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Nuno Coração
2023-01-29 22:30:24 +00:00
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Copyright 2010-2021 Mike Bostock
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-polygon
This module provides a few basic geometric operations for two-dimensional polygons. Each polygon is represented as an array of two-element arrays [[<i>x1</i>, <i>y1</i>], [<i>x2</i>, <i>y2</i>], …], and may either be closed (wherein the first and last point are the same) or open (wherein they are not). Typically polygons are in counterclockwise order, assuming a coordinate system where the origin ⟨0,0⟩ is in the top-left corner.
## Installing
If you use npm, `npm install d3-polygon`. You can also download the [latest release on GitHub](https://github.com/d3/d3-polygon/releases/latest). For vanilla HTML in modern browsers, import d3-polygon from Skypack:
```html
<script type="module">
import {polygonHull} from "https://cdn.skypack.dev/d3-polygon@3";
const hull = polygonHull(points);
</script>
```
For legacy environments, you can load d3-polygons UMD bundle from an npm-based CDN such as jsDelivr; a `d3` global is exported:
```html
<script src="https://cdn.jsdelivr.net/npm/d3-polygon@3"></script>
<script>
const hull = d3.polygonHull(points);
</script>
```
## API Reference
<a href="#polygonArea" name="polygonArea">#</a> d3.<b>polygonArea</b>(<i>polygon</i>) [<>](https://github.com/d3/d3-polygon/blob/master/src/area.js "Source Code")
Returns the signed area of the specified *polygon*. If the vertices of the polygon are in counterclockwise order (assuming a coordinate system where the origin ⟨0,0⟩ is in the top-left corner), the returned area is positive; otherwise it is negative, or zero.
<a href="#polygonCentroid" name="polygonCentroid">#</a> d3.<b>polygonCentroid</b>(<i>polygon</i>) [<>](https://github.com/d3/d3-polygon/blob/master/src/centroid.js "Source Code")
Returns the [centroid](https://en.wikipedia.org/wiki/Centroid) of the specified *polygon*.
<a href="#polygonHull" name="polygonHull">#</a> d3.<b>polygonHull</b>(<i>points</i>) [<>](https://github.com/d3/d3-polygon/blob/master/src/hull.js#L23 "Source Code")
<a href="http://bl.ocks.org/mbostock/6f14f7b7f267a85f7cdc"><img src="https://raw.githubusercontent.com/d3/d3-polygon/master/img/hull.png" width="250" height="250"></a>
Returns the [convex hull](https://en.wikipedia.org/wiki/Convex_hull) of the specified *points* using [Andrews monotone chain algorithm](http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain). The returned hull is represented as an array containing a subset of the input *points* arranged in counterclockwise order. Returns null if *points* has fewer than three elements.
<a href="#polygonContains" name="polygonContains">#</a> d3.<b>polygonContains</b>(<i>polygon</i>, <i>point</i>) [<>](https://github.com/d3/d3-polygon/blob/master/src/contains.js "Source Code")
Returns true if and only if the specified *point* is inside the specified *polygon*.
<a href="#polygonLength" name="polygonLength">#</a> d3.<b>polygonLength</b>(<i>polygon</i>) [<>](https://github.com/d3/d3-polygon/blob/master/src/length.js "Source Code")
Returns the length of the perimeter of the specified *polygon*.

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// https://d3js.org/d3-polygon/ v3.0.1 Copyright 2010-2021 Mike Bostock
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
typeof define === 'function' && define.amd ? define(['exports'], factory) :
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, factory(global.d3 = global.d3 || {}));
}(this, (function (exports) { 'use strict';
function area(polygon) {
var i = -1,
n = polygon.length,
a,
b = polygon[n - 1],
area = 0;
while (++i < n) {
a = b;
b = polygon[i];
area += a[1] * b[0] - a[0] * b[1];
}
return area / 2;
}
function centroid(polygon) {
var i = -1,
n = polygon.length,
x = 0,
y = 0,
a,
b = polygon[n - 1],
c,
k = 0;
while (++i < n) {
a = b;
b = polygon[i];
k += c = a[0] * b[1] - b[0] * a[1];
x += (a[0] + b[0]) * c;
y += (a[1] + b[1]) * c;
}
return k *= 3, [x / k, y / k];
}
// Returns the 2D cross product of AB and AC vectors, i.e., the z-component of
// the 3D cross product in a quadrant I Cartesian coordinate system (+x is
// right, +y is up). Returns a positive value if ABC is counter-clockwise,
// negative if clockwise, and zero if the points are collinear.
function cross(a, b, c) {
return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]);
}
function lexicographicOrder(a, b) {
return a[0] - b[0] || a[1] - b[1];
}
// Computes the upper convex hull per the monotone chain algorithm.
// Assumes points.length >= 3, is sorted by x, unique in y.
// Returns an array of indices into points in left-to-right order.
function computeUpperHullIndexes(points) {
const n = points.length,
indexes = [0, 1];
let size = 2, i;
for (i = 2; i < n; ++i) {
while (size > 1 && cross(points[indexes[size - 2]], points[indexes[size - 1]], points[i]) <= 0) --size;
indexes[size++] = i;
}
return indexes.slice(0, size); // remove popped points
}
function hull(points) {
if ((n = points.length) < 3) return null;
var i,
n,
sortedPoints = new Array(n),
flippedPoints = new Array(n);
for (i = 0; i < n; ++i) sortedPoints[i] = [+points[i][0], +points[i][1], i];
sortedPoints.sort(lexicographicOrder);
for (i = 0; i < n; ++i) flippedPoints[i] = [sortedPoints[i][0], -sortedPoints[i][1]];
var upperIndexes = computeUpperHullIndexes(sortedPoints),
lowerIndexes = computeUpperHullIndexes(flippedPoints);
// Construct the hull polygon, removing possible duplicate endpoints.
var skipLeft = lowerIndexes[0] === upperIndexes[0],
skipRight = lowerIndexes[lowerIndexes.length - 1] === upperIndexes[upperIndexes.length - 1],
hull = [];
// Add upper hull in right-to-l order.
// Then add lower hull in left-to-right order.
for (i = upperIndexes.length - 1; i >= 0; --i) hull.push(points[sortedPoints[upperIndexes[i]][2]]);
for (i = +skipLeft; i < lowerIndexes.length - skipRight; ++i) hull.push(points[sortedPoints[lowerIndexes[i]][2]]);
return hull;
}
function contains(polygon, point) {
var n = polygon.length,
p = polygon[n - 1],
x = point[0], y = point[1],
x0 = p[0], y0 = p[1],
x1, y1,
inside = false;
for (var i = 0; i < n; ++i) {
p = polygon[i], x1 = p[0], y1 = p[1];
if (((y1 > y) !== (y0 > y)) && (x < (x0 - x1) * (y - y1) / (y0 - y1) + x1)) inside = !inside;
x0 = x1, y0 = y1;
}
return inside;
}
function length(polygon) {
var i = -1,
n = polygon.length,
b = polygon[n - 1],
xa,
ya,
xb = b[0],
yb = b[1],
perimeter = 0;
while (++i < n) {
xa = xb;
ya = yb;
b = polygon[i];
xb = b[0];
yb = b[1];
xa -= xb;
ya -= yb;
perimeter += Math.hypot(xa, ya);
}
return perimeter;
}
exports.polygonArea = area;
exports.polygonCentroid = centroid;
exports.polygonContains = contains;
exports.polygonHull = hull;
exports.polygonLength = length;
Object.defineProperty(exports, '__esModule', { value: true });
})));

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// https://d3js.org/d3-polygon/ v3.0.1 Copyright 2010-2021 Mike Bostock
!function(n,e){"object"==typeof exports&&"undefined"!=typeof module?e(exports):"function"==typeof define&&define.amd?define(["exports"],e):e((n="undefined"!=typeof globalThis?globalThis:n||self).d3=n.d3||{})}(this,(function(n){"use strict";function e(n,e){return n[0]-e[0]||n[1]-e[1]}function t(n){const e=n.length,t=[0,1];let o,r=2;for(o=2;o<e;++o){for(;r>1&&(f=n[t[r-2]],l=n[t[r-1]],u=n[o],(l[0]-f[0])*(u[1]-f[1])-(l[1]-f[1])*(u[0]-f[0])<=0);)--r;t[r++]=o}var f,l,u;return t.slice(0,r)}n.polygonArea=function(n){for(var e,t=-1,o=n.length,r=n[o-1],f=0;++t<o;)e=r,r=n[t],f+=e[1]*r[0]-e[0]*r[1];return f/2},n.polygonCentroid=function(n){for(var e,t,o=-1,r=n.length,f=0,l=0,u=n[r-1],i=0;++o<r;)e=u,u=n[o],i+=t=e[0]*u[1]-u[0]*e[1],f+=(e[0]+u[0])*t,l+=(e[1]+u[1])*t;return[f/(i*=3),l/i]},n.polygonContains=function(n,e){for(var t,o,r=n.length,f=n[r-1],l=e[0],u=e[1],i=f[0],g=f[1],h=!1,a=0;a<r;++a)t=(f=n[a])[0],(o=f[1])>u!=g>u&&l<(i-t)*(u-o)/(g-o)+t&&(h=!h),i=t,g=o;return h},n.polygonHull=function(n){if((r=n.length)<3)return null;var o,r,f=new Array(r),l=new Array(r);for(o=0;o<r;++o)f[o]=[+n[o][0],+n[o][1],o];for(f.sort(e),o=0;o<r;++o)l[o]=[f[o][0],-f[o][1]];var u=t(f),i=t(l),g=i[0]===u[0],h=i[i.length-1]===u[u.length-1],a=[];for(o=u.length-1;o>=0;--o)a.push(n[f[u[o]][2]]);for(o=+g;o<i.length-h;++o)a.push(n[f[i[o]][2]]);return a},n.polygonLength=function(n){for(var e,t,o=-1,r=n.length,f=n[r-1],l=f[0],u=f[1],i=0;++o<r;)e=l,t=u,e-=l=(f=n[o])[0],t-=u=f[1],i+=Math.hypot(e,t);return i},Object.defineProperty(n,"__esModule",{value:!0})}));

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{
"name": "d3-polygon",
"version": "3.0.1",
"description": "Operations for two-dimensional polygons.",
"homepage": "https://d3js.org/d3-polygon/",
"repository": {
"type": "git",
"url": "https://github.com/d3/d3-polygon.git"
},
"keywords": [
"d3",
"d3-module",
"polygon",
"hull",
"geometry",
"graphics"
],
"license": "ISC",
"author": {
"name": "Mike Bostock",
"url": "http://bost.ocks.org/mike"
},
"type": "module",
"files": [
"dist/**/*.js",
"src/**/*.js"
],
"module": "src/index.js",
"main": "src/index.js",
"jsdelivr": "dist/d3-polygon.min.js",
"unpkg": "dist/d3-polygon.min.js",
"exports": {
"umd": "./dist/d3-polygon.min.js",
"default": "./src/index.js"
},
"sideEffects": false,
"devDependencies": {
"eslint": "7",
"mocha": "8",
"rollup": "2",
"rollup-plugin-terser": "7"
},
"scripts": {
"test": "mocha 'test/**/*-test.js' && eslint src test",
"prepublishOnly": "rm -rf dist && yarn test && rollup -c",
"postpublish": "git push && git push --tags && cd ../d3.github.com && git pull && cp ../${npm_package_name}/dist/${npm_package_name}.js ${npm_package_name}.v${npm_package_version%%.*}.js && cp ../${npm_package_name}/dist/${npm_package_name}.min.js ${npm_package_name}.v${npm_package_version%%.*}.min.js && git add ${npm_package_name}.v${npm_package_version%%.*}.js ${npm_package_name}.v${npm_package_version%%.*}.min.js && git commit -m \"${npm_package_name} ${npm_package_version}\" && git push && cd -"
},
"engines": {
"node": ">=12"
}
}

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export default function(polygon) {
var i = -1,
n = polygon.length,
a,
b = polygon[n - 1],
area = 0;
while (++i < n) {
a = b;
b = polygon[i];
area += a[1] * b[0] - a[0] * b[1];
}
return area / 2;
}

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export default function(polygon) {
var i = -1,
n = polygon.length,
x = 0,
y = 0,
a,
b = polygon[n - 1],
c,
k = 0;
while (++i < n) {
a = b;
b = polygon[i];
k += c = a[0] * b[1] - b[0] * a[1];
x += (a[0] + b[0]) * c;
y += (a[1] + b[1]) * c;
}
return k *= 3, [x / k, y / k];
}

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export default function(polygon, point) {
var n = polygon.length,
p = polygon[n - 1],
x = point[0], y = point[1],
x0 = p[0], y0 = p[1],
x1, y1,
inside = false;
for (var i = 0; i < n; ++i) {
p = polygon[i], x1 = p[0], y1 = p[1];
if (((y1 > y) !== (y0 > y)) && (x < (x0 - x1) * (y - y1) / (y0 - y1) + x1)) inside = !inside;
x0 = x1, y0 = y1;
}
return inside;
}

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// Returns the 2D cross product of AB and AC vectors, i.e., the z-component of
// the 3D cross product in a quadrant I Cartesian coordinate system (+x is
// right, +y is up). Returns a positive value if ABC is counter-clockwise,
// negative if clockwise, and zero if the points are collinear.
export default function(a, b, c) {
return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]);
}

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import cross from "./cross.js";
function lexicographicOrder(a, b) {
return a[0] - b[0] || a[1] - b[1];
}
// Computes the upper convex hull per the monotone chain algorithm.
// Assumes points.length >= 3, is sorted by x, unique in y.
// Returns an array of indices into points in left-to-right order.
function computeUpperHullIndexes(points) {
const n = points.length,
indexes = [0, 1];
let size = 2, i;
for (i = 2; i < n; ++i) {
while (size > 1 && cross(points[indexes[size - 2]], points[indexes[size - 1]], points[i]) <= 0) --size;
indexes[size++] = i;
}
return indexes.slice(0, size); // remove popped points
}
export default function(points) {
if ((n = points.length) < 3) return null;
var i,
n,
sortedPoints = new Array(n),
flippedPoints = new Array(n);
for (i = 0; i < n; ++i) sortedPoints[i] = [+points[i][0], +points[i][1], i];
sortedPoints.sort(lexicographicOrder);
for (i = 0; i < n; ++i) flippedPoints[i] = [sortedPoints[i][0], -sortedPoints[i][1]];
var upperIndexes = computeUpperHullIndexes(sortedPoints),
lowerIndexes = computeUpperHullIndexes(flippedPoints);
// Construct the hull polygon, removing possible duplicate endpoints.
var skipLeft = lowerIndexes[0] === upperIndexes[0],
skipRight = lowerIndexes[lowerIndexes.length - 1] === upperIndexes[upperIndexes.length - 1],
hull = [];
// Add upper hull in right-to-l order.
// Then add lower hull in left-to-right order.
for (i = upperIndexes.length - 1; i >= 0; --i) hull.push(points[sortedPoints[upperIndexes[i]][2]]);
for (i = +skipLeft; i < lowerIndexes.length - skipRight; ++i) hull.push(points[sortedPoints[lowerIndexes[i]][2]]);
return hull;
}

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export {default as polygonArea} from "./area.js";
export {default as polygonCentroid} from "./centroid.js";
export {default as polygonHull} from "./hull.js";
export {default as polygonContains} from "./contains.js";
export {default as polygonLength} from "./length.js";

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export default function(polygon) {
var i = -1,
n = polygon.length,
b = polygon[n - 1],
xa,
ya,
xb = b[0],
yb = b[1],
perimeter = 0;
while (++i < n) {
xa = xb;
ya = yb;
b = polygon[i];
xb = b[0];
yb = b[1];
xa -= xb;
ya -= yb;
perimeter += Math.hypot(xa, ya);
}
return perimeter;
}