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ImplicitPlot options (undocumented)

  • To: mathgroup at
  • Subject: [mg14573] ImplicitPlot options (undocumented)
  • From: "Ersek, Ted R" <ErsekTR at>
  • Date: Fri, 30 Oct 1998 03:07:42 -0500
  • Sender: owner-wri-mathgroup at

I wrote:
>Recent messages under the subject "shading implicit plot" discussed the
>use of the option ColorFunction with the ImplicitPlot package.  I was
>surprised ImplicitPlot uses the ColorFunction option because it isn't
>included in the list returned by  Options[ImplicitPlot].>
>After studying the code for the package and doing some investigating I
>found other options ImplicitPlot can use.  In particular ImplicitPlot
>will take the options ColorFunction, Compiled, ContourLines,
>ContourShading, ContourStyle, FormatType, ImageSize, and TextStyle even
>though they aren't returned by Options[ImplicitPlot].  Use of each of
>these options except Compiled is demonstrated below.
Several people replied with something like:

>The on-line documentation for Graphics`ImplicitPlot` states that 
>"Both methods can accept standard graphics options; the Solve method
>accepts the options of Plot, while the ContourPlot method accepts
>ContourPlot options."
>Options[ContourPlot] lists all of the options that you have listed.

OK I missed that, but 
PlotDivision and MaxBend are options used by Plot, but they are not
recognized by ImplicitPlot (contrary to what the documentation
suggests). Go ahead and try it.  Also you can look at the code for
ImplicitPlot and I think you will see the solve method uses
Options[Graphics]. ____________________

Either way I think all options recognized by ImplicitPlot should be
returned by Options[ImplicitPlot].  So I went into the ImplicitPlot
package and added the appropriate options where the package defines
Options[ImplicitPlot].  On my computer the code now reads.

Options[ImplicitPlot] =
  {AspectRatio -> Automatic, Axes -> Automatic, AxesLabel -> None,
  AxesOrigin -> Automatic, AxesStyle -> Automatic, 
  Background -> Automatic, ColorFunction -> Automatic, 
  ColorOutput -> Automatic, Compiled->True, ContourLines -> True, 
  ContourShading -> False, ContourStyle -> Automatic,
  DefaultColor -> Automatic, Epilog -> {}, FormatType:>$FormatType, 
  Frame -> False, FrameLabel -> None, FrameStyle -> Automatic, 
  FrameTicks -> Automatic, GridLines -> None, ImageSize-> Automatic, 
  PlotLabel -> None, PlotPoints -> 25, PlotRange -> Automatic, 
  PlotRegion -> Automatic, PlotStyle -> Automatic, Prolog -> {}, 
  RotateLabel -> True, TextStyle:>$TextStyle, Ticks -> Automatic, 
  DefaultFont :> $DefaultFont, DisplayFunction :> $DisplayFunction}

After I evaluate In[2] below I see that having options such as
ContourShading included in ImplicitPlot[Options] doesn't interfere with
proper performance when ImplicitPlot uses the Solve method.


(* Graphic not shown *)

Now that ContourLines, ContourStyle, etc. are included in
Options[ImplicitPlot] there is less confusion about what options are
supported by ImplicitPlot.  At In[3] I change the default setting of
ContourStyle, and I see it takes effect at In[4].  When ContourStyle
wasn't included in Options[ImplicitPlot] I couldn't use the line at


ImplicitPlot[x^3 - x^2 == y^2 - y,{x,-1,2},{y,-2,2}]; (* Graphic not
shown *)

I evaluate In[5] and I see the default setting of ContourStyle for
ImplicitPlot and ContourPlot are independent.  I think that's a good

ContourPlot[Sin[x y],{x,-2,2},{y,-2,2},ContourShading->False]; (*
Graphic not shown *)

Now the next thing is annoying. In a line above I evaluated
SetOptions[ImplicitPlot,ContourStyle->Thickness[0.01]]; This has no
effect when ImplicitPlot uses the solve method.  For that I have to use
the PlotStyle option.  Bottom line, ImplicitPlot has two options for
the same thing (ContourStyle, PlotStyle).


Ted Ersek

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