       Re: Aligning 2 Sets of Axes at {0,0}; Rotated & Standard Position

• To: mathgroup at smc.vnet.net
• Subject: [mg123139] Re: Aligning 2 Sets of Axes at {0,0}; Rotated & Standard Position
• From: Peter Pein <petsie at dordos.net>
• Date: Thu, 24 Nov 2011 06:57:49 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jaio5e\$epq\$1@smc.vnet.net>

```Am 23.11.2011 13:15, schrieb Bill:
> Subj: Aligning Two Sets of Axes at {0,0}; Rotated and Standard Position in one plot.
>
>
> Hi:
>
> I have the following Mathematica 8.0.4 code that gives me a satisfactory plot:
>
> a=17;b=-48;c=31;
> (ArcTan[b/(a-c)])/2;
> N[(%)*(180/Pi)];
> Print["Majoraxis: Angle in Decimal Degrees= ",%]
> axes=Graphics[Point[{0,0}],PlotRange->{{-12,12},{-12,12}},Axes->True,AxesStyle->{Directive[{Red,Thin}],Directive[{Black,Thin}]},AxesLabel->{"'x","'y"},AspectRatio->1,ImageSize->500];
> ContourPlot[17*x^2-48*x*y+31*y^2+49==0,{x,-12,12},{y,-12,12},AspectRatio->1,Axes->True,AxesStyle->{Directive[{Red,Thin}],Directive[{Black,Thin}]},AxesLabel->{"X","Y"},Background->LightGray,ImageSize->500,Prolog->Inset[Rotate[Graphics[axes],36.8699Degree],{.1,.7}]]
>
> However, my objective here is to combine the two plots with the two sets of axes centered automatically.
> As my code is now, I have to use a trial-and-error visual inspection method, and manually input the location of the rotated axes to match the main plot axes' center at standard position.
>
> Ref: See {.1,.7} in ...Inset[Rotate[Graphics[axes],36.8699Degree],{.1,.7}]]
> (In another example using another equation that I ploted, the alignment values were different yet. So for some reason, these numbers don't seem to be constants from one plot to another.)
>
> I have tried AxesOrigin->{0,0} in the plots, but this doesn't seem to matter. Any help will be appreciated.
>
>
> Tia,
>
> Bill
>

Hi Bill!

Phew! This one was a lot of trial and error here.
I changed:

1.) Omitted the conversion of the angle to degree and back to radians
and moved the axes-related Options out of Graphics[]
2.) I use the rotation and translation inside Inset
3.) became finally aware that it seems to be necessary that the axes
Graphics and the ContourPlot have got the same ImagePadding.

And I added a grey circle to verify that the axes in the plot and in the
inset are of same length.

a = 17; b = -48; c = 31;
alpha = ArcTan[b/(a - c)]/2;
axes = Show[Graphics[Point[{0, 0}]],
PlotRange -> {{-12, 12}, {-12, 12}}, Axes -> True,
AxesStyle -> {Directive[{Red, Thin}], Directive[{Black, Thin}]},
AxesLabel -> {"'x", "'y"}, ImagePadding -> 20];
ContourPlot[17*x^2 - 48*x*y + 31*y^2 + 49 == 0,
{x, -12, 12}, {y, -12, 12}, PlotRange -> {{-12, 12}, {-12, 12}},
AspectRatio -> Automatic, Axes -> True,
AxesStyle -> {Directive[{Red, Thin}], Directive[{Black, Thin}]},
AxesLabel -> {"X", "Y"}, Background -> LightGray,
Prolog -> {GrayLevel[0.7], AbsoluteThickness, Circle[{0, 0}, 12],
Inset[axes, {0, 0}, {0, 0}, ImageScaled,
Through[{Cos, Sin}[alpha]]]},
ImageSize -> 500, ImagePadding -> 20]

hth,

Peter

```

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