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Re: parametric plot and filling

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  • Subject: [mg131546] Re: parametric plot and filling
  • From: W Craig Carter <ccarter at MIT.EDU>
  • Date: Fri, 23 Aug 2013 05:31:54 -0400 (EDT)
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  • References: <20130820113651.16A216A17@smc.vnet.net> <20130822045123.4269D6A0C@smc.vnet.net> <7334302B-45FD-478D-91FD-56DF876D6311@mit.edu> <E989DA8C-114A-424A-9423-AA6DD686B4E9@math.umass.edu>

Hello Murray---I agree. But, a perhaps a trick might be in finding a 
parameterization that does the particular filling that the user has in 
mind?  My first guess is that one would want ParametricPlot only to be 
able to fill when two curves are available, and then fill according to 
the positions corresponding to the same parameters.

(*My students always like this example...  If you try a Manipulate on 
this example---it gives puzzling results that I haven't tracked down 
yet; but are probably associated with the fast rendering not getting 
updated in the manipulate when a Mesh is rendered. *)

Cheers, Craig

W Craig Carter
Professor of Materials Science, MIT



On Aug 22, 13, at 11:10 AM, Murray Eisenberg wrote:

> Nice! But that doesn't answer my question as to what, _in general_ an 
option of Filling should do with arbitrary ParametricPlot output.
>
> On Aug 22, 2013, at 10:32 AM, W Craig Carter <ccarter at mit.edu> wrote:
>
>> Here is another way to get filling:
>>
>> OrbitOrbit[ r_, t_, n_] :=  { r Cos[n t ] + Cos[t], r  Sin[n t] + Sin[t]}
>>
>> ParametricPlot[OrbitOrbit[r, t, 6], {t, -Pi, Pi}, {r, .25, .9},
>> PlotStyle -> {Thick, Red}, Mesh -> False, PlotPoints -> 36,
>> ColorFunction -> (Hue[#3, 1, 1, 0.25] &)]
>>
>>
>>
>> W Craig Carter
>> Professor of Materials Science, MIT
>>
>>
>>
>> On Aug 22, 13, at 0:51 AM, Murray Eisenberg wrote:
>>
>>> Right, Filling is not a permissible option to ParametricPlot.
>>>
>>> But suppose Wolfram wanted to make it an option. What, exactly, do you
>>> propose it should do. For example, in what way would you expect a
>>> Filling option to work with each of the following?
>>>
>>> ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2 Pi}]
>>> ParametricPlot[{s, t}, {s, -2, 2}, {t, 1, 3}]
>>> ParametricPlot[{t, 2}, {x, -5, 5}]
>>> ParametricPlot[{t Sin[t], t Cos[t]}, {t, 0, 6 Pi}]
>>>
>>>
>>> On Aug 20, 2013, at 7:36 AM, Francisco Gutierrez
>>> <fgutiers2002 at yahoo.com> wrote:
>>>
>>>>
>>>> DoesParametricPlot admit the Filling option? Seems it not? How then to
>>> perform it?
>>>> Lokk at the following simple example:
>>>>
>>>> ParametricPlot[{{2 t,-t^2},{6+ 2 t,-t^2}},
>>> {t,-2,2},Axes->{True,False}, Ticks->None,
>>> PlotStyle->{{Thick,Cyan},{Thick,Green}}]
>>>>
>>>> The if I introduce the Filling command inside PlotStyle nothing
>>> happens, and outside it produces an error. Any ideas?
>>>> francisco
>>>
>>> ---
>>> Murray Eisenberg                                   
>>> murray at math.umass.edu
>>> Mathematics & Statistics Dept.     
>>> Lederle Graduate Research Tower          
>>> University of Massachusetts
>>> 710 North Pleasant Street 
>>> Amherst, MA 01003-9305
>>>
>>>
>>>
>>>
>>>
>>>
>
> ---
> Murray Eisenberg                                    
murray at math.umass.edu
> Mathematics & Statistics Dept.      
> Lederle Graduate Research Tower           
> University of Massachusetts 
> 710 North Pleasant Street  
> Amherst, MA 01003-9305
>
>
>
>
>




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