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

*To*: mathgroup at smc.vnet.net*Subject*: [mg123121] Re: Aligning 2 Sets of Axes at {0,0}; Rotated & Standard Position*From*: Heike Gramberg <heike.gramberg at gmail.com>*Date*: Thu, 24 Nov 2011 06:54:33 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111231208.HAA15016@smc.vnet.net>

You could try something like this: a = 17; b = -48; c = 31; alpha = (ArcTan[b/(a - c)])/2; 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[axes, {Axis, Axis}, {Axis, Axis}, Automatic, RotationMatrix[-alpha]]] Heike. On 23 Nov 2011, at 13:08, Bill wrote: > 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 >

**References**:**Aligning 2 Sets of Axes at {0,0}; Rotated & Standard Position***From:*Bill <WDWNORWALK@aol.com>