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Based on [Delaunator](https://github.com/mapbox/delaunator), d3-delaunay is 5-10× faster than d3-voronoi to construct the Delaunay triangulation or the Voronoi diagram, is more robust numerically, has Canvas rendering built-in, allows traversal of the Delaunay graph, and a variety of other improvements.\n\n---\n\nThis module implements [Steven J. Fortune’s algorithm](https://en.wikipedia.org/wiki/Fortune's_algorithm) for computing the [Voronoi diagram](https://en.wikipedia.org/wiki/Voronoi_diagram) or [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation) of a set of two-dimensional points. This implementation is largely based on [work by Raymond Hill](http://www.raymondhill.net/voronoi/rhill-voronoi.html).\n\nVoronoi diagrams are not only [visually](http://bl.ocks.org/mbostock/4360892) [attractive](http://bl.ocks.org/mbostock/4636377) but practical tools for interaction, such as to increase the target area of points in a scatterplot. See [“Strikeouts on the Rise”](http://www.nytimes.com/interactive/2013/03/29/sports/baseball/Strikeouts-Are-Still-Soaring.html) in *The New York Times* and this [multi-line chart](http://bl.ocks.org/mbostock/8033015) for examples; also see Tovi Grossman’s paper on [bubble cursors](http://www.tovigrossman.com/BubbleCursor) for a related technique. Voronoi diagrams can also be used to [automate label positioning](http://bl.ocks.org/mbostock/6909318), and Delaunay meshes are useful in computing adjacency or grouping of visual elements.\n\n\n\n\n\n\n\n\n\n\n\n\n## Installing\n\nIf you use NPM, `npm install d3-voronoi`. Otherwise, download the [latest release](https://github.com/d3/d3-voronoi/releases/latest). You can also load directly from [d3js.org](https://d3js.org), either as a [standalone library](https://d3js.org/d3-voronoi.v1.min.js) or as part of [D3 4.0](https://github.com/d3/d3). AMD, CommonJS, and vanilla environments are supported. In vanilla, a `d3` global is exported:\n\n```html\n\n\n```\n\n[Try d3-voronoi in your browser.](https://tonicdev.com/npm/d3-voronoi)\n\n## API Reference\n\n# d3.voronoi() [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js \"Source\")\n\nCreates a new Voronoi layout with default [*x*-](#voronoi_x) and [*y*-](#voronoi_y) accessors and a null [extent](#voronoi_extent).\n\n# voronoi(data) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L10 \"Source\")\n\nComputes the [Voronoi diagram](#voronoi-diagrams) for the specified *data* points.\n\n# voronoi.x([x]) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L31 \"Source\")\n\nIf *x* is specified, sets the *x*-coordinate accessor. If *x* is not specified, returns the current *x*-coordinate accessor, which defaults to:\n\n```js\nfunction x(d) {\n return d[0];\n}\n```\n\n# voronoi.y([y]) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L35 \"Source\")\n\nIf *y* is specified, sets the *y*-coordinate accessor. If *y* is not specified, returns the current *y*-coordinate accessor, which defaults to:\n\n```js\nfunction y(d) {\n return d[1];\n}\n```\n\n# voronoi.extent([extent]) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L39 \"Source\")\n\nIf *extent* is specified, sets the clip extent of the Voronoi layout to the specified bounds and returns the layout. The *extent* bounds are specified as an array \\[\\[x0, y0\\], \\[x1, y1\\]\\], where x0 is the left side of the extent, y0 is the top, x1 is the right and y1 is the bottom. If *extent* is not specified, returns the current clip extent which defaults to null. A clip extent is required when using [*voronoi*.polygons](#voronoi_polygons).\n\n# voronoi.size([size]) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L43 \"Source\")\n\nAn alias for [*voronoi*.extent](#voronoi_extent) where the minimum *x* and *y* of the extent are ⟨0,0⟩. Equivalent to:\n\n```js\nvoronoi.extent([[0, 0], size]);\n```\n\n# voronoi.polygons(data) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L19 \"Source\")\n\nReturns a sparse array of polygons, one for each unique input point in the specified *data* points, corresponding to the cells in the computed Voronoi diagram. Equivalent to:\n\n```js\nvoronoi(data).polygons();\n```\n\nSee [*diagram*.polygons](#diagram_polygons) for more detail. Note: an [extent](#voronoi_extent) is required.\n\n# voronoi.triangles(data) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L27 \"Source\")\n\nReturns the Delaunay triangulation of the specified *data* array as an array of triangles. Each triangle is a three-element array of elements from *data*. Equivalent to:\n\n```js\nvoronoi(data).triangles();\n```\n\nSee [*diagram*.triangles](#diagram_triangles) for more detail.\n\n# voronoi.links(data) [<>](https://github.com/d3/d3-voronoi/blob/master/src/voronoi.js#L23 \"Source\")\n\nReturns the Delaunay triangulation of the specified *data* array as an array of links. Each link has `source` and `target` attributes referring to elements in *data*. Equivalent to:\n\n```js\nvoronoi(data).links();\n```\n\nSee [*diagram*.links](#diagram_links) for more detail.\n\n### Voronoi Diagrams\n\n# diagram [<>](https://github.com/d3/d3-voronoi/blob/master/src/Diagram.js \"Source\")\n\nThe computed Voronoi diagram returned by [*voronoi*](#_voronoi) has the following properties:\n\n* `edges` - an array of [edges](#diagram_edge).\n* `cells` - a sparse array of [cells](#diagram_cell), one for each unique input point.\n\nFor each set of coincident input points, one of the points is chosen arbitrarily and assigned the associated cell; the other coincident input points’ entries are missing from the returned sparse array.\n\n# diagram.polygons() [<>](https://github.com/d3/d3-voronoi/blob/master/src/Diagram.js#L72 \"Source\")\n\nReturns a sparse array of polygons clipped to the [*extent*](#voronoi_extent), one for each cell (each unique input point) in the diagram. Each polygon is represented as an array of points \\[*x*, *y*\\] where *x* and *y* are the point coordinates, and a `data` field that refers to the corresponding element in *data*. Polygons are open: they do not contain a closing point that duplicates the first point; a triangle, for example, is an array of three points. Polygons are also counterclockwise, assuming the origin ⟨0,0⟩ is in the top-left corner.\n\nFor each set of coincident input points, one of the points is chosen arbitrarily and assigned the associated polygon; the other coincident input points’ entries are missing from the returned sparse array.\n\n# diagram.triangles() [<>](https://github.com/d3/d3-voronoi/blob/master/src/Diagram.js#L82 \"Source\")\n\nReturns the Delaunay triangulation of the specified *data* array as an array of triangles. Each triangle is a three-element array of elements from *data*. Since the triangulation is computed as the dual of the Voronoi diagram, and the Voronoi diagram is clipped by the [extent](#voronoi_extent), a subset of the Delaunay triangulation is returned.\n\n# diagram.links() [<>](https://github.com/d3/d3-voronoi/blob/master/src/Diagram.js#L108 \"Source\")\n\nReturns the Delaunay triangulation of the specified *data* array as an array of links, one for each edge in the mesh. Each link has the following attributes:\n\n* `source` - the source node, an element in *data*.\n* `target` - the target node, an element in *data*.\n\nSince the triangulation is computed as the dual of the Voronoi diagram, and the Voronoi diagram is clipped by the [extent](#voronoi_extent), a subset of the Delaunay links is returned.\n\n# diagram.find(x, y[, radius]) [<>](https://github.com/d3/d3-voronoi/blob/master/src/Diagram.js#L119 \"Source\")\n\nReturns the nearest site to point \\[*x*, *y*\\]. If *radius* is specified, only sites within *radius* distance are considered.\n\nSee Philippe Rivière’s [bl.ocks.org/1b7ddbcd71454d685d1259781968aefc](http://bl.ocks.org/Fil/1b7ddbcd71454d685d1259781968aefc) for an example.\n\n# cell\n\nEach cell in the diagram is an object with the following properties:\n\n* `site` - the [site](#site) of the cell’s associated input point.\n* `halfedges` - an array of indexes into [*diagram*.edges](#diagram) representing the cell’s polygon.\n\n# site\n\nEach site in the diagram is an array \\[*x*, *y*\\] with two additional properties:\n\n* `index` - the site’s index, corresponding to the associated input point.\n* `data` - the input data corresponding to this site.\n\n# edge\n\nEach edge in the diagram is an array \\[\\[*x0*, *y0*\\], \\[*x1*, *y1*\\]\\] with two additional properties:\n\n* `left` - the [site](#site) on the left side of the edge.\n* `right` - the [site](#site) on the right side of the edge; null for a clipped border edge." }