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MathGroup Archive 1994

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Re: Scale Transformations

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Scale Transformations
  • From: matteo at cns.nyu.edu (Matteo Carandini)
  • Date: Sat, 11 Jun 94 12:09:18 EDT

	Jean Peccoud writes:

> Does anybody know a package to modify the scales of 2D graphics. I would
> like to apply with other functions a transformation similar to the Log
> transformation in a LogLog or semiLog plot. My particular interest is in
> gaussian plots.

I have been using the following hack for a while, and it works fine. 
The nice thing about it is that you can build a Graphics object however you 
like (with Plot, ListPlot, Graphics, whatever), and only at the end play with 
the axes. Changing the axis scale of a graph is usually a snap on 
even the most pathetic piece of software, but not with Mma. 
I find it useful because often I want to see the same graphs on 
Linear and Log scales, and my graphs contain many functions, data points,
and error bars. So I find this little hack much more useful than most of 
Graphics.m (WRI, are you there?). You can use it to warp the axes with 
any transormation. I am too lazy to have it adjust the labels and the ticks, 
so there is plenty of room for improvement. Hope this helps,

-Matteo

					*
				Matteo Carandini	
				Center for Neural Science	
				New York University		
				6 Washington Place, #809	
				New York NY 10003	
				(212) 998 7898 (voice)
				(212) 995 4011 (fax)
				matteo at cns.nyu.edu
					*

P.S.
	I think that Mma is a GREAT environment to do science (and education),
so I am surprised at how bad it is at generating simple, 
publication-quality graphs. For example, in my last posting I showed how 
making a nice Bode plot is a headache. I received many letters of people
asking to post a solution. I don't have a solution! ask WRI.


(* ********************* super hack to warp the axes *********************** *)
(* ********************* (does not deserve a package) <********************** *)

<<Utilities/FilterOptions.m
 
Options[ WarpShow ]:= { XWarp->Identity, YWarp->Identity }

WarpShow[ graphics_Graphics, opts___ ]:= 
    Block[ 
	{ 	xwarp = XWarp /. {opts} /. Options[WarpShow], 
		ywarp = YWarp /. {opts} /. Options[WarpShow] },
	Show[
	    MapAt[ 
		( # /. { {x_?NumberQ,y_?NumberQ}->N[{xwarp[x],ywarp[y]}] } )&,
		graphics,
		1
		],
	    FilterOptions[ Graphics, opts ]
	    ]
	]

(* example:

mygraph = Plot[ x^2/(0.25+x^2), {x,0,1} ]
WarpShow[ mygraph ]
WarpShow[ mygraph, XWarp->Log ]
WarpShow[ mygraph, XWarp->(Log[2,#]&), YWarp->(Log[10,#]&) ]

bizarrewarp[ x_ ]:= Exp[ x^2 ]
WarpShow[ mygraph, XWarp->bizarrewarp, PlotRange->All ]
*)
(* *************************************************************** *)








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