Handle collinear (and cocircular) points?

[m-rutter]

So I stumbled upon this bug with d3.voronoi with this particular dataset: http://jsbin.com/sogamotefo/edit?html,js,console

The bug also exists in the most recent version of d3v3, and if you swap the accessors for x & y it actually causes the browser to hang indefinitely with no error messages as though it it stuck in a loop:

// warning, replacing voronoiGen in the jsbin with this snippet will cause the browser to hang.
var voronoiGen = d3.voronoi()
  .x(function(d) {return y(d.y);})
  .y(function(d) {return x(d.x);})
  .extent([[0, 0], [500, 500]]);

[mbostock]

The problem is that your input is (approximately) collinear:

Unfortunately, this Voronoi implementation doesn’t gracefully handle such input. As Jason wrote in https://github.com/d3/d3/issues/1895#issuecomment-45931450,

This is a specific instance of a more general problem: there is more than one possible Delaunay triangulation for n ≥ 4 cocircular points; otherwise there is always a unique triangulation satisfying the Delaunay property. I think a reasonable fix is to pick an arbitrary Delaunay triangulation in this situtation.

Your input data exhibits a similar error here:

http://www.raymondhill.net/voronoi/rhill-voronoi.html

If you click “Clear all sites”, paste this in, and then click “Parse as sites”:

0.03638187704872731,464.2891731435667
18.726131781749977,447.97448002565795
79.47054617672242,394.9493467555858
126.61481653614429,353.7960778727167
178.5339693099149,308.4747092741625
197.96420712404677,291.51362799902915
266.8323214526062,231.39713866083747
343.10585755513114,164.81629403340833
421.6683900355436,96.23733420146249
497.7763624024437,29.80101379463332

You’ll see a TypeError: Cannot read property 'site' of undefined.

I probably won’t be able to fix this in the near future… Sorry. You can probably work around by adding a tiny amount of random jitter to your points (though that is no guarantee, in the extremely unlikely case your jittered input happens to still be collinear or cocircular).

Related d3/d3#235 d3/d3#1895 gorhill/Javascript-Voronoi#12.

[m-rutter]

Yeah, I thought it might be related to that existing issue as those sets of values are highly correlated. I'm building an interface in which I'm allowing users to plot different sets of values, including that rather uninteresting pair. It would be nice if it could fail gracefully so I could plot something else or render a message in its place. Right now the user has the potential to kill the browser window with an indefinite loop if they are an especially boring and/or unlucky individual :P

I would like to take the opportunity Mike to thank you for this library, and the continuing work and support you have put in including the countless examples and high quality tutorials. Taking the time to learn your library helped me get my first job as a developer, and so I'm personally very grateful.

[mbostock]

Thank you. I expect that adding a tiny bit of random jitter would be safe if you don’t mind sacrificing accuracy.

[m-rutter]

Yep, adding jitter with Math.random() to the scaled value in the accessors is a good enough trade off for my (and I imagine the majority of) cases.

const voronoiGen = voronoi()
      .x(d => x(d.x) + Math.random())
      .y(d => y(d.y) + Math.random())
      .extent([[0, 0], [w, h]]);

[mbostock]

I’d recommend subtracting by 0.5 so that the average jitter is still zero, like this example:

var voronoi = d3.voronoi()
    .x(function(d) { return d.x + Math.random() - 0.5; })
    .y(function(d) { return d.y + Math.random() - 0.5; });