How to display label text outside plot range and enable PlotRangeClipping?

Question

I have been trying to modify a clipped graph by adding a text a label outside the frame, with no success so far.

Code for contour per request to get the rest of the code to run:

    ClearAll[Sbase, Vbase, Zbase, countour];
    Sbase = 50 10^3;
    Vbase = 240;
    Zbase = Vbase^2/Sbase;
    countour[M_, Zpu_, XR_] := 
        Circle[{M/Z Cos[\[Phi]], -M/Z Sin[\[Phi]]}, 1/Z] /. {Z -> Zpu Zbase, \[Phi] -> ArcTan[XR]}

This is my graph:

g1 = Graphics[
   Flatten[
    {Red,
     Table[countour[M, 0.02, 3], {M, 0.98, 1.02, 0.001}],
     Blue,
     Table[countour[M, 0.04, 1], {M, 0.98, 1.02, 0.001}]
     }
    ],
   Axes -> True, PlotRangeClipping -> True, AxesStyle -> Thick, 
   AxesLabel -> {x, y}, ImagePadding -> {{All, 50}, {All, All}}, 
   Frame -> True, PlotRange -> {{-0.3, 0.3}, {-0.3, 0.3}}];

The contour function just produces circles with differing centers and radii. I am zooming in close to the origin and clipping everything else to get this:

All is fine up to now, but I also want to add text labels outside the clipped frame. My successful trials, along with what I see suggested online(including StackExchange), hinge on setting PlotRangeClipping to False, for example as suggested here: "insert a text outside the frame".

That does not work for me, because when I try it I get:

ClearAll[g1, addLabel];
addLabel = Show[#,
    Epilog -> Text[#2, Scaled[{1.02, 0.7}], {-1, -1}],
    PlotRangeClipping -> False, 
    ImagePadding -> {{All, 50}, {All, All}}] &;
g1 = Graphics[
   Flatten[
    {Red,
     Table[countour[M, 0.02, 3], {M, 0.98, 1.02, 0.001}],
     Blue,
     Table[countour[M, 0.04, 1], {M, 0.98, 1.02, 0.001}]
     }
    ],
   Axes -> True, AxesStyle -> Thick, AxesLabel -> {x, y}, 
   Frame -> True, PlotRange -> {{-0.3, 0.3}, {-0.3, 0.3}}];
addLabel[g1, Style["M\[Equal]1", 16, Red]]

Which is not what I want at all. If I try to keep PlotRangeClipping as 'True` I lose the text label.

Any recommended workarounds ?

Answer 1

First, create a graphics object with your primitives, using the desired plot range, with clipping and no image padding:

g1 = Graphics[
    Flatten[{
        Red,
        Table[countour[M,0.02,3],{M,0.98,1.02,0.001}],
        Blue,
        Table[countour[M,0.04,1],{M,0.98,1.02,0.001}]
    }],
    PlotRangeClipping->True,
    ImagePadding->0,
    PlotRange->{{-0.3,0.3},{-0.3,0.3}}
];

Then, inset this graphics object into your graphic, along with the text labels and your overall axes/frame specifications:

Graphics[
    {
    Inset[g1, {0, 0}, {0, 0}, {.6, .6}],
    Text[Style["M\[Equal]1",16,Red],Scaled[{1.02,0.7}],{-1,-1}]
    },
    PlotRange -> {{-.3, .3}, {-.3, .3}},
    ImagePadding -> {{Automatic, 50}, {Automatic, Automatic}},
    Frame -> True,
    Axes -> True,
    AxesLabel -> {x,y},
    AxesStyle -> Thick
]

Answer 2

You can also clip the graphics primitives:

ClearAll[clip]
clip[prange_] := RegionIntersection[Rectangle @@ Transpose[prange], #] /. _EmptyRegion -> {} &;

Wrap your countour[...]s with clip[plotrange]

plotrange = {{-0.3, 0.3}, {-0.3, 0.3}};

g2 = Graphics[Flatten[{Red, 
     Table[clip[plotrange] @ countour[M, 0.02, 3], {M, 0.98, 1.02, 0.001}], 
     Blue, Table[clip[plotrange] @ countour[M, 0.04, 1], {M, 0.98, 1.02, 0.001}]}], 
   Axes -> True, AxesStyle -> Thick, 
   AxesLabel -> {x, y}, Frame -> True, PlotRange -> plotrange];

addLabel[g2, Style["M\[Equal]1", 16, Red]]

Caveat: This approach does not work with primitives like FilledCurve, BezierCurve, BSPlineCurve, and transformed primitives (e.g. primitives wrapped inside GeometricTransformation, Translate, Rotate, Scale etc.) which do not work with RegionIntersection.

Answer 3

I'm a little late to the party, but I find any time I'm forced to deal with PlotRangeClipping and ImagePadding things start to get janky. My preferred way of doing this via the Overlay[] function.

It's lightweight, fairly intuitive, and doesn't require moving all the labels out of your current plot.

(*Your Plot*)
ClearAll[Sbase, Vbase, Zbase, contour];

Sbase = 50 10^3;
Vbase = 240;
Zbase = Vbase^2/Sbase;
countour[M_, Zpu_, XR_] := 
 Circle[{M/Z Cos[\[Phi]], -M/Z Sin[\[Phi]]}, 
   1/Z] /. {Z -> Zpu Zbase, \[Phi] -> ArcTan[XR]}

g1 = Graphics[Flatten[{
     Red, Table[countour[M, 0.02, 3], {M, 0.98, 1.02, 0.001}],
     Blue, Table[countour[M, 0.04, 1], {M, 0.98, 1.02, 0.001}]
     }],
   Axes -> True,
   PlotRangeClipping -> True,
   AxesStyle -> Thick,
   AxesLabel -> {x, y},
   ImagePadding -> {{All, 50}, {All, All}},
   Frame -> True,
   PlotRange -> {{-0.3, 0.3}, {-0.3, 0.3}}];

(*My Overlay*)
Overlay[{
  g1,
  Style["M=1", Red, FontSize -> 20, FontFamily -> "Times"]},
 Alignment -> {0.95, 0.4}]

Which produces the following.

Alignment isn't explained super well in the Overlay documentation, so for those that need it:

Alignment->{-1,-1} is bottom left,

Alignment->{1,1} is top right,

Alignment->{0,0} is in the middle (not of the graph, but the entire graphic/plot).