First attempt at histogram3d/legoplot

[briederer]

As already mentioned in #3379 I wanted to add a histogram3d() function for plotting.
Therefore I took over the ides from the issue and translated it in a recipe, however now I am a bit stuck.

The main problems + possible solutions are:

1. wireframe is not reliable across the different backends (very different behaviours) so I switched to surface
2. surface does not provide a mesh option (like surface + wireframe) and so one does not get a lot of information from the plots.
   • solution 1: adding all the lines manually? may be very resource intensive
   • solution 2: Adding a wireframe? does not provide the correct overlay properties depending on the backend
3. color: Should it be one color like it is done for usual histograms or would it be nicer to have colored bars depending on their height (like a heatmap not seen from above)?
4. Additionally I wanted to add the same possibility as in 2d-histograms to use the attribute show_empty_bins which turned out to be really hard. Especially the plotly() backend seems to have a lot of trouble with a mixture of NaN and numeric-values at the same x-y position.
   • Additionally this needs the _allneighbours function which checks if all neighbours in a matrix are the same value, which I need to set the NaN-values for the plot. I really dislike this function a lot but I couldn't wrap my head around another idea to resolve this

Figures

All plots are created by

x=rand(100)
y=rand(100)
histogram3d(x,y,bins=(10,10),camera=(20,60),xlabel="x")

GR

One-coloured surface plot

• Good: Shows bins as expected
• Bad: Not very useful without lines at the edges (Problem 2 from above)
  

Multi-coloured surface plot

• Good: Shows bins as expected, able to separate different bins by color
• Bad: Color gradient messes here with the plot, would be better to have one fixed color for each bar instead of a gradient (How to resolve this?)
  

Single-coloured surface + wireframe plot

Not possible with the current solution, wince wireframe in GR needs x and y values in ascending (i.e. repeated values are forbidden). Therefore one would need again the workaround with repeateps() in #3379 which I have discarded for now.

Plotly

One-coloured surface plot

• Good: Bins separable by eye due to automatic shadows in plotly
• Bad: lines at the edges would still be helpful (Problem 2 from above), NaN-values are not completely correct rendered as can be seen at for instance x=0.2 and y = 0.0 to 0.1 by a missing part of the wall.
  

Multi-coloured surface plot

• Good: Shows bins as expected, able to separate different bins by color
• Bad: Color gradient messes here with the plot, would be better to have one fixed color for each bar instead of a gradient (How to resolve this?), also here problem with NaN-values e.g. at x=0.4
  
  

Single-coloured surface + wireframe plot

• Good: Bins separable by eye due to automatic shadows in plotly
• Bad: Wireframe lines are definitely not displayed as expected
  

Pyplot

Already worked yesterday, but somehow is not compiling at the moment on my PC. I'll try to add figures as soon as possible.

Further info

I am totally willing to expand this myself but I also definitely need some help (and also style-decisions) here. So let me know if you have any idea. Also @dorn-gerhard it would be really nice if your colleagues could add their solutions as proposed in #3379

Thanks already and Cheers.

[briederer]

And please could someone add the help wanted label since I don't have permissions to add labels 😅

[codecov]

Codecov Report

Merging #3507 (a74007e) into master (97036e6) will decrease coverage by 0.30%.
The diff coverage is 0.00%.

❗ Current head a74007e differs from pull request most recent head 1482874. Consider uploading reports for the commit 1482874 to get more accurate results

@@            Coverage Diff             @@
##           master    #3507      +/-   ##
==========================================
- Coverage   64.05%   63.75%   -0.31%     
==========================================
  Files          27       27              
  Lines        6611     6643      +32     
==========================================
  Hits         4235     4235              
- Misses       2376     2408      +32     

Impacted Files	Coverage Δ
src/recipes.jl	54.53% <0.00%> (-1.98%)	⬇️
src/shorthands.jl	45.83% <ø> (ø)

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[briederer]

Added now another possibility to tackle this problem, by really plotting 3d-bars at each x-y-spot as a separate series.
This works more reliable across backends but becomes very unfeasible for too much bins i.e. bins=(10,10) already creates 100 bars which uses a lot of memory.

Also in gr() the order of the series matters because otherwise a bar in the background overlay one in the front.

I will try to resolve this by not plotting one bar at each x-y-spot but instead plot one surface for each connected area (e.g. one slice from x[i] to x[i+1] for all y-values, or really trying to identify isolated areas). This should reduce the amount of unnecessary planes by a huge amount.

[briederer]

I will try to resolve this by not plotting one bar at each x-y-spot but instead plot one surface for each connected area (e.g. one slice from x[i] to x[i+1] for all y-values, or really trying to identify isolated areas). This should reduce the amount of unnecessary planes by a huge amount.

However this will make it harder again to have differently colored bars.