Combine absolute and relative (scaled) coordinates

Question

I am using Inset to add an Epilog to a plot. The position of the images (in my case: framed numbers) can be specified as an option of Inset.

I would like the y-coordinate to be the same for all Inset elements (they are created via Table), relative to the plot size. Say, for example, it should be the y-coordinate of Scaled[*,0.9]. The x-coordinate should, for each element, be an absolute value, depending on its position in the table.

While I know how to specify relative and absolute coordinates, also as functions of the table position, I can't get Scaled to work for only one coordinate: specifying my Inset coordinates via something like

{*abs. value*, Scaled[.9]}

yields the following error message:

Coordinate {*abs. value*, Scaled[0.9]} should be a pair of numbers, or a Scaled or Offset form.

Any help on this?

---

Update: I also tried snippets like Scaled[*some value*,.9][[2]] to extract the y-coordinate, but to no avail.

Answer 1

Great question, to which I would like to know the answer myself, other than manual scaling as mentioned by J. M.

---

A partial solution is to use the second parameter of Scaled. Here I place a point at y scaled 1/2, and x plot coordinate 9. Note that y origin 5 must be known:

Graphics[{
  AbsolutePointSize[25],
  Point @ Scaled[{0, 1/2}, {9, 5}]
  },
 PlotRange -> {{5, 10}, {5, 10}},
 Frame -> True,
 GridLines -> Automatic
]

---

Another limited method I am aware of uses Offset, but that specifies position in printer's points rather than plot coordinates (resize the graphic to see the result of that):

Graphics[{
  AbsolutePointSize[25],
  Point @ Offset[{75, 0}, Scaled[{0, 1/2}]]
  },
 PlotRange -> {{5, 10}, {5, 10}},
 Frame -> True
]

Answer 2

Following method does not require any knowledge about PlotRange because MMA knows it. :)

This function is not pretty, I suspect it will crush sometimes due to it's naive form. Report me then :)

However, it works and You can DumpSave it if You don't want to look at it. :)

 MixedCoordinates[plot_] := Composition[
  ReplaceAll[#[[1]], {
   {x_?NumericQ, Scaled@y_?NumericQ} :> {x, (#1 + Abs[#1 - #2] y) & @@ #[[2, 1, 2]]},
   {Scaled@x_?NumericQ, y_?NumericQ} :> {(#1 + Abs[#1 - #2] x) & @@ #[[2, 1, 1]], y}
  }] &,
 {#[[1]], Cases[#[[2]], x : Rule[PlotRange, _] :> x[[2]]]} &,
 {#, AbsoluteOptions@#} &
 ][plot]

Lets test it. This two Shows have the same content, except of second argument, Plot with different domain.

MixedCoordinates@Show[
    ListPlot[{{-.5, .5}, {.5, 2}}, PlotStyle -> Directive@AbsolutePointSize@12],
    Plot[x, {x, ##}],
    Graphics[{AbsolutePointSize@12, Blue, Point[{{.5, .5}}],
              Red, Point[{{Scaled@1, .2}}]}]
    ,
    PlotLabel -> Style["Red points have mixed coordinates", Bold, 15],
    PlotRange -> All, AspectRatio -> Automatic, AxesOrigin -> {0, 0},
    Frame -> True, Epilog -> {AbsolutePointSize@12, Red, Point[{{.4, [email protected]}}]},
    ImageSize -> 400, GridLines -> Automatic, BaseStyle -> Thick
] & @@@ {{-1, 1}, {-2, 2}}

Possible issues:

• PlotRange->All seems to be necessary at the end od Show
• If You want to put Epilog somewhere, it has to be either in Show or in it's first argument. Why? Because Show takes options from it's first argument and other's arguments options are not exposed.

Short description:

MixedCoordinates@[] is taking information from PlotRange given by AbsoluteOptions. And then, with this information it is rescaling elements Scaled[_]

---

I do not consider it is finished, but it could be a good start. Looking forward for Your remarks.

Answer 3

Late answer.. I thought some might find this useful:

I had a need to also use the plot aspect ratio, so develeped this variation on @kuba's answer..

 ctransform = Module[{plotrange, plotratio, aspect},
         plotrange = Last@Cases[ AbsoluteOptions[#] , 
                          x : Rule[PlotRange, _] :> x[[2]]];
         aspect =  Last@Cases[ AbsoluteOptions[#] , 
                         x : Rule[AspectRatio, _] :> x[[2]]];
         plotratio = Divide @@ (Subtract @@ # & /@ plotrange);
         ReplaceAll[#, {
       scaleratio -> 1/plotratio/aspect,
       scalev[i_, x_] :> plotrange[[i, 1]] (1 - x) + plotrange[[i, 2]] (x)}]] &;

ctransform@
  Show[{
      Plot[ x^2 + 5, {x, 1, 5}, PlotStyle -> Thick,   PlotRange -> {{0, 6}, {0, 30}}], 
      Graphics[ Table[Circle[{i,   scalev[2, .1] + .1 i scaleratio}, 
            .1 i {1, scaleratio}], {i, 1,  5}]]},   AspectRatio -> 1/GoldenRatio, 
      PlotRange -> {{0, 6}, {0, 30}}]

Note I'm not using the bultin Scaled at all, so there is no conflict issue if yuo needed to use that for something as well.

You could also do this with Composition, but it gets a bit unwieldy

Answer 4

This is not exactly what you asked for, but it will work in many situations, although not in v6 :/

insets = Table[Framed[i], {i, 0, 9}];

plot = Plot[Sin[x], {x, -1, 10},
  Epilog -> MapIndexed[
             Translate[Inset[#1, {0, Top}, Scaled[{0.5, 1.5}]], {First@#2 - 1, 0}] &, 
             insets]
  ]

Combining with other plots, the insets move up automatically:

Show[plot, Plot[2 Cos[x], {x, -2, 8}], PlotRange -> All]

Now the above works well if the insets all have the same vertical size. If not, one can use Pane:

SeedRandom[1];
insets2 = Table[Framed[Style[i, RandomInteger[20, 40]]], {i, 0, 9}];
vsize = Max[Rasterize[#, "RasterSize"] & /@ insets2];

Plot[Sin[x], {x, -1, 10},
 Epilog -> 
  MapIndexed[
   Translate[Inset[#1, {0, Top}, Scaled[{0.5, 1.5}]], {First@#2 - 1, 0}] &, 
   Pane[#, {Automatic, vsize}, Alignment -> Center] & /@ insets2]]

The main way it fails to do exactly what the OP asks is that the vertical offset is relative to the (max) size of the insets, not relative to the size of the graphics.