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Copyright 2018 Observable, Inc.
Permission to use, copy, modify, and/or distribute this software for any purpose
with or without fee is hereby granted, provided that the above copyright notice
and this permission notice appear in all copies.
THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
THIS SOFTWARE.

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# d3-delaunay
<p align="center"><img src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/voronator.jpg" width="300">
<p align="center">Georgy “The Voronator” Voronoy
This is a fast, no-dependency library for computing the [Voronoi diagram](https://en.wikipedia.org/wiki/Voronoi_diagram) of a set of two-dimensional points. It is based on [Delaunator](https://github.com/mapbox/delaunator), a fast library for computing the [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation) using [sweep algorithms](https://github.com/mapbox/delaunator/blob/master/README.md#papers). The Voronoi diagram is constructed by connecting the circumcenters of adjacent triangles in the Delaunay triangulation.
For an interactive explanation of how this library works, see [The Delaunays Dual](https://observablehq.com/@mbostock/the-delaunays-dual).
## Installing
To install, `npm install d3-delaunay` or `yarn add d3-delaunay`. You can also download the [latest release](https://github.com/d3/d3-delaunay/releases/latest) or load directly from [unpkg](https://unpkg.com/d3-delaunay/). AMD, CommonJS and ES6+ environments are supported. In vanilla, a `d3` global is exported.
```js
import {Delaunay} from "d3-delaunay";
const points = [[0, 0], [0, 1], [1, 0], [1, 1]];
const delaunay = Delaunay.from(points);
const voronoi = delaunay.voronoi([0, 0, 960, 500]);
```
## API Reference
### Delaunay
<a href="#new_Delaunay" name="new_Delaunay">#</a> new <b>Delaunay</b>(<i>points</i>) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns the Delaunay triangulation for the given flat array [*x0*, *y0*, *x1*, *y1*, …] of *points*.
```js
const delaunay = new Delaunay(Float64Array.of(0, 0, 0, 1, 1, 0, 1, 1));
```
<a href="#delaunay_from" name="delaunay_from">#</a> Delaunay.<b>from</b>(<i>points</i>[, <i>fx</i>[, <i>fy</i>[, <i>that</i>]]]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns the Delaunay triangulation for the given array or iterable of *points*. If *fx* and *fy* are not specified, then *points* is assumed to be an array of two-element arrays of numbers: [[*x0*, *y0*], [*x1*, *y1*], …]. Otherwise, *fx* and *fy* are functions that are invoked for each element in the *points* array in order, and must return the respective *x*- and *y*-coordinate for each point. If *that* is specified, the functions *fx* and *fy* are invoked with *that* as *this*. (See [Array.from](https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Array/from) for reference.)
```js
const delaunay = Delaunay.from([[0, 0], [0, 1], [1, 0], [1, 1]]);
```
<a href="#delaunay_points" name="delaunay_points">#</a> <i>delaunay</i>.<b>points</b>
The coordinates of the points as an array [*x0*, *y0*, *x1*, *y1*, …]. Typically, this is a Float64Array, however you can use any array-like type in the [constructor](#new_Delaunay).
<a href="#delaunay_halfedges" name="delaunay_halfedges">#</a> <i>delaunay</i>.<b>halfedges</b>
The halfedge indexes as an Int32Array [*j0*, *j1*, …]. For each index 0 ≤ *i* < *halfedges*.length, there is a halfedge from triangle vertex *j* = *halfedges*[*i*] to triangle vertex *i*. Equivalently, this means that triangle ⌊*i* / 3⌋ is adjacent to triangle ⌊*j* / 3⌋. If *j* is negative, then triangle ⌊*i* / 3⌋ is an exterior triangle on the [convex hull](#delaunay_hull). For example, to render the internal edges of the Delaunay triangulation:
```js
const {points, halfedges, triangles} = delaunay;
for (let i = 0, n = halfedges.length; i < n; ++i) {
const j = halfedges[i];
if (j < i) continue;
const ti = triangles[i];
const tj = triangles[j];
context.moveTo(points[ti * 2], points[ti * 2 + 1]);
context.lineTo(points[tj * 2], points[tj * 2 + 1]);
}
```
See also [*delaunay*.render](#delaunay_render).
<a href="#delaunay_hull" name="delaunay_hull">#</a> <i>delaunay</i>.<b>hull</b>
An Int32Array of point indexes that form the convex hull in counterclockwise order. If the points are collinear, returns them ordered.
See also [*delaunay*.renderHull](#delaunay_renderHull).
<a href="#delaunay_triangles" name="delaunay_triangles">#</a> <i>delaunay</i>.<b>triangles</b>
The triangle vertex indexes as an Uint32Array [*i0*, *j0*, *k0*, *i1*, *j1*, *k1*, …]. Each contiguous triplet of indexes *i*, *j*, *k* forms a counterclockwise triangle. The coordinates of the triangles points can be found by going through [*delaunay*.points](#delaunay_points). For example, to render triangle *i*:
```js
const {points, triangles} = delaunay;
const t0 = triangles[i * 3 + 0];
const t1 = triangles[i * 3 + 1];
const t2 = triangles[i * 3 + 2];
context.moveTo(points[t0 * 2], points[t0 * 2 + 1]);
context.lineTo(points[t1 * 2], points[t1 * 2 + 1]);
context.lineTo(points[t2 * 2], points[t2 * 2 + 1]);
context.closePath();
```
See also [*delaunay*.renderTriangle](#delaunay_renderTriangle).
<a href="#delaunay_inedges" name="delaunay_inedges">#</a> <i>delaunay</i>.<b>inedges</b>
The incoming halfedge indexes as a Int32Array [*e0*, *e1*, *e2*, …]. For each point *i*, *inedges*[*i*] is the halfedge index *e* of an incoming halfedge. For coincident points, the halfedge index is -1; for points on the convex hull, the incoming halfedge is on the convex hull; for other points, the choice of incoming halfedge is arbitrary. The *inedges* table can be used to traverse the Delaunay triangulation; see also [*delaunay*.neighbors](#delaunay_neighbors).
<a href="#delaunay_find" name="delaunay_find">#</a> <i>delaunay</i>.<b>find</b>(<i>x</i>, <i>y</i>[, <i>i</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns the index of the input point that is closest to the specified point ⟨*x*, *y*⟩. The search is started at the specified point *i*. If *i* is not specified, it defaults to zero.
<a href="#delaunay_neighbors" name="delaunay_neighbors">#</a> <i>delaunay</i>.<b>neighbors</b>(<i>i</i>) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns an iterable over the indexes of the neighboring points to the specified point *i*. The iterable is empty if *i* is a coincident point.
<a href="#delaunay_render" name="delaunay_render">#</a> <i>delaunay</i>.<b>render</b>([<i>context</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
<img alt="delaunay.render" src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/delaunay-mesh.png">
Renders the edges of the Delaunay triangulation to the specified *context*. The specified *context* must implement the *context*.moveTo and *context*.lineTo methods from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). If a *context* is not specified, an SVG path string is returned instead.
<a href="#delaunay_renderHull" name="delaunay_renderHull">#</a> <i>delaunay</i>.<b>renderHull</b>([<i>context</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
<img alt="delaunay.renderHull" src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/delaunay-hull.png">
Renders the convex hull of the Delaunay triangulation to the specified *context*. The specified *context* must implement the *context*.moveTo and *context*.lineTo methods from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). If a *context* is not specified, an SVG path string is returned instead.
<a href="#delaunay_renderTriangle" name="delaunay_renderTriangle">#</a> <i>delaunay</i>.<b>renderTriangle</b>(<i>i</i>[, <i>context</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
<img alt="delaunay.renderTriangle" src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/delaunay-triangle.png">
Renders triangle *i* of the Delaunay triangulation to the specified *context*. The specified *context* must implement the *context*.moveTo, *context*.lineTo and *context*.closePath methods from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). If a *context* is not specified, an SVG path string is returned instead.
<a href="#delaunay_renderPoints" name="delaunay_renderPoints">#</a> <i>delaunay</i>.<b>renderPoints</b>(\[<i>context</i>\]\[, <i>radius</i>\]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Renders the input points of the Delaunay triangulation to the specified *context* as circles with the specified *radius*. If *radius* is not specified, it defaults to 2. The specified *context* must implement the *context*.moveTo and *context*.arc methods from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). If a *context* is not specified, an SVG path string is returned instead.
<a href="#delaunay_hullPolygon" name="delaunay_hullPolygon">#</a> <i>delaunay</i>.<b>hullPolygon()</b> [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns the closed polygon [[*x0*, *y0*], [*x1*, *y1*], …, [*x0*, *y0*]] representing the convex hull.
<a href="#delaunay_trianglePolygons" name="delaunay_trianglePolygons">#</a> <i>delaunay</i>.<b>trianglePolygons()</b> [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns an iterable over the [polygons for each triangle](#delaunay_trianglePolygon), in order.
<a href="#delaunay_trianglePolygon" name="delaunay_trianglePolygon">#</a> <i>delaunay</i>.<b>trianglePolygon(<i>i</i>)</b> [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns the closed polygon [[*x0*, *y0*], [*x1*, *y1*], [*x2*, *y2*], [*x0*, *y0*]] representing the triangle *i*.
<a href="#delaunay_update" name="delaunay_update">#</a> <i>delaunay</i>.<b>update</b>() [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Updates the triangulation after the points have been modified in-place.
<a href="#delaunay_voronoi" name="delaunay_voronoi">#</a> <i>delaunay</i>.<b>voronoi</b>([<i>bounds</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/delaunay.js "Source")
Returns the [Voronoi diagram](#voronoi) for the associated [points](#delaunay_points). When rendering, the diagram will be clipped to the specified *bounds* = [*xmin*, *ymin*, *xmax*, *ymax*]. If *bounds* is not specified, it defaults to [0, 0, 960, 500]. See [To Infinity and Back Again](https://observablehq.com/@mbostock/to-infinity-and-back-again) for an interactive explanation of Voronoi cell clipping.
The Voronoi diagram is returned even in degenerate cases where no triangulation exists — namely 0, 1 or 2 points, and collinear points.
### Voronoi
<a href="#voronoi_delaunay" name="voronoi_delaunay">#</a> <i>voronoi</i>.<b>delaunay</b>
The Voronoi diagrams associated [Delaunay triangulation](#delaunay).
<a href="#voronoi_circumcenters" name="voronoi_circumcenters">#</a> <i>voronoi</i>.<b>circumcenters</b>
The [circumcenters](http://mathworld.wolfram.com/Circumcenter.html) of the Delaunay triangles as a Float64Array [*cx0*, *cy0*, *cx1*, *cy1*, …]. Each contiguous pair of coordinates *cx*, *cy* is the circumcenter for the corresponding triangle. These circumcenters form the coordinates of the Voronoi cell polygons.
<a href="#voronoi_vectors" name="voronoi_vectors">#</a> <i>voronoi</i>.<b>vectors</b>
A Float64Array [*vx0*, *vy0*, *wx0*, *wy0*, …] where each non-zero quadruple describes an open (infinite) cell on the outer hull, giving the directions of two open half-lines.
<a href="#voronoi_xmin" name="voronoi_xmin">#</a> <i>voronoi</i>.<b>xmin</b><br>
<a href="#voronoi_ymin" name="voronoi_ymin">#</a> <i>voronoi</i>.<b>ymin</b><br>
<a href="#voronoi_xmax" name="voronoi_xmax">#</a> <i>voronoi</i>.<b>xmax</b><br>
<a href="#voronoi_ymax" name="voronoi_ymax">#</a> <i>voronoi</i>.<b>ymax</b><br>
The bounds of the viewport [*xmin*, *ymin*, *xmax*, *ymax*] for rendering the Voronoi diagram. These values only affect the rendering methods ([*voronoi*.render](#voronoi_render), [*voronoi*.renderBounds](#voronoi_renderBounds), [*cell*.render](#cell_render)).
<a href="#voronoi_contains" name="voronoi_contains">#</a> <i>voronoi</i>.<b>contains</b>(<i>i</i>, <i>x</i>, <i>y</i>) [<>](https://github.com/d3/d3-delaunay/blob/master/src/cell.js "Source")
Returns true if the cell with the specified index *i* contains the specified point ⟨*x*, *y*⟩. (This method is not affected by the associated Voronoi diagrams viewport [bounds](#voronoi_xmin).)
<a href="#voronoi_neighbors" name="voronoi_neighbors">#</a> <i>voronoi</i>.<b>neighbors</b>(<i>i</i>) [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
Returns an iterable over the indexes of the cells that share a common edge with the specified cell *i*. Voronoi neighbors are always neighbors on the Delaunay graph, but the converse is false when the common edge has been clipped out by the Voronoi diagrams viewport.
<a href="#voronoi_render" name="voronoi_render">#</a> <i>voronoi</i>.<b>render</b>([<i>context</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
<img alt="voronoi.render" src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/voronoi-mesh.png">
Renders the mesh of Voronoi cells to the specified *context*. The specified *context* must implement the *context*.moveTo and *context*.lineTo methods from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). If a *context* is not specified, an SVG path string is returned instead.
<a href="#voronoi_renderBounds" name="voronoi_renderBounds">#</a> <i>voronoi</i>.<b>renderBounds</b>([<i>context</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
<img alt="voronoi.renderBounds" src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/voronoi-bounds.png">
Renders the viewport extent to the specified *context*. The specified *context* must implement the *context*.rect method from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). Equivalent to *context*.rect(*voronoi*.xmin, *voronoi*.ymin, *voronoi*.xmax - *voronoi*.xmin, *voronoi*.ymax - *voronoi*.ymin). If a *context* is not specified, an SVG path string is returned instead.
<a href="#voronoi_renderCell" name="voronoi_renderCell">#</a> <i>voronoi</i>.<b>renderCell</b>(<i>i</i>[, <i>context</i>]) [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
<img alt="cell.render" src="https://raw.githubusercontent.com/d3/d3-delaunay/master/img/spectral.png">
Renders the cell with the specified index *i* to the specified *context*. The specified *context* must implement the *context*.moveTo , *context*.lineTo and *context*.closePath methods from the [CanvasPathMethods API](https://www.w3.org/TR/2dcontext/#canvaspathmethods). If a *context* is not specified, an SVG path string is returned instead.
<a href="#voronoi_cellPolygons" name="voronoi_cellPolygons">#</a> <i>voronoi</i>.<b>cellPolygons</b>() [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
Returns an iterable over the non-empty [polygons for each cell](#voronoi_cellPolygon), with the cell index as property.
<a href="#voronoi_cellPolygon" name="voronoi_cellPolygon">#</a> <i>voronoi</i>.<b>cellPolygon</b>(<i>i</i>) [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
Returns the convex, closed polygon [[*x0*, *y0*], [*x1*, *y1*], …, [*x0*, *y0*]] representing the cell for the specified point *i*.
<a href="#voronoi_update" name="voronoi_update">#</a> <i>voronoi</i>.<b>update</b>() [<>](https://github.com/d3/d3-delaunay/blob/master/src/voronoi.js "Source")
Updates the Voronoi diagram and underlying triangulation after the points have been modified in-place — useful for Lloyds relaxation.

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"author": {
"name": "Mike Bostock",
"url": "https://bost.ocks.org/mike"
},
"bugs": {
"url": "https://github.com/d3/d3-delaunay/issues"
},
"bundleDependencies": false,
"contributors": [
{
"name": "Vladimir Agafonkin",
"url": "https://agafonkin.com"
},
{
"name": "Philippe Rivière",
"url": "https://visionscarto.net"
}
],
"dependencies": {
"delaunator": "4"
},
"deprecated": false,
"description": "Compute the Voronoi diagram of a set of two-dimensional points.",
"devDependencies": {
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"name": "d3-delaunay",
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import Delaunator from "delaunator";
import Path from "./path.js";
import Polygon from "./polygon.js";
import Voronoi from "./voronoi.js";
const tau = 2 * Math.PI, pow = Math.pow;
function pointX(p) {
return p[0];
}
function pointY(p) {
return p[1];
}
// A triangulation is collinear if all its triangles have a non-null area
function collinear(d) {
const {triangles, coords} = d;
for (let i = 0; i < triangles.length; i += 3) {
const a = 2 * triangles[i],
b = 2 * triangles[i + 1],
c = 2 * triangles[i + 2],
cross = (coords[c] - coords[a]) * (coords[b + 1] - coords[a + 1])
- (coords[b] - coords[a]) * (coords[c + 1] - coords[a + 1]);
if (cross > 1e-10) return false;
}
return true;
}
function jitter(x, y, r) {
return [x + Math.sin(x + y) * r, y + Math.cos(x - y) * r];
}
export default class Delaunay {
static from(points, fx = pointX, fy = pointY, that) {
return new Delaunay("length" in points
? flatArray(points, fx, fy, that)
: Float64Array.from(flatIterable(points, fx, fy, that)));
}
constructor(points) {
this._delaunator = new Delaunator(points);
this.inedges = new Int32Array(points.length / 2);
this._hullIndex = new Int32Array(points.length / 2);
this.points = this._delaunator.coords;
this._init();
}
update() {
this._delaunator.update();
this._init();
return this;
}
_init() {
const d = this._delaunator, points = this.points;
// check for collinear
if (d.hull && d.hull.length > 2 && collinear(d)) {
this.collinear = Int32Array.from({length: points.length/2}, (_,i) => i)
.sort((i, j) => points[2 * i] - points[2 * j] || points[2 * i + 1] - points[2 * j + 1]); // for exact neighbors
const e = this.collinear[0], f = this.collinear[this.collinear.length - 1],
bounds = [ points[2 * e], points[2 * e + 1], points[2 * f], points[2 * f + 1] ],
r = 1e-8 * Math.hypot(bounds[3] - bounds[1], bounds[2] - bounds[0]);
for (let i = 0, n = points.length / 2; i < n; ++i) {
const p = jitter(points[2 * i], points[2 * i + 1], r);
points[2 * i] = p[0];
points[2 * i + 1] = p[1];
}
this._delaunator = new Delaunator(points);
} else {
delete this.collinear;
}
const halfedges = this.halfedges = this._delaunator.halfedges;
const hull = this.hull = this._delaunator.hull;
const triangles = this.triangles = this._delaunator.triangles;
const inedges = this.inedges.fill(-1);
const hullIndex = this._hullIndex.fill(-1);
// Compute an index from each point to an (arbitrary) incoming halfedge
// Used to give the first neighbor of each point; for this reason,
// on the hull we give priority to exterior halfedges
for (let e = 0, n = halfedges.length; e < n; ++e) {
const p = triangles[e % 3 === 2 ? e - 2 : e + 1];
if (halfedges[e] === -1 || inedges[p] === -1) inedges[p] = e;
}
for (let i = 0, n = hull.length; i < n; ++i) {
hullIndex[hull[i]] = i;
}
// degenerate case: 1 or 2 (distinct) points
if (hull.length <= 2 && hull.length > 0) {
this.triangles = new Int32Array(3).fill(-1);
this.halfedges = new Int32Array(3).fill(-1);
this.triangles[0] = hull[0];
this.triangles[1] = hull[1];
this.triangles[2] = hull[1];
inedges[hull[0]] = 1;
if (hull.length === 2) inedges[hull[1]] = 0;
}
}
voronoi(bounds) {
return new Voronoi(this, bounds);
}
*neighbors(i) {
const {inedges, hull, _hullIndex, halfedges, triangles, collinear} = this;
// degenerate case with several collinear points
if (collinear) {
const l = collinear.indexOf(i);
if (l > 0) yield collinear[l - 1];
if (l < collinear.length - 1) yield collinear[l + 1];
return;
}
const e0 = inedges[i];
if (e0 === -1) return; // coincident point
let e = e0, p0 = -1;
do {
yield p0 = triangles[e];
e = e % 3 === 2 ? e - 2 : e + 1;
if (triangles[e] !== i) return; // bad triangulation
e = halfedges[e];
if (e === -1) {
const p = hull[(_hullIndex[i] + 1) % hull.length];
if (p !== p0) yield p;
return;
}
} while (e !== e0);
}
find(x, y, i = 0) {
if ((x = +x, x !== x) || (y = +y, y !== y)) return -1;
const i0 = i;
let c;
while ((c = this._step(i, x, y)) >= 0 && c !== i && c !== i0) i = c;
return c;
}
_step(i, x, y) {
const {inedges, hull, _hullIndex, halfedges, triangles, points} = this;
if (inedges[i] === -1 || !points.length) return (i + 1) % (points.length >> 1);
let c = i;
let dc = pow(x - points[i * 2], 2) + pow(y - points[i * 2 + 1], 2);
const e0 = inedges[i];
let e = e0;
do {
let t = triangles[e];
const dt = pow(x - points[t * 2], 2) + pow(y - points[t * 2 + 1], 2);
if (dt < dc) dc = dt, c = t;
e = e % 3 === 2 ? e - 2 : e + 1;
if (triangles[e] !== i) break; // bad triangulation
e = halfedges[e];
if (e === -1) {
e = hull[(_hullIndex[i] + 1) % hull.length];
if (e !== t) {
if (pow(x - points[e * 2], 2) + pow(y - points[e * 2 + 1], 2) < dc) return e;
}
break;
}
} while (e !== e0);
return c;
}
render(context) {
const buffer = context == null ? context = new Path : undefined;
const {points, halfedges, triangles} = this;
for (let i = 0, n = halfedges.length; i < n; ++i) {
const j = halfedges[i];
if (j < i) continue;
const ti = triangles[i] * 2;
const tj = triangles[j] * 2;
context.moveTo(points[ti], points[ti + 1]);
context.lineTo(points[tj], points[tj + 1]);
}
this.renderHull(context);
return buffer && buffer.value();
}
renderPoints(context, r = 2) {
const buffer = context == null ? context = new Path : undefined;
const {points} = this;
for (let i = 0, n = points.length; i < n; i += 2) {
const x = points[i], y = points[i + 1];
context.moveTo(x + r, y);
context.arc(x, y, r, 0, tau);
}
return buffer && buffer.value();
}
renderHull(context) {
const buffer = context == null ? context = new Path : undefined;
const {hull, points} = this;
const h = hull[0] * 2, n = hull.length;
context.moveTo(points[h], points[h + 1]);
for (let i = 1; i < n; ++i) {
const h = 2 * hull[i];
context.lineTo(points[h], points[h + 1]);
}
context.closePath();
return buffer && buffer.value();
}
hullPolygon() {
const polygon = new Polygon;
this.renderHull(polygon);
return polygon.value();
}
renderTriangle(i, context) {
const buffer = context == null ? context = new Path : undefined;
const {points, triangles} = this;
const t0 = triangles[i *= 3] * 2;
const t1 = triangles[i + 1] * 2;
const t2 = triangles[i + 2] * 2;
context.moveTo(points[t0], points[t0 + 1]);
context.lineTo(points[t1], points[t1 + 1]);
context.lineTo(points[t2], points[t2 + 1]);
context.closePath();
return buffer && buffer.value();
}
*trianglePolygons() {
const {triangles} = this;
for (let i = 0, n = triangles.length / 3; i < n; ++i) {
yield this.trianglePolygon(i);
}
}
trianglePolygon(i) {
const polygon = new Polygon;
this.renderTriangle(i, polygon);
return polygon.value();
}
}
function flatArray(points, fx, fy, that) {
const n = points.length;
const array = new Float64Array(n * 2);
for (let i = 0; i < n; ++i) {
const p = points[i];
array[i * 2] = fx.call(that, p, i, points);
array[i * 2 + 1] = fy.call(that, p, i, points);
}
return array;
}
function* flatIterable(points, fx, fy, that) {
let i = 0;
for (const p of points) {
yield fx.call(that, p, i, points);
yield fy.call(that, p, i, points);
++i;
}
}

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node_modules/d3-delaunay/src/index.js generated vendored Normal file
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export {default as Delaunay} from "./delaunay.js";
export {default as Voronoi} from "./voronoi.js";

37
node_modules/d3-delaunay/src/path.js generated vendored Normal file
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const epsilon = 1e-6;
export default class Path {
constructor() {
this._x0 = this._y0 = // start of current subpath
this._x1 = this._y1 = null; // end of current subpath
this._ = "";
}
moveTo(x, y) {
this._ += `M${this._x0 = this._x1 = +x},${this._y0 = this._y1 = +y}`;
}
closePath() {
if (this._x1 !== null) {
this._x1 = this._x0, this._y1 = this._y0;
this._ += "Z";
}
}
lineTo(x, y) {
this._ += `L${this._x1 = +x},${this._y1 = +y}`;
}
arc(x, y, r) {
x = +x, y = +y, r = +r;
const x0 = x + r;
const y0 = y;
if (r < 0) throw new Error("negative radius");
if (this._x1 === null) this._ += `M${x0},${y0}`;
else if (Math.abs(this._x1 - x0) > epsilon || Math.abs(this._y1 - y0) > epsilon) this._ += "L" + x0 + "," + y0;
if (!r) return;
this._ += `A${r},${r},0,1,1,${x - r},${y}A${r},${r},0,1,1,${this._x1 = x0},${this._y1 = y0}`;
}
rect(x, y, w, h) {
this._ += `M${this._x0 = this._x1 = +x},${this._y0 = this._y1 = +y}h${+w}v${+h}h${-w}Z`;
}
value() {
return this._ || null;
}
}

17
node_modules/d3-delaunay/src/polygon.js generated vendored Normal file
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export default class Polygon {
constructor() {
this._ = [];
}
moveTo(x, y) {
this._.push([x, y]);
}
closePath() {
this._.push(this._[0].slice());
}
lineTo(x, y) {
this._.push([x, y]);
}
value() {
return this._.length ? this._ : null;
}
}

320
node_modules/d3-delaunay/src/voronoi.js generated vendored Normal file
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import Path from "./path.js";
import Polygon from "./polygon.js";
export default class Voronoi {
constructor(delaunay, [xmin, ymin, xmax, ymax] = [0, 0, 960, 500]) {
if (!((xmax = +xmax) >= (xmin = +xmin)) || !((ymax = +ymax) >= (ymin = +ymin))) throw new Error("invalid bounds");
this.delaunay = delaunay;
this._circumcenters = new Float64Array(delaunay.points.length * 2);
this.vectors = new Float64Array(delaunay.points.length * 2);
this.xmax = xmax, this.xmin = xmin;
this.ymax = ymax, this.ymin = ymin;
this._init();
}
update() {
this.delaunay.update();
this._init();
return this;
}
_init() {
const {delaunay: {points, hull, triangles}, vectors} = this;
// Compute circumcenters.
const circumcenters = this.circumcenters = this._circumcenters.subarray(0, triangles.length / 3 * 2);
for (let i = 0, j = 0, n = triangles.length, x, y; i < n; i += 3, j += 2) {
const t1 = triangles[i] * 2;
const t2 = triangles[i + 1] * 2;
const t3 = triangles[i + 2] * 2;
const x1 = points[t1];
const y1 = points[t1 + 1];
const x2 = points[t2];
const y2 = points[t2 + 1];
const x3 = points[t3];
const y3 = points[t3 + 1];
const dx = x2 - x1;
const dy = y2 - y1;
const ex = x3 - x1;
const ey = y3 - y1;
const bl = dx * dx + dy * dy;
const cl = ex * ex + ey * ey;
const ab = (dx * ey - dy * ex) * 2;
if (!ab) {
// degenerate case (collinear diagram)
x = (x1 + x3) / 2 - 1e8 * ey;
y = (y1 + y3) / 2 + 1e8 * ex;
}
else if (Math.abs(ab) < 1e-8) {
// almost equal points (degenerate triangle)
x = (x1 + x3) / 2;
y = (y1 + y3) / 2;
} else {
const d = 1 / ab;
x = x1 + (ey * bl - dy * cl) * d;
y = y1 + (dx * cl - ex * bl) * d;
}
circumcenters[j] = x;
circumcenters[j + 1] = y;
}
// Compute exterior cell rays.
let h = hull[hull.length - 1];
let p0, p1 = h * 4;
let x0, x1 = points[2 * h];
let y0, y1 = points[2 * h + 1];
vectors.fill(0);
for (let i = 0; i < hull.length; ++i) {
h = hull[i];
p0 = p1, x0 = x1, y0 = y1;
p1 = h * 4, x1 = points[2 * h], y1 = points[2 * h + 1];
vectors[p0 + 2] = vectors[p1] = y0 - y1;
vectors[p0 + 3] = vectors[p1 + 1] = x1 - x0;
}
}
render(context) {
const buffer = context == null ? context = new Path : undefined;
const {delaunay: {halfedges, inedges, hull}, circumcenters, vectors} = this;
if (hull.length <= 1) return null;
for (let i = 0, n = halfedges.length; i < n; ++i) {
const j = halfedges[i];
if (j < i) continue;
const ti = Math.floor(i / 3) * 2;
const tj = Math.floor(j / 3) * 2;
const xi = circumcenters[ti];
const yi = circumcenters[ti + 1];
const xj = circumcenters[tj];
const yj = circumcenters[tj + 1];
this._renderSegment(xi, yi, xj, yj, context);
}
let h0, h1 = hull[hull.length - 1];
for (let i = 0; i < hull.length; ++i) {
h0 = h1, h1 = hull[i];
const t = Math.floor(inedges[h1] / 3) * 2;
const x = circumcenters[t];
const y = circumcenters[t + 1];
const v = h0 * 4;
const p = this._project(x, y, vectors[v + 2], vectors[v + 3]);
if (p) this._renderSegment(x, y, p[0], p[1], context);
}
return buffer && buffer.value();
}
renderBounds(context) {
const buffer = context == null ? context = new Path : undefined;
context.rect(this.xmin, this.ymin, this.xmax - this.xmin, this.ymax - this.ymin);
return buffer && buffer.value();
}
renderCell(i, context) {
const buffer = context == null ? context = new Path : undefined;
const points = this._clip(i);
if (points === null || !points.length) return;
context.moveTo(points[0], points[1]);
let n = points.length;
while (points[0] === points[n-2] && points[1] === points[n-1] && n > 1) n -= 2;
for (let i = 2; i < n; i += 2) {
if (points[i] !== points[i-2] || points[i+1] !== points[i-1])
context.lineTo(points[i], points[i + 1]);
}
context.closePath();
return buffer && buffer.value();
}
*cellPolygons() {
const {delaunay: {points}} = this;
for (let i = 0, n = points.length / 2; i < n; ++i) {
const cell = this.cellPolygon(i);
if (cell) cell.index = i, yield cell;
}
}
cellPolygon(i) {
const polygon = new Polygon;
this.renderCell(i, polygon);
return polygon.value();
}
_renderSegment(x0, y0, x1, y1, context) {
let S;
const c0 = this._regioncode(x0, y0);
const c1 = this._regioncode(x1, y1);
if (c0 === 0 && c1 === 0) {
context.moveTo(x0, y0);
context.lineTo(x1, y1);
} else if (S = this._clipSegment(x0, y0, x1, y1, c0, c1)) {
context.moveTo(S[0], S[1]);
context.lineTo(S[2], S[3]);
}
}
contains(i, x, y) {
if ((x = +x, x !== x) || (y = +y, y !== y)) return false;
return this.delaunay._step(i, x, y) === i;
}
*neighbors(i) {
const ci = this._clip(i);
if (ci) for (const j of this.delaunay.neighbors(i)) {
const cj = this._clip(j);
// find the common edge
if (cj) loop: for (let ai = 0, li = ci.length; ai < li; ai += 2) {
for (let aj = 0, lj = cj.length; aj < lj; aj += 2) {
if (ci[ai] == cj[aj]
&& ci[ai + 1] == cj[aj + 1]
&& ci[(ai + 2) % li] == cj[(aj + lj - 2) % lj]
&& ci[(ai + 3) % li] == cj[(aj + lj - 1) % lj]
) {
yield j;
break loop;
}
}
}
}
}
_cell(i) {
const {circumcenters, delaunay: {inedges, halfedges, triangles}} = this;
const e0 = inedges[i];
if (e0 === -1) return null; // coincident point
const points = [];
let e = e0;
do {
const t = Math.floor(e / 3);
points.push(circumcenters[t * 2], circumcenters[t * 2 + 1]);
e = e % 3 === 2 ? e - 2 : e + 1;
if (triangles[e] !== i) break; // bad triangulation
e = halfedges[e];
} while (e !== e0 && e !== -1);
return points;
}
_clip(i) {
// degenerate case (1 valid point: return the box)
if (i === 0 && this.delaunay.hull.length === 1) {
return [this.xmax, this.ymin, this.xmax, this.ymax, this.xmin, this.ymax, this.xmin, this.ymin];
}
const points = this._cell(i);
if (points === null) return null;
const {vectors: V} = this;
const v = i * 4;
return V[v] || V[v + 1]
? this._clipInfinite(i, points, V[v], V[v + 1], V[v + 2], V[v + 3])
: this._clipFinite(i, points);
}
_clipFinite(i, points) {
const n = points.length;
let P = null;
let x0, y0, x1 = points[n - 2], y1 = points[n - 1];
let c0, c1 = this._regioncode(x1, y1);
let e0, e1;
for (let j = 0; j < n; j += 2) {
x0 = x1, y0 = y1, x1 = points[j], y1 = points[j + 1];
c0 = c1, c1 = this._regioncode(x1, y1);
if (c0 === 0 && c1 === 0) {
e0 = e1, e1 = 0;
if (P) P.push(x1, y1);
else P = [x1, y1];
} else {
let S, sx0, sy0, sx1, sy1;
if (c0 === 0) {
if ((S = this._clipSegment(x0, y0, x1, y1, c0, c1)) === null) continue;
[sx0, sy0, sx1, sy1] = S;
} else {
if ((S = this._clipSegment(x1, y1, x0, y0, c1, c0)) === null) continue;
[sx1, sy1, sx0, sy0] = S;
e0 = e1, e1 = this._edgecode(sx0, sy0);
if (e0 && e1) this._edge(i, e0, e1, P, P.length);
if (P) P.push(sx0, sy0);
else P = [sx0, sy0];
}
e0 = e1, e1 = this._edgecode(sx1, sy1);
if (e0 && e1) this._edge(i, e0, e1, P, P.length);
if (P) P.push(sx1, sy1);
else P = [sx1, sy1];
}
}
if (P) {
e0 = e1, e1 = this._edgecode(P[0], P[1]);
if (e0 && e1) this._edge(i, e0, e1, P, P.length);
} else if (this.contains(i, (this.xmin + this.xmax) / 2, (this.ymin + this.ymax) / 2)) {
return [this.xmax, this.ymin, this.xmax, this.ymax, this.xmin, this.ymax, this.xmin, this.ymin];
}
return P;
}
_clipSegment(x0, y0, x1, y1, c0, c1) {
while (true) {
if (c0 === 0 && c1 === 0) return [x0, y0, x1, y1];
if (c0 & c1) return null;
let x, y, c = c0 || c1;
if (c & 0b1000) x = x0 + (x1 - x0) * (this.ymax - y0) / (y1 - y0), y = this.ymax;
else if (c & 0b0100) x = x0 + (x1 - x0) * (this.ymin - y0) / (y1 - y0), y = this.ymin;
else if (c & 0b0010) y = y0 + (y1 - y0) * (this.xmax - x0) / (x1 - x0), x = this.xmax;
else y = y0 + (y1 - y0) * (this.xmin - x0) / (x1 - x0), x = this.xmin;
if (c0) x0 = x, y0 = y, c0 = this._regioncode(x0, y0);
else x1 = x, y1 = y, c1 = this._regioncode(x1, y1);
}
}
_clipInfinite(i, points, vx0, vy0, vxn, vyn) {
let P = Array.from(points), p;
if (p = this._project(P[0], P[1], vx0, vy0)) P.unshift(p[0], p[1]);
if (p = this._project(P[P.length - 2], P[P.length - 1], vxn, vyn)) P.push(p[0], p[1]);
if (P = this._clipFinite(i, P)) {
for (let j = 0, n = P.length, c0, c1 = this._edgecode(P[n - 2], P[n - 1]); j < n; j += 2) {
c0 = c1, c1 = this._edgecode(P[j], P[j + 1]);
if (c0 && c1) j = this._edge(i, c0, c1, P, j), n = P.length;
}
} else if (this.contains(i, (this.xmin + this.xmax) / 2, (this.ymin + this.ymax) / 2)) {
P = [this.xmin, this.ymin, this.xmax, this.ymin, this.xmax, this.ymax, this.xmin, this.ymax];
}
return P;
}
_edge(i, e0, e1, P, j) {
while (e0 !== e1) {
let x, y;
switch (e0) {
case 0b0101: e0 = 0b0100; continue; // top-left
case 0b0100: e0 = 0b0110, x = this.xmax, y = this.ymin; break; // top
case 0b0110: e0 = 0b0010; continue; // top-right
case 0b0010: e0 = 0b1010, x = this.xmax, y = this.ymax; break; // right
case 0b1010: e0 = 0b1000; continue; // bottom-right
case 0b1000: e0 = 0b1001, x = this.xmin, y = this.ymax; break; // bottom
case 0b1001: e0 = 0b0001; continue; // bottom-left
case 0b0001: e0 = 0b0101, x = this.xmin, y = this.ymin; break; // left
}
if ((P[j] !== x || P[j + 1] !== y) && this.contains(i, x, y)) {
P.splice(j, 0, x, y), j += 2;
}
}
if (P.length > 4) {
for (let i = 0; i < P.length; i+= 2) {
const j = (i + 2) % P.length, k = (i + 4) % P.length;
if (P[i] === P[j] && P[j] === P[k]
|| P[i + 1] === P[j + 1] && P[j + 1] === P[k + 1])
P.splice(j, 2), i -= 2;
}
}
return j;
}
_project(x0, y0, vx, vy) {
let t = Infinity, c, x, y;
if (vy < 0) { // top
if (y0 <= this.ymin) return null;
if ((c = (this.ymin - y0) / vy) < t) y = this.ymin, x = x0 + (t = c) * vx;
} else if (vy > 0) { // bottom
if (y0 >= this.ymax) return null;
if ((c = (this.ymax - y0) / vy) < t) y = this.ymax, x = x0 + (t = c) * vx;
}
if (vx > 0) { // right
if (x0 >= this.xmax) return null;
if ((c = (this.xmax - x0) / vx) < t) x = this.xmax, y = y0 + (t = c) * vy;
} else if (vx < 0) { // left
if (x0 <= this.xmin) return null;
if ((c = (this.xmin - x0) / vx) < t) x = this.xmin, y = y0 + (t = c) * vy;
}
return [x, y];
}
_edgecode(x, y) {
return (x === this.xmin ? 0b0001
: x === this.xmax ? 0b0010 : 0b0000)
| (y === this.ymin ? 0b0100
: y === this.ymax ? 0b1000 : 0b0000);
}
_regioncode(x, y) {
return (x < this.xmin ? 0b0001
: x > this.xmax ? 0b0010 : 0b0000)
| (y < this.ymin ? 0b0100
: y > this.ymax ? 0b1000 : 0b0000);
}
}