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Re: Not Plotting Vertical Assymptotes

• To: mathgroup at smc.vnet.net
• Subject: [mg18930] Re: Not Plotting Vertical Assymptotes
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Tue, 27 Jul 1999 22:17:29 -0400
• References: <7m6ivl$2l5@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Patrick McLean <p_mclean at postoffice.utas.edu.au> wrote in message
news:7m6ivl$2l5 at smc.vnet.net...
> Anyone have any idea how to stop Plot putting a (near) vertical line at
> x=2 in the command:
>
>       Plot[1/(1-x),{x,0,2}]
>
> ie. detect that the function 1/(1-x) has a singularity at x=2 and do
> something about it. This is analagous to numerically integrating over a
> (integrable) singularity, where the following remedy works:
>
>       NIntegrate[1/Abs[Sqrt[x-1]]^2,{x,0,1,2}]
>
> But in this case it doesn't work. Decreasing MaxBend works a bit but the
> line is still there.
>
> (I am really interested in drawing paths in the plane using ParmetricPlot)
>
> Any ideas or comments
>
> --
> Patrick McLean
>
> No news is good news...

Patrick

Here is a way: more work will be needed with ParametricPlot

Using Split we can write a function that operates on Graphics objects and
splits lines at points where the absolute slope gets big,

 DeleteVerticals[gr_Graphics, slopeMax_] :=
 gr /. Line[lst_] :>
        Map[Line,
       Split[lst, Abs[Divide @@ Reverse[#1 - #2]] < slopeMax &],
          1];

Test: some experimentiation to get the right value for slopeMax may be
needed.

Show[DeleteVerticals[Plot[1/(1-x),{x,0,2}]
, 20000]]

Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565