Improved antialiased mean reduction

[ianthomas23]

This improves the output of Canvas.line using an antialiased mean reduction.

Example code:

import datashader as ds
import numpy as np
import pandas as pd

x = np.asarray([0, 0.5, 1])
df = pd.DataFrame(dict(
    y0    = [0.0, 0.5, 1.0],
    y1    = [1.0, 0.0, 0.5],
    y2    = [0.0, 1.0, 0.2],
    value = [1.1, 2.2, 3.3],
))

canvas = ds.Canvas(plot_height=100, plot_width=150, x_range=(-0.1, 1.1), y_range=(-0.1, 1.1))
agg = canvas.line(source=df, x=x, y=["y0", "y1", "y2"], line_width=10, agg=ds.mean("value"), axis=1)
ds.transfer_functions.shade(agg, how="linear")

Image produced, before and after this PR:

and zoomed in by a factor of 3 (before and after):

Before this PR a mean reduction was implemented by dividing a sum reduction by a count reduction. If you imagine sum("value") where all the value are 1 then the sum and count produce identical results with larger values at the middle of lines and smaller antialiased values at the edges. Dividing one by the other therefore loses the antialiasing.

This PR changes the mean to be a sum divided by a new reduction _count_ignore_antialiasing and the latter, as the name suggests, ignores the antialiasing factor. Hence the result produced is antialiased.

It isn't actually quite that simple as at the edges of joins artifacts were produced where the line goes over itself. Pixels where this occurred are visited twice, the second time with a larger antialiasing factor. Now when this occurs both of the antialiasing factors are passed to Reduction.append functions so that the reduction can better deal with it. There is no change to the low-level antialiasing code which has always calculated both values, but now both values are used rather than just one.

[codecov]

Codecov Report

Merging #1300 (fd57632) into main (5eb4b22) will increase coverage by 0.01%.
Report is 4 commits behind head on main.
The diff coverage is 92.06%.

@@            Coverage Diff             @@
##             main    #1300      +/-   ##
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+ Coverage   85.64%   85.65%   +0.01%     
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  Files          52       52              
  Lines       11264    11288      +24     
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+ Hits         9647     9669      +22     
- Misses       1617     1619       +2     

[jbednar]

Looks great; thanks for following up on this!