       • To: mathgroup at smc.vnet.net
• Subject: [mg126611] Re: Question about ColorFunction
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 24 May 2012 03:33:04 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205230729.DAA04974@smc.vnet.net>

```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 <ywdr1987 at gmail.com> wrote:

> 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 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 #=
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: ywdr1987 at gmail.com
> Contact me: [image: Google Talk] ywdr1987 at gmail.com [image: MSN]
> ywdr at live.cn [image: QQ] ywdr at qq.com
wdr1987>
>   [image: Blog RSS] <http://xiaochoublog.appspot.com/feed>  [image:
kut.com/Main#Profile?uid=10216865585918422690>
>
>
>
>
>
> On Wed, May 23, 2012 at 9:23 PM, Bob Hanlon <hanlonr357 at 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 <ywdr1987 at 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

```

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