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Topic: parametric plot and filling
Replies: 9   Last Post: Aug 23, 2013 4:56 AM

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W. Craig Carter

Posts: 265
Registered: 9/10/05
Re: parametric plot and filling
Posted: Aug 23, 2013 4:56 AM
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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@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@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@math.umass.edu
>>> Mathematics & Statistics Dept.
>>> Lederle Graduate Research Tower
>>> University of Massachusetts
>>> 710 North Pleasant Street
>>> Amherst, MA 01003-9305
>>>
>>>
>>>
>>>
>>>
>>>

>
> ---
> Murray Eisenberg

murray@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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