Re: [matplotlib-devel] path simplification can decrease the smoothness of data plots

[Michael D. <md...@st...>]

Michael Droettboom wrote:
> Andrew Hawryluk wrote:
>   
>> I’m really excited about the new path simplification option for vector 
>> output formats. I tried it the first time yesterday and reduced a PDF 
>> from 231 kB to 47 kB. Thanks very much for providing this feature!
>>
>> However, I have noticed that the simplified paths often look more 
>> jagged than the original, at least for my data. I can recreate the 
>> effect with the following:
>>
>> [start]
>>
>> import numpy as np
>>
>> import matplotlib.pyplot as plt
>>
>> x = np.arange(-3,3,0.001)
>>
>> y = np.exp(-x**2) + np.random.normal(scale=0.001,size=x.size)
>>
>> plt.plot(x,y)
>>
>> plt.savefig('test.png')
>>
>> plt.savefig('test.pdf')
>>
>> [end]
>>
>> A sample output is attached, and close inspection shows that the PNG 
>> is a smooth curve with a small amount of noise while the PDF version 
>> has very noticeable changes in direction from one line segment to the 
>> next.
>>
>> <<test.png>> <<test.pdf>>
>>
>> The simplification algorithm (agg_py_path_iterator.h) does the following:
>>
>> If line2 is nearly parallel to line1, add the parallel component to 
>> the length of line1, leaving it direction unchanged
>>
>> which results in a new data point, not contained in the original data. 
>> Line1 will continue to be lengthened until it has deviated from the 
>> data curve enough that the next true data point is considered 
>> non-parallel. The cycle then continues. The result is a line that 
>> wanders around the data curve, and only the first point is guaranteed 
>> to have existed in the original data set.
>>
>> Instead, could the simplification algorithm do:
>>
>> If line2 is nearly parallel to line1, combine them by removing the 
>> common point, leaving a single line where both end points existed in 
>> the original data
>>     
I've attached a patch that will only include points from the original 
data in the simplified path.  I hesitate to commit it to SVN, as these 
things are very hard to get right -- and just because it appears to work 
better on this data doesn't mean it doesn't create a regression on 
something else... ;)  That said, it would be nice to confirm that this 
solution works, because it has the added benefit of being a little 
simpler computationally.  Be sure to blitz your build directory when 
testing the patch -- distutils won't pick it up as a dependency.

I've attached two PDFs -- one with the original (current trunk) 
behavior, and one with the new behavior.  I plotted the unsimplified 
plot in thick blue behind the simplified plot in green, so you can see 
how much deviation there is between the original data and the simplified 
line (you'll want to zoom way in with your PDF viewer to see it.)

I've also included a new version of your test script which detects "new" 
data values in the simplified path, and also seeds the random number 
generator so that results are comparable.  I also set the 
solid_joinstyle to "round", as it makes the wiggliness less pronounced.  
(There was another thread on this list recently about making that the 
default setting).

Cheers,
Mike

-- 
Michael Droettboom
Science Software Branch
Operations and Engineering Division
Space Telescope Science Institute
Operated by AURA for NASA