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Re: Labelling each curve and changing grid in ParametricPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg129651] Re: Labelling each curve and changing grid in ParametricPlot
• From: Themis Matsoukas <tmatsoukas at me.com>
• Date: Sun, 3 Feb 2013 02:44:22 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net

Here is one way to label the curves:

plot[\[Tau]_, \[CapitalOmega]_] := 
 Module[{arg, abs}, {arg, abs} = 
   Through[{Arg, 
      Abs}[(1 + I*2*\[CapitalOmega])/(1 + 
        I*2*\[Tau]*\[CapitalOmega])]];
  {arg/Degree, 20*Log10[abs]}]

\[Tau]list = {7, 8, 9, 10, 11, 12, 13, 14, 15};

txtlist = 
  Table[plot[\[Tau], \[CapitalOmega]], {\[Tau], \[Tau]list}] /. \
\[CapitalOmega] -> -0.52;

Show[ParametricPlot[
  Table[plot[\[Tau], \[CapitalOmega]], {\[Tau], \[Tau]list}], {\
\[CapitalOmega], -0.5, -0.01}, AspectRatio -> 1, 
  GridLines -> Automatic, GridLinesStyle -> Dashed, 
  ImageSize -> Large], 
 Graphics[Table[
   Text[\[Tau]list[[ii]], txtlist[[ii]]], {ii, 
    1, \[Tau]list // Length}]]]

I am not sure what exactly you want to do with the grid but you can specify your own regular or irregular grid using the option GridLines. See the examples in documentation. 

Themis