Add a hex tiling glyph

[birdsarah]

hex binning is useful (https://cran.r-project.org/web/packages/hexbin/vignettes/hexagon_binning.pdf) and I've seen a lot of cool hexmaps recently: http://www.theguardian.com/politics/ng-interactive/2016/jun/23/eu-referendum-live-results-and-analysis

[crashMOGWAI]

merge with #4342

[bryevdv]

Drawing a hex glyph would be trivial, I guess the interesting part is integrating a hex coordinate system reasonably.

[birdsarah]

Well if it was basically a marker (so it was just an x y center) then users could figure it out for now.

Sarah Bird
sbird@continuum.io

On Jul 12, 2016, at 2:55 PM, Bryan Van de Ven notifications@github.com wrote:

Drawing a hex glyph would be trivial, I guess the interesting part is integrating a hex coordinate system reasonably.

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[crashMOGWAI]

Would need to be more robust than a marker for feature rich binning visualizations

[bryevdv]

@birdsarah I'm -1 on adding a hard-to-use for things-people-really-want interface, and accumulating knowledge on here, SO and the mailing list that will only have to be updated/countered/deprecated later. Offhand, I think a Hex glyphs might have:

origin = Tuple # cartesian axis coords to "anchor" hex coord system, default (0,0)

size = Float # how big the hex tiles grid is (measured along diag?)

angle = Float # global rotation about origin for the hex grid (optional)

hx = DataSpec # "hex" x coords -- should be integer only 

hy = DataSpec # "hex" y coords -- should be integer only 

This is off the top of my head. We should compare to what other systems do. Whatever we do, I think there are the same/similar problems that e.g. circles have in non 1-1 coordinate systems.

[StevenCHowell]

Looking at the matplotlib and R implementation of hexbin, this seems like two separate issues:

1. Adding a hexagon marker than can be used for representing data points
2. Adding a hexagonal binning and plotting algorithm

The hexagonal binning and plotting algorithm could use hexagon markers/glyphs but this would likely lead to overlapping similar to issue #3315, in which histogram bars overlap. Also, it makes sense for the hexagon marker (point 1) to have a symmetric shape regardless of the plot aspect ratio. For binning and plotting data using a hexagonal grid, it would make sense to have non-symmetric hexagons which match the aspect ratio of the plot. See attached demo showing a zoomed in version of matplotlib's implementation.

[crashMOGWAI]

Agree with @stvn66. Looks like there are a couple of ideas bouncing around that could compliment each other as incremental development goals.

• hex glyph for data points/ markers
• 'respect aspect' mode for hex glyph (suggested by @brevdv in Glyph/Zoom Sanity Check #4802)
• hex binning and plotting algorithm/ multi-purpose mesh or grid feature

[StevenCHowell]

These examples from the D3 gallery show two options of visualizing a hexbin plot:

1. Color Encoding (used for the matplotlib implementation of hexbin)
2. Area Encoding

This second option may be more complicated to get the scaling of markers/glyphs to match the scaling of the plotting area when using different scaling for the x/y axes.

[StevenCHowell]

How much overlap is there between the bokehjs in rbokeh and python bokeh? I just saw that rbokeh has hexbin plots.

[bryevdv]

100% overlap, RBokeh uses the same BokehJS as-is. AFAIK (or have to assume) RBokeh supports hex charts by computing hexagon coordinates in R and drawing as Patches

[hafen]

That's correct.

[bryevdv]

This is obviously an old discussion but I'm interested in reviving it. I think there are two separate things, both worth doing:

• a Hex marker, that is just an x,y,size, angle scatter marker. This should pretty trivial, ref previous work: Stvn66 4786 hex markers #4827

• HexTileglyph that draws non-overlapping hex tiles in a hex tile coordinate system.

[bryevdv]

I've made #7638 to describe the marker, this issue can be for the hex tiling glyph

[bryevdv]

PR coming tomorrow

[birdsarah]

That's very exciting

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[bryevdv]

@birdsarah do you know how the larger outlined regions in your original example are specified? I could imagine a couple of possible ways to spell that but not sure if there is a standard way

[tritemio]

In matplotlib the X-Y span is a rectangular range that is the range of the data or the regione defined by the extent keyword. Then, the keyword mincnts allows choosing a minimum count per bin for visible bins. Choosing mincnts=1, shows only bins with at least one count. The result is similar to your example. With mincnts=0 (default), hex tiles will cover a rectangular region.

[bryevdv]

@tritemio this work is not concerned with binning, and it's not clear that core bokeh itself will have any binning built in. This PR adds a basic glyph for drawing regular (data-space) hex tiles in an axial coordinate system. This is the foundation upon which a "hexbin" command might be built (e.g. by Holoviews)

For reference, the above image was generated by hand with this code:

np.random.seed(0)
n = 10000
x = 2 + 3*np.random.standard_normal(n)
y = 2 + 3*np.random.standard_normal(n)

size=0.5

x = (x - size) / (2*size);

t1 = y / size
t2 = np.floor(x + t1)
r = np.floor((np.floor(t1 - x) + t2) / 3)
q = np.floor((np.floor(2 * x + 1) + t2) / 3) - r

df = pd.DataFrame(dict(r=r.astype(int), q=q.astype(int)))
bins = df.groupby(['q', 'r']).size().reset_index(name='counts')

plot = figure(title=None, match_aspect=True, tools="hover")

source = ColumnDataSource(data=dict(
    q=bins.q,
    r=bins.r,
    c=bins.counts
))

plot.hex_tile(q="q", r="r", size=size, 
              fill_color=linear_cmap('c', Viridis256, 0, max(bins.counts)),
              line_color=None, source=source)

[tritemio]

I see, thanks for the clarification. So this is actually a rectangular binning plotted with contiguous hex tiles. Sorry if OT, any idea or references on how to compute (not plot) the actual hex binning?

[bryevdv]

So this is actually a rectangular binning plotted with contiguous hex tiles.

No, that is not correct, the example code above is doing a real hex binning. The block of the code with floor computes the axial (q,r) integer hex coordinate of the hexagon that contains each point, then a pandas groupby bins over each (q,r) coordinate pair.

[tritemio]

Ops, thanks for the correction. I'll look into it more carefully!

[bryevdv]

@tritemio just as an update, I don't think that opaque code with floors is correctly doing a hex binning, at least not for the version of axial coords I am using. So we are looking to find or implement something a bit more straightforward and comprehensible

[bryevdv]

PR is merged with API docs and some examples. User's Guide docs coming in a separate PR.