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MathGroup Archive 1998

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Re: Reversing the axis of a plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15191] Re: Reversing the axis of a plot
  • From: Thomas Wachtler <thomas at NOSPAM.salk.edu>
  • Date: Fri, 18 Dec 1998 02:11:07 -0500
  • Organization: The Scripps Research Institute, La Jolla, CA
  • References: <757jb6$cm9$7@dragonfly.wolfram.com>
  • Sender: owner-wri-mathgroup at wolfram.com

 John,

 I had the same problem, and I tried to write a function that 
 would generate a reversed plot from a given Graphics object. 
 It turned out to be a pain, without knowing what goes on 
 inside Show[]. The result (see below) works in many cases, but 
 would have to be extended to account for all possible Options
 you might want to use.
 
 I think the only good solution to this can be to incorporate 
 this feature as a Graphics Option. I would appreciate comments 
 from the developers on the list as to whether anything like that 
 is intended for a future version.

  Thomas


(* Code for plots with reversed axis *) (* the basic idea is to map the
coordinate values of the graphics
   primitives as well as the Tick marks back to the same interval, 
   but in reversed order. *)

(* In order to get reversed Tick marks, I found it necessary to 
   modify the definition of TickFunction *) (* add the lines marked with
(**) to the code in `ExtendGraphics`Ticks *)

 Options[ TickFunction] =
    {
    MajorLength -> {0.00625, 0},
    MinorLength -> {0.003125, 0},
    MajorStyle -> {Thickness[0.002]},
    MinorStyle -> {Thickness[0.001]},
    TextFunction -> Automatic,
    TickLabels -> Automatic,
    TickNumbers -> {8, 32},
(**)    Reverse -> False
    }

 TickFunction[ x0_, x1_, opts___] :=
    Block[{maj, min, majlen, minlen, opt, tnums,
           majstyle, minstyle, textfun, labs (**)       , rev
        },
        opt = Join[ {opts}, Options[ TickFunction]] ;
        majlen = MajorLength /. opt ;
        minlen = MinorLength /. opt ;
        majstyle = MajorStyle /. opt ;
        minstyle = MinorStyle /. opt ;
        textfun = TextFunction /. opt ;
        labs = TickLabels /. opt ;
(**)       rev = Reverse /. opt ;
        tnums = CheckNumbers[ TickNumbers /. opt] ;
        If[ textfun === Automatic, textfun = TrimDecimal] ;
        maj = TickPosition[ x0, x1, First[ tnums]] ;
        min = TickPosition[ x0, x1, Last[ tnums]] ;
        min = Complement[ min, maj] ;
        maj = If[ MatrixQ[ labs],
                    Map[ {#, ""}&, maj],
                    Transpose[ {maj, textfun[ maj]}]] ;
        maj = Map[ {#[[1]], #[[2]], majlen, majstyle}&, maj] ;
        If[ Apply[ Plus, minlen] =!= 0,
                min = Map[ {#, "", minlen, minstyle}&, min] ;
        maj = Join[ maj, min]] ;
        If[ MatrixQ[ labs],
            maj = Join[ maj, Map[ Join[#, {{0,0}}]&, labs]]] ; (**)     
If[ NumberQ[ rev],
(**)        Map[ Join[ {rev - #[[1]]}, Drop[ #, 1]]&, maj ], 
        maj 
(**)       ]
    ]


(* functions to reverse Graphics primitives - extend for other
   primitive as needed *) 

LineReverseX[ lst_, xr_] := Line[Map[{xr-#[[1]], #[[2]]}&, lst]];
PointReverseX[ {x_,y_}, xr_] := Point[{xr-x,y}];


(* ShowReverseX reverses a plot along the x axis *)

ShowReverseX[ gr_Graphics, opts___] := Module[
 {xr,tcks,frmtcks,pltrng,axorig,tckfct,revrule,newgr},
 xr = Plus@@{Min[#],Max[#]}&[
   Join[Cases[Flatten[ gr[[1]]], _Line], Cases[Flatten[ gr[[1]]],
_Point]] /.
    {Line -> ((Transpose[#][[1]])&), Point -> ((#[[1]])&)}];
 tckfct[x_] := TickFunction[ #1, #2, Reverse->x ]&;
 tcks = Ticks /. Join[{opts}, gr[[2]]];
 If[ Length[tcks] < 2, tcks = {tcks,tcks}];
 tcks = {tckfct[xr], tcks[[2]]};
 pltrng = PlotRange /. Join[{opts}, gr[[2]]];
 If[Length[pltrng] == 2, pltrng = { xr-pltrng[[1]], pltrng[[2]] },
Null];
 axorig = AxesOrigin /. Join[{opts}, gr[[2]]];
 If[Length[axorig] == 2, axorig = {xr, 0} + {-1,1}*axorig, Null];
 Return[ Show[ Graphics[ gr[[1]] /.
  { Line -> (LineReverseX[#, xr]&), 
    Point -> (PointReverseX[#,xr]&) },
  Join[{Ticks->tcks, AxesOrigin->axorig,
PlotRange->pltrng},{opts},gr[[2]]]
 ]]];
];


(* Example: *)
(*
>>I want to reverse the x-axis of the
>>plot of 3x^2+5x+2.
*)

ShowReverseX[ Plot[ 3 x^2 + 5 x + 2, {x,1,5},
DisplayFunction->Identity],
   DisplayFunction->$DisplayFunction]



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