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Re: RE: GridPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg45917] Re: [mg45869] RE: [mg45795] GridPlot
• From: Selwyn Hollis <sh2.7183 at misspelled.erthlink.net>
• Date: Thu, 29 Jan 2004 05:36:36 -0500 (EST)
• References: <200401281019.FAA18467@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Harmut,

Thank you. Your approach is definitely an improvement over my clumsy 
hack.  :-)

Cheers,

Selwyn



On Jan 28, 2004, at 5:19 AM, Wolf, Hartmut wrote:

>
>> -----Original Message-----
>> From: Selwyn Hollis [mailto:sh2.7183 at misspelled.erthlink.net]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
>> Sent: Sunday, January 25, 2004 9:05 AM
>> To: mathgroup at smc.vnet.net
>> Subject: [mg45917] [mg45869] [mg45795] GridPlot
>>
>>
>> I've never much liked the way the GridLines option works in Plot. So
>> for my own amusement I decided to try something different, and it
>> turned into a nice exercise, I think. I thought some of you might be
>> interested in the result, which is the following (rough)
>> function named
>> GridPlot. What it basically does is stretch automatically-generated
>> tickmarks out to form grid lines. (The GridColor option lets you can
>> change their color.)
>>
>>
>> GridPlot[f_, {x_, xmin_, xmax_}, opts___] :=
>>  Module[{a, b, c, d, grph, fullgrph, gridcolor},
>>    	gridcolor = GridColor /. {opts} /.
>> 		{GridColor -> GrayLevel[0.85]};
>>     fullgrph = FullGraphics[grph = Plot[f, {x, xmin, xmax},
>> 		DisplayFunction -> Identity,
>> 		Evaluate[DeleteCases[{opts},GridColor->_]]]];
>>     {{a, b}, {c, d}} = PlotRange /. AbsoluteOptions[grph];
>>     Show[ fullgrph /.{
>> 	  {GrayLevel[0.], AbsoluteThickness[t_],
>> 		 Line[{{u_,y1_},{u_,y2_}}]}/; (y2-y1<d-c) ->
>>        {gridcolor, AbsoluteThickness[t], Line[{{u,c},{u,d}}]},
>> 	  {GrayLevel[0.], AbsoluteThickness[t_],
>> 		Line[{{x1_,y_},{x2_,y_}}]}/; (x2-x1<b-a) ->
>>         {gridcolor, AbsoluteThickness[t], Line[{{a,y},{b,y}}]}
>> 			},
>>        grph, PlotRange -> {{a,b},{c,d}}, Axes -> True] ]
>>
>> GridPlot[{1/x, Cos[x], Sin[x]}, {x, 0, 2Pi}]
>>
>>
>>
>> Regards,
>> -----
>> Selwyn Hollis
>> http://www.math.armstrong.edu/faculty/hollis
>> (edit reply-to to reply)
>>
>
> Selwyn,
>
> as you declare this as a programming exercise I'm free to make 
> comments and
> to propose an alternative.
>
> First, I agree that the Plot options in general, and for the GridLines 
> in
> particular are not easy to master.  If this constitutes a problem for 
> the
> (not so experienced) users of your code, your students e.g., it appears
> appropriate to supply a more convenient interface.
>
> My own private attitude is different however: try to understand -- 
> albeight
> this might cost some effort -- the basics (as is part of core 
> Mathematica)
> precisely.  This avoids irritations if something goes wrong: I then 
> simply
> have one interface _less_ to struggle with. The point may be simply
> illustrated by
>
> GridPlot[{1/x, Cos[x], Sin[x]}, {x, 0, 2Pi}, AspectRatio -> Automatic]
>
> against
>
> Plot[{1/x, Cos[x], Sin[x]}, {x, 0, 2Pi}, AspectRatio -> Automatic,
>   GridLines -> ({Thread[{Range[.2, 6.4, .2], xStyle}],
>           Thread[{Range[-1., 4., .2], yStyle}]} /. {xStyle |
>               yStyle -> {GrayLevel[.85]}})]
>
> I would not say that the GridLines option was overly complex (but 
> might need
> some trial and error).
>
>
> As you see, your proposed GridPlot looses the option AspectRatio, e.g. 
> There
> are other minor points of passing the options, which you can read off 
> my
> alternative example (coming below soon). Obviously you had to struggle 
> to
> get at the Ticks to make your gridlines from. The solution appears to 
> be
> delicate. Drawing the gridlines as primitives (instead of options to 
> Show)
> forces you to draw the graphics twice (which redundantly blows up the
> Graphics objects). Finally everything is dedicated to Plot.
>
>
>
> Here I propose a different solution, namely wrapper code which is 
> thought to
> cooperate with more (all?) plot functions. I also define the default
> coloring of the grid as a default option.
>
> Needs["Utilities`FilterOptions`"]
>
> Options[makeGrid] = {GridStyle -> GrayLevel[0.85]};
>
> Attributes[makeGrid] = HoldAll;
>
> makeGrid[plotfcn_[args__, opts___?OptionQ]] := Module[{grph, 
> gridstyle},
>
>     gridstyle = Flatten[{GridStyle /. Flatten[{opts}] /.
> Options[makeGrid]}];
>
>     grph =
>       Block[{$DisplayFunction = Identity},
>         With[{plotopts = FilterOptions[plotfcn, opts]},
>           plotfcn[args, plotopts]]];
>
>     Show[grph,
>       GridLines ->
>           Take[If[Frame /. Options[grph, Frame], FrameTicks, Ticks] /.
>               FullOptions[grph], 2] /. {pos_, _, _, _} :> {pos, 
> gridstyle},
>       FilterOptions[Graphics, opts]]]
>
>
> As you see, I extract the grid positions from the FrameTicks or Ticks 
> via
> the standard (stable?) interface. I also allow to specify more than one
> graphical directive for the grid lines.
>
>
> Examples of usage:
>
> Needs["Graphics`Graphics`"]
>
> Plot[{1/x, Cos[x], Sin[x]}, {x, 0, 2Pi},
>     GridStyle -> {Hue[0, .2, 1], Thickness[.01]},
>     AspectRatio -> Automatic] // makeGrid
>
> pp = LogLogPlot[Exp[2x/Pi + Sin[x]], {x, 0., 6}] // makeGrid
>
> PolarPlot[{4/(2 + Cos[t]), 4 Cos[t] - 2}, {t, 0, 2 Pi},
>     AspectRatio -> Automatic, Frame -> True,
>     PlotStyle -> {Hue[2/3], Hue[0]}] // makeGrid
>
>
> So you just add the new GridStyle option to the other plotting options 
>  and
> wrap with makeGrid.
>
>
> A warning in place: this is just a coding example, *not* released 
> production
> code. It should be put into a package first, then its should defend 
> against
> misuse (with not a plot function), and this must be done in a way as 
> not to
> introduce problems with the sequence of loading graphical packages. 
> Another
> point of weakness is the grabbing of the frame ticks. I simply take 
> them
> from the bottom and the left; but there might be none there. It's 
> however
> not difficult to solve this ("I leave it as an exercise"), and similar
> cases. Then you must go through extensive testing, of course -- but I 
> will
> not do this work, that is beyond a post to the newsgroup.
>
> Perhaps the best way would be to incorporate this into the
> Graphics`Graphics` package (which then also would supply the necessary
> extension for Plot), and leave the function makeGrid invisible to the 
> user
> (everthing would be directed by the option then). However, this should 
> be
> released from WRI, I myself would never do that, in order to keep my 
> code
> compatible with the "mainstream".
>
> Kind regards, yours,
> Hartmut
>
>

• References:
  • RE: GridPlot
    • From: "Wolf, Hartmut" <Hartmut.Wolf@t-systems.com>