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>

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