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Groups > comp.soft-sys.math.mathematica > #2055

Re: Huge file for a several-line plot

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I think the problem is that you're varying both s and t for each of the curves. Since
the curves either depend on s or on t but not both you're effectively plotting at least
PlotPoints copies of the same set of curves on top of each other. To correct this you could plot
the curves for s is constant and t is constant separately and then combine them with Show:

Show[{ParametricPlot[
   Table[xy[i/4, t], {i, 1, 10}] /. w -> 1, {t, -Pi, Pi},
   PlotPoints -> 30],
  ParametricPlot[
   Table[xy[s, \[Pi]/6*j], {j, 0, 11}] /. w -> 1, {s, 0, 10},
   PlotPoints -> 30]}, PlotRange -> {{0, 4.2}, {-2, 2}}]

On my machine that produces a file of 184 kB.

Heike.

  

On 2 May 2011, at 18:23, Dushan Mitrovich wrote:

> Heike Gramberg wrote:
>> How are you plotting the graphs? If I use the following:
>>
>> pt[s_, t_] := CoordinatesToCartesian[{s, t, 0}, Bipolar][[{1, 2}]]
>>
>> ParametricPlot[pt[s, t], {s, 0, 2 Pi}, {t, -5, 5},
>>  PlotRange ->  {{-10, 10}, {-8, 8}}, Mesh ->  22,
>>  PlotStyle ->  Opacity[0], MeshStyle ->  Darker[Gray],
>>  PlotPoints ->  100, ImageSize ->  600]
>>
>> I end up with a file of about 631 kB on Mathematica 8.0.1 for OS X.
>>
>> Heike
>>  
>
> That size is a lot more reasonable, especially for a much larger value of
> 'PlotPoints' than I used.
>
> Here are the instructions I used (the first two could be lumped into one):
>
>    {x[s_, t_], y[s_, t_]} := {(w Sinh[s])/(Cosh[s] + Cos[t]),
>      (w Sin[t])/(Cosh[s] + Cos[t])}
>
>    xy[s_, t_] := {x[s, t], y[s, t]}
>
>    ParametricPlot[{Table[xy[i/4, t], {i, 1, 10}] /. w->1,
>      Table[xy[s, \[Pi]/6*j], {j, 0, 11}] /. w -> 1}, {s, 0., 10},
>      {t, -\[Pi], \[Pi]}, PlotRange -> {{0, 4.2}, {-2, 2}}, PlotPoints -> 30]
>
> Comparing with your sample instructions above, I didn't recognize anything
> as a crucial difference.  Suggestions?
>
> - Dushan
>
>> On 2 May 2011, at 11:51, Dushan Mitrovich wrote:
>>  
>>> I wanted to plot a number of the orthogonal coordinate lines of a
>>> Bi-polar coordinate system - a total of 22 curves.  All the curves
>>> are circles.  With PlotPoints unspecified, some of the circles had
>>> polygonal parts, so to eliminate this I added the option PlotPoints->50.
>>>  That took a long time to plot (on a 4-CPU Mac Pro),
>>> and generated a notebook size of 10.5 MB.  (Using PlotPoints->30 drops
>>> the size to 4.5 MB.)
>>>
>>> With that plot cell deleted the size is 53 KB.  The file labels
>>> the graphic as 'CompressedData', but there simply isn't that much
>>> information in the plot.  It's as tho Mathematica were storing every
>>> pixel of the plot, with very inefficient compression.
>>>
>>> With that plot the spinning beachball (computer busy) would appear
>>> every few seconds, and it was impossible to alter the graphic size.
>>>
>>> How can I instruct Mathematica to make more sensible choices for
>>> generating and storing the plot?
>>>
>>> - Dushan
>>>   [ reverse the middle word of address to reply ]
>>>
>>>    
>>
>>
>>  
>

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Re: Huge file for a several-line plot Heike Gramberg <heike.gramberg@gmail.com> - 2011-05-03 09:46 +0000

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