d3 / d3-delaunay

Compute the Voronoi diagram of a set of two-dimensional points.

d3-delaunay

This is a fast library for computing the Voronoi diagram of a set of two-dimensional points. It is based on Delaunator, a fast library for computing the Delaunay triangulation using sweep algorithms. The Voronoi diagram is constructed by connecting the circumcenters of adjacent triangles in the Delaunay triangulation.

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• Examples
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d3-delaunay's Issues

Missing corners in cell polygons?

It seems like we are occasionally missing a corner in Voronoi cell polygons:

[optimization] Don’t copy if no clipping is required.

voronoi._clipFinite currently always makes a copy, but it only needs to if clipping is needed.

voronoi.update?

How is delaunay.update supposed to interact with delaunay.voronoi? I assume you are expected to call delaunay.voronoi again after calling delaunay.update, but it’d be nice if there were an equivalent voronoi.update method.

not supported edge cases

i found few edge cases,

when points provided to Delaunay are on one line (x or y axis) delaunay is not able to produce correct result, and it throwing error with

Error: No Delaunay triangulation exists for this input.

that's a case even no matter how many points there in single line.
this was not a case with d3-voronoi

points

[20,0,107.24319391634981,0,188.8577946768061,0,275.9837262357414,0,360.4126235741445,0,447.6558174904943,0,532.0847148288974,0,619.3279087452472,0,706.5711026615969,0,791,0]

Document behavior for coincident points.

Currently, cell.triangles is undefined.

We should probably change cell.render(context) to be a no-op in this case, too.

delaunay.renderPoints(context)

For convenience.

Maybe also delaunay.renderPoint(i, context).

Empty vectors when circumcenter is coincident with midpoint.

The red Voronoi edge that should be pointing diagonally down and to the right is missing here:

The input is:

Delaunay.from([[100, 100], [200, 100], [100, 200]])

The issue is that the circumcenter of the triangle [150, 150] is coincident with the midpoint of the triangle vertexes on the convex hull [200, 100] and [100, 200], so we’re not able to compute the direction of the vector.

voronoi.find radius?

In d3-voronoi voronoi.find accepts a third argument, radius, which returns the nearest point from that distance. In this case the third argument i, specifies the index where the search starts.

I find the radius useful for creating distance-limited interactions. Is this something that you may consider adding?

Module "delaunator" not found. Only listed as devDependency.

Not sure if this is intended, but it looks like "delaunator" might need to be added as a production dependency to not get this error.

Define Voronoi diagram for entirely-collinear input?

This throws an error (No Delaunay triangulation exists for this input):

Delaunay.from([[0, 0], [1, 1], [2, 2]])

But like #19, there is a valid Voronoi diagram for this input! The problem is that all the cells have infinite sides and no points. Hrm.

Flatten hull into an array of indices

In Delaunator, the convex hull is kept as a circular doubly linked list internally for convenience/performance during the Delaunay sweep phase, but I think there's no point in exposing it like this in a public API — it would be simpler to flatten it after Delaunay construction and remove the "Node" section in Voronator API reference.

The only question is whether we should do this in Delaunator (and expose hull as a Uint32Array publicly), or Voronator.

[optimization] Use zipped coordinates [x0, y0, x1, y1, …].

A lot faster than [[x0, y0], [x1, y1], …].

delaunay.find fails when i is a coincident point.

I'm working with a set of lines that sometimes have coincident start points. I use d3-delaunay to find the nearest point to the cursor in order to highlight the line this point belongs to.

If it occurs that there is a point coincident to the first point of the first line, inedges[0] will be -1. Therefore, find(x, y, i = 0) will return -1 independent of x and y (because of how the _step function is implemented) — but find(x, y, i = 1) will not return -1 (or maybe only for i = 2, 3,...).

Question:

• Should this case be handled by me (by iteratively incrementing i and calling find(x, y, i)) or by d3-delaunay?

Clipped Voronoi cells sometimes have zero-length edges.

Not sure if this is a bug per se, but it would be nice to avoid them.

I'm trying to inline d3-delaunay but must be doing something wrong

See this section in my "Lloyd’s Algorithm With Velocities" notebook.

As far as I can tell I inlined all of Delaunator + d3-delaunay. Then I added caching of the typed arrays used in the constructor, plus an update method on each. The idea is to re-use those arrays and reduce allocation/GC pressure.

However, trying to use this version fails because... well, I'm not sure? I can't see anything that am I missing from the original libraries.

It breaks on line 35 of delaunay.js. The problem, as far as I can tell, is that hull is a typed array. Yet somehow, in this library, it has been extended with a next, i and t property. But I can't actually find any of that in the original Delaunator code so I guess I must be missing something?

    constructor(points) {
      const { halfedges, hull, triangles } = this.delaunator = new Delaunator(points);

     /* ... */

      // For points on the hull, index both the incoming and outgoing halfedges.
      let node0, node1 = hull;
      do {
        node0 = node1, node1 = node1.next;
        inedges[node1.i] = node0.t;
        outedges[node0.i] = node1.t;
      } while (node1 !== hull);
    }

Please transpile `dist/delaunay.js`

My library currently depends on d3-voronoi, and I'm trying to upgrade to d3-delaunay for performance improvements. Unfortunately, the lack of a transpiled target is a blocker. Transpiling it myself with webpack works for publishing the dist version of my library, but I'm currently also providing a transpiled lib which is how most of my users consume my library. At the moment, including this package would force all of those people to alter their builds to accommodate the change.

Flat storage for cell data

The current way of associating cells with their triangles brings a high performance and memory footprint cost, because we have to create a new Cell object and a triangles array for every input vertex.

A more efficient way to store cell triangles would be to keep a single Uint32Array holding all the triangles, with cells only keeping offsets for looking into this array (e.g. index and length). Like this:

for (let i = 0; i < cellLength; i++) {
  console.log(cellTriangles.subarray(cellIndex, cellIndex + cellLength));
}

Moreover, we could ditch Cell class altogether and keep associated data in a flat typed array too. This would make Voronoi data structures optimal in terms of performance and memory footprint and make the API consistent with that of Delaunator. However, this would require breaking the API — e.g. replacing methods like cell.contains(x, y) with voronoi.cellContains(cellIndex, x, y).

cc @mbostock

Update documentation for voronoi.edges etc.

These are still marked as TODO in the README.

Logo

delaunay.update should return this for easy chaining.

Production build includes new ECMAScript features.

Because of d3-delaunay uses a lot of ECMAScript new and experimental feature (e.g. class, exponential operator) for production build, it causes issues for production use.

Do you have a plan to use transpiler like babel to build a production module?

Upgrade to delaunator@3.

More performance!

See also #49 ;)

Almost collinear points break the Voronoi

See demo at https://observablehq.com/d/b31c2945b6082f94

I'm creating these test points with a linear formula, so it's just rounding errors that make the points "almost collinear". But the consequence is that Delaunator finds triangles — which could OK except that d3-delaunay then fails when it computes the Voronoi (rounding errors in the circumcenters I suspect).

I'm not sure if this should be dealt with upstream or here. I managed to fix it by changing the test on minRadius from minRadius === Infinity to minRadius < 1e30, so that the second chance of #64 (jittering) kicks in. It might be the solution, but then it breaks the Delaunator tests.

Get cells on either side of an edge

d3-voronoi has an edge object with edge.left and edge.right properties to get the index of the cell on either side.

Is there any chance you'd consider adding something similar to d3-delaunay? I've been trying to figure it out for the last while without success.

FeatureCollection properties are not applied to generated regions

As it was mentioned use this new module instead d3-voronoi since its faster I tried to upgrade turf js voronoi to use this feature.
But it seems cellPolygons doesn't preserve the order.

import { collectionOf } from '@turf/invariant';
import { Delaunay } from 'd3-delaunay';
import * as turf from '@turf/helpers';

function coordsToPolygon(coords) {
  coords = coords.slice();
  coords.push(coords[0]);
  return turf.polygon([coords]);
}

function voronoi(points, options) {
  // Optional params
  options = options || {};
  const bbox = options.bbox || [-180, -85, 180, 85];

  // Input Validation
  if (!points) { throw new Error('points is required'); }
  if (!Array.isArray(bbox)) { throw new Error('bbox is invalid'); }
  collectionOf(points, 'Point', 'points');

  const delaunay = Delaunay.from(points.features,
    feature => feature.geometry.coordinates[0],
    feature => feature.geometry.coordinates[1]);

  const voronator = delaunay.voronoi([bbox[0], bbox[1], bbox[2], bbox[3]]);

  const fc = turf.featureCollection(
    Array.from(voronator.cellPolygons()).map(coordsToPolygon)
  );

  if (options.keepProperties) {
    fc.features.forEach((polygon, i) => polygon.properties = JSON.parse(JSON.stringify(points.features[i].properties));
  }
  return fc;
}

export default voronoi;

Will keep properties will work for this package?

Counterclockwise cells instead of clockwise cells?

Delaunator uses counterclockwise triangles, so we should probably be consistent.

Hang?

If you modify this notebook so that the voronoi extent is [0, 0, width, height], it will crash shortly:

https://beta.observablehq.com/@mbostock/voronoi-particles

Edit: It seems to hang even with a larger extent. Just less often. Hmmm.

Render methods should return an SVG string if no context is specified.

Support flat array input format.

Now that mapbox/delaunator#17 is fixed, we should support the same API for the Delaunay constructor. Or, if we want to retain the current private copy constructor API, we’d need to expose a new factory method. Delaunay.of(array) comes to mind, but that seems like a bad idea—that should be reserved for Delaunay.of(…values) for consistency with Array.of. So some options:

1. Remove the copy constructor and just do new Delaunay(array). Pros: simple. Cons: copying a Delaunay instance would then require Object.create, but I don’t really anticipate this being a common pattern anyway; requires the new operator.

2. Rename Delaunay.from to Delaunay.fromPoints and introduce a new Delaunay.from that takes the flat array. Pros: retains copy constructor. Cons: confusing terminology, as both constructors accept “points”.

3. Add Delaunay.fromFlat(array), and keep existing constructor and Delaunay.from. Pros: does everything. Cons: fromFlat is the ugliest name for the use case we want to encourage.

4. Detect in Delaunay.from whether the given array is flat or not. Pros: “just works”. Cons: sometimes it doesn’t, and overloading by type is icky.

Feels like the first option is the “obvious” choice, but wanted to consider the others.

Can't render Voronoi diagram for particular set of points

Hello,

I'm having trouble rendering a Voronoi diagram for a set of points with a certain structure. The set of points looks like this:

Here is a notebook that describes the issue in more detail.

This sounds like it might be related to #20, though no error is thrown in this case.

Tests!

Stitch together cells into polygons.

We’re computing the polygon edges correctly (although we haven’t yet implemented clipping), but we’re not yet stitching them together into rings. #2

delaunay.find(x, y)

https://github.com/d3/d3-voronoi/blob/c59798a02fb2fd8e1dd37461a1ee1bfef44499bf/src/Diagram.js#L120-L141

Find edge between two cells

I'm looking to use Voronoi cells to represent movement for a game. I have a starting point/cell i, and a neighboring point/cell j - I'd like to use the edges for movement cost, walls, etc.

If I understand correctly, my ij pair is a half edge common to two adjacent triangles. The cell edge I'm looking for is the line connecting the circumcenter of these two triangles, but I can't find a way to determine the connections to get there. I think I'm missing how to find which half edge connects i and j, but maybe I'm missing something. Is there a simpler way that I'm not seeing?

Implement a linear cell edges connection algorithm

Currently, the voronoi() method is much slower than it could be — 2.3x slower on a million-point sample than the Delaunay pass, despite the fact that Delaunay is O(n log n) and getting its dual should in theory be only O(n).

It's slow due to the way cell edges are connected in Cell.js. Each cell keeps an array of disjoint connected components which it attempts to join with each incoming half-edge, having to loop through all components constantly, allocate tons of small arrays, and connect with very expensive concat/splice array operations.

Instead, I believe cells can be connected with a simple linear-time algorithm. Each half-edge belongs to only one cell. So we'll go through each half-edge whose cell hasn't yet been connected and connect it through other half-edges of the cell at once. Here's a rough illustration:

cc @mbostock

voronoi.path([context]) for rendering the cell edges.

No Delaunay triangulation for n = 3 array

Delaunay.from([[0,171],[0,62],[0,15]])

complains with:

index.js:91 Uncaught Error: No Delaunay triangulation exists for this input.
    at new Delaunator (index.js:91)
    at new Delaunay (delaunay.js:18)

Find Voronoi cell and neighbors

Is there a way to find the voronoi cell covering a point? And once you have a cell, is there a way of getting all the neighboring cells?

Sometimes cells only have v0 and vn.

These two corner cells, for example:

Which makes sense—they are essentially infinite triangles. We need to handle them accordingly.

Update observable demo to current version of the module

https://beta.observablehq.com/d/3b28638926bcac75 fixes the last part of https://beta.observablehq.com/@mbostock/the-delaunays-dual

(sorry for the weird alignments, they're prettier)

Clip polygon edges to the extent.

If we want to apply Liang–Barsky clipping, the Voronator will also need to know the clip extent.

delaunay.hull.render(context)

Instead of delaunay.renderHull(context). Would require forking Delaunator to create a Node prototype.

Math problem with `voronoi.cellPolygon`

What

Some wrong voronoi.cellPolygon results maybe related to floating points precision.

How

Hi! I've tried to reproduce the famous @mbostock Mike & Mario sketch rotating-voronoi.

But I noticed some problems. Talking with @Fil in the d3 slack he came up with a observable nootbook to reproduce the problem.

MWE to show the bug:

https://observablehq.com/d/bd8a95abd9a01c79

Notes:

I've tried with both d3-delaunay version 5.0.2 and 4.0.2

@Fil added this note:

change 253.74999999999997 to 253.75

Thanks!

Add an update method for relaxation algorithms

Delaunator v4 got an update method to update triangulation after editing coordinates in place, avoiding a lot of new memory allocations for use cases like the Lloyd's algorithm (see mapbox/delaunator#36).

It would be great to make a corresponding change in d3-delaunay as well. The Delaunay class would have to hold on to the whole delaunator object then (instead of just triangles, halfedges and hull), and update inedges/outedges after calling delaunator.update in a potential update method.

Define Delaunay triangulation for n = 0, n = 1 and n = 2.

Currently we throw an error from Delaunator:

Error: No Delaunay triangulation exists for this input.

There is a valid Voronoi diagram for n = 1 and n = 2, so we should allow an empty Delaunay triangulation with no triangles in these cases. And similarly for n = 0, we can have an empty Voronoi diagram with no cells.

Case conflict for Polygon.js

I get the following error when I try to use this library on Linux:

Module not found: Can't resolve './polygon' in '/home/brent/git/terrain3/node_modules/d3-delaunay/src'

This is because the file is named Polygon.js, but gets imported as "polygon".
https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js#L3

Renaming the file to "polygon.js" in my node_modules fixes the issue.

voronoi.index of triangle vertexes?

What if voronoi.index pointed to the first triangle vertex for a given cell, and then we used the halfedge traversal algorithm lazily? Then we wouldn’t need to precompute voronoi.edges.

Match cell with input site?

Since cells are in sorted order we need a way to match up with the original input site. Is delaunay.ids sufficient?

cell.contains(x, y)

It’s already implemented; we might as well expose it.

voronoi.find(x, y) doesn’t traverse the convex hull.

Currently voronoi.find only traverses internal edges of the Delaunay triangulation; it doesn’t traverse edges on the convex hull.