voronoi don't cover the rectangle? about d3-delaunay

[madcowfpb]

Here's a version exhibiting the issue with 9 points. It makes no sense to me, but the issue does not seem to occur unless the input array of points is copied.

html source:

<style> body {padding: 0; margin: 0;} </style> <script src="https://cdn.jsdelivr.net/npm/[email protected]/lib/p5.js"></script> <script src="https://cdn.jsdelivr.net/npm/d3-delaunay@6"></script> <script>

let delaunay;
let voronoi;
let npts = 0;
let npts1 = 0;
let pt1 = [];
let pt = [];

function setup() {

pixelDensity(1);

angleMode(DEGREES);
noLoop();

createCanvas(1200,900);

pt[npts++] = [447.27981036477433, 698.9400262172304];
pt[npts++] = [485.27830313288746, 668.9946483670656];
pt[npts++] = [611.9525697080425, 397.71056371206487];
pt[npts++] = [491.44637766366105, 692.071157339428];
pt[npts++] = [697.553622336339, 692.071157339428];
pt[npts++] = [497.00778156318086, 667.1990851383492];
pt[npts++] = [691.9922184368191, 667.1990851383492];
pt[npts++] = [544.9897579870977, 407.0828550310619];
pt[npts++] = [543.1738215956482, 437.35879519252677];

npts1 = 0
for (i=0; i<npts; i++) {
pt1[npts1++] = pt[i];
}
delaunay = d3.Delaunay.from(pt1);
voronoi = delaunay.voronoi([440, 380, 740, 850]);

}

function draw() {
noLoop();
console.log(pt1);
fill(255,0,0);

for (i=0; i<npts1; i++) {
point(pt1[i][0],pt1[i][1]);
let polygon = voronoi.cellPolygon(i);
if (polygon != null) {
console.log(polygon);
beginShape();
for (j=0; j<polygon.length; j++) {
vertex(polygon[j][0],polygon[j][1]);
}
endShape(CLOSE);
}
}
fill(0);
for (i=0; i<npts; i++) {
text(i,pt[i][0],pt[i][1]);
}
}
</script>

[Fil]

Thanks! I traced the problem to the code that we introduced for #88 in order to simplify the polygons when three consecutive points are aligned.

See #140 for a fix, build at https://observablehq.com/@d3/voronoi-issue-136

[mbostock]

I’ve reproduced this in a notebook: https://observablehq.com/d/cbcdfb87c58882b4. See the gap in cell 96.

I suspect that this is a numerical precision problem with the finite clipping implementation, and given that this library doesn’t use robust predicates (other than to compute the Delaunay triangulation thanks to the underlying delaunator library), I’m not sure it’s readily fixable. But maybe there’s a way.

[Fil]

Slightly tweaking the coordinates fixes the notebook:

    Plot.voronoi(delaunay136, {
      x: (d,i) => d[0] + i * 1e-13,
      y: (d) => d[1],

Fixing the bug is another matter; the fun part is that it happens at the bottom of the screen, but it is not triggered if you remove the points at the top with delaunay136.filter(d => d[1] > 183).

[madcowfpb]

Walking through the execution of this, it looks like there's a bug in the clipping implementation. The circumcenters for the botched cell are correctly computed and passed to _clipfinite. The first two circumcenters are in the region (these are coincidentally the same, and are the top right point of the botched cell). The third is out of (below) the region and this segment is correctly clipped at the bottom of the enclosing rectangle. The problem arises when dealing with the fourth circumcenter which is back in the region. I don't understand exactly where the bug is, but instead of adding a segment along the edge and another clipped segment to the fourth circumcenter what happens is the array holding the clipped version is reinitialized and ends up containing only the clipped segment from the third circumcenter to the fourth.

[madcowfpb]

@Fil - Any idea when this fix will show up in the version at https://cdn.jsdelivr.net/npm/d3-delaunay@6 ?

[mbostock]

@madcowfpb I just published it and it is live now. Thank you again for the bug report.