feat: Map coloring

[mszell]

Is your feature request related to a problem?
After a call with @MoritzStefaner on how to visualize sb's output nicely, we agreed that it would be nice if the map coloring problem was already solved by sb. (I am though not sure if it is already solved? If so, sorry and please close this issue!)

Proposed Solution
For example, an int parameter num_colors >= 4, (4 because of https://en.wikipedia.org/wiki/Four_color_theorem) that would give each superblock its own color class, such that all adjacent superblocks have a different class. Adjacency would be defined by the rook contiguity, if we think about the blocks as polygons.

Alternative Solutions
This feature could be handy especially in succession with #106 , after too small or too big superblocks have been merged/split or discarded.

Use Cases
Describe specific use cases for this feature:

1. As someone who wants to visualize the output of sb, I want to ensure that all adjacent superblocks have a different color, and that I can regulate how many colors to use, because the aesthetically best number might depend on the size of the city or blocks.

Additional Context
Some Python map coloring package might already exist.

Willing to Contribute?
Unfortunately I don't have enough time to develop it, and this feature suggestion is definitely not a request! More a nice to have. Happy to help test/document.

• I'm willing to submit a PR for this feature
• I can help test this feature
• I can help document this feature

[cbueth]

Hey @mszell, thank you for creating this Issue with @MoritzStefaner's impulse. This feature is not yet implemented, but I see the clear added value. You mention that it could be a follow-up on #106 / #129 . Feature-wise, do you see some dependency? Otherwise, this could be tackled already before.
The most work on this would be a) creating a neighbour graph to find out which blocks are neighbours and b) integrating it with the existing color system and a num_color the user can choose. The coloring should be done via the neighbour graph, which is, as you said, a solved problem.
When exporting, one can then access this color number for each superblock and choose any color programmatically.

[mszell]

Thx! No dependency, but good synergy, as dropping or merging too small sbs might already get rid of a lot of "color-clutter".

Agree on everything. Would need some polygonization of the sbs, in a way they fill out all space and actually touch, and then the spatial weight matrix with rook contiguity (for example as implemented in pysal), plus the coloring.