFunction works? Why Plot3D[Sin[x + y],
>> {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[Sin[#1 + #2]] &)] and
>> Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[#3] &)]
>> return different color distributions?
>> >
>>
>
>
Bob Hanlon
Chris Degnen
May 24, 2012, 3:31:04 AM5/24/12
to
on ColorFunction, at:
http://reference.wolfram.com/mathematica/ref/ColorFunction.html
I.e.
ColorFunction->"name" is equivalent to ColorFunction->(ColorData["name"][#i]&) where the slot used is as follows: Plot, ListPlot, etc.: #2 (y); ArrayPlot, ReliefPlot: #1 (a); ContourPlot, DensityPlot, etc.: #1 (f); ContourPlot3D, etc.: #4 (f); Plot3D, etc.: #3 (z).
So in your example:
Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> (Hue[Sin[#1 + #2]] &)]
Using #3 uses the z value.
Sseziwa Mukasa
May 24, 2012, 3:31:34 AM5/24/12
to
The arguments to ColorFunction are scaled, from the help documentation:
With the usual default setting ColorFunctionScaling->True, all arguments supplied to func are scaled to lie in the range 0 to 1.
Plot3D[Sin[x + y], {x, 0, 3}, {y, 0, 3},
Regards,
Sseziwa
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