arcade-physics
Version:
Use Arcade Physics without Phaser.
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JavaScript
"use strict";
/**
* @author Richard Davey <rich@photonstorm.com>
* @copyright 2020 Photon Storm Ltd.
* @license {@link https://opensource.org/licenses/MIT|MIT License}
*/
Object.defineProperty(exports, "__esModule", { value: true });
/**
* This module implements a modified ear slicing algorithm, optimized by z-order curve hashing and extended to
* handle holes, twisted polygons, degeneracies and self-intersections in a way that doesn't guarantee correctness
* of triangulation, but attempts to always produce acceptable results for practical data.
*
* Example:
*
* ```javascript
* const triangles = Phaser.Geom.Polygon.Earcut([10,0, 0,50, 60,60, 70,10]); // returns [1,0,3, 3,2,1]
* ```
*
* Each group of three vertex indices in the resulting array forms a triangle.
*
* ```javascript
* // triangulating a polygon with a hole
* earcut([0,0, 100,0, 100,100, 0,100, 20,20, 80,20, 80,80, 20,80], [4]);
* // [3,0,4, 5,4,0, 3,4,7, 5,0,1, 2,3,7, 6,5,1, 2,7,6, 6,1,2]
*
* // triangulating a polygon with 3d coords
* earcut([10,0,1, 0,50,2, 60,60,3, 70,10,4], null, 3);
* // [1,0,3, 3,2,1]
* ```
*
* If you pass a single vertex as a hole, Earcut treats it as a Steiner point.
*
* If your input is a multi-dimensional array (e.g. GeoJSON Polygon), you can convert it to the format
* expected by Earcut with `Phaser.Geom.Polygon.Earcut.flatten`:
*
* ```javascript
* var data = earcut.flatten(geojson.geometry.coordinates);
* var triangles = earcut(data.vertices, data.holes, data.dimensions);
* ```
*
* After getting a triangulation, you can verify its correctness with `Phaser.Geom.Polygon.Earcut.deviation`:
*
* ```javascript
* var deviation = earcut.deviation(vertices, holes, dimensions, triangles);
* ```
* Returns the relative difference between the total area of triangles and the area of the input polygon.
* 0 means the triangulation is fully correct.
*
* For more information see https://github.com/mapbox/earcut
*
* @function Phaser.Geom.Polygon.Earcut
* @since 3.50.0
*
* @param {number[]} data - A flat array of vertex coordinate, like [x0,y0, x1,y1, x2,y2, ...]
* @param {number[]} [holeIndices] - An array of hole indices if any (e.g. [5, 8] for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11).
* @param {number} [dimensions=2] - The number of coordinates per vertex in the input array (2 by default).
*
* @return {number[]} An array of triangulated data.
*/
// Earcut 2.2.2 (January 21st 2020)
/*
* ISC License
*
* Copyright (c) 2016, Mapbox
*
* 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.
*/
function earcut(data, holeIndices, dim) {
dim = dim || 2;
const hasHoles = holeIndices && holeIndices.length;
const outerLen = hasHoles ? holeIndices[0] * dim : data.length;
let outerNode = linkedList(data, 0, outerLen, dim, true);
const triangles = [];
if (!outerNode || outerNode.next === outerNode.prev)
return triangles;
let minX, minY, maxX, maxY, x, y, invSize;
if (hasHoles)
outerNode = eliminateHoles(data, holeIndices, outerNode, dim);
// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
if (data.length > 80 * dim) {
minX = maxX = data[0];
minY = maxY = data[1];
for (let i = dim; i < outerLen; i += dim) {
x = data[i];
y = data[i + 1];
if (x < minX)
minX = x;
if (y < minY)
minY = y;
if (x > maxX)
maxX = x;
if (y > maxY)
maxY = y;
}
// minX, minY and invSize are later used to transform coords into integers for z-order calculation
invSize = Math.max(maxX - minX, maxY - minY);
invSize = invSize !== 0 ? 1 / invSize : 0;
}
earcutLinked(outerNode, triangles, dim, minX, minY, invSize);
return triangles;
}
// create a circular doubly linked list from polygon points in the specified winding order
function linkedList(data, start, end, dim, clockwise) {
let i, last;
if (clockwise === signedArea(data, start, end, dim) > 0) {
for (i = start; i < end; i += dim)
last = insertNode(i, data[i], data[i + 1], last);
}
else {
for (i = end - dim; i >= start; i -= dim)
last = insertNode(i, data[i], data[i + 1], last);
}
if (last && equals(last, last.next)) {
removeNode(last);
last = last.next;
}
return last;
}
// eliminate colinear or duplicate points
function filterPoints(start, end) {
if (!start)
return start;
if (!end)
end = start;
let p = start, again;
do {
again = false;
if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) {
removeNode(p);
p = end = p.prev;
if (p === p.next)
break;
again = true;
}
else {
p = p.next;
}
} while (again || p !== end);
return end;
}
// main ear slicing loop which triangulates a polygon (given as a linked list)
function earcutLinked(ear, triangles, dim, minX, minY, invSize, pass) {
if (!ear)
return;
// interlink polygon nodes in z-order
if (!pass && invSize)
indexCurve(ear, minX, minY, invSize);
let stop = ear, prev, next;
// iterate through ears, slicing them one by one
while (ear.prev !== ear.next) {
prev = ear.prev;
next = ear.next;
if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) {
// cut off the triangle
triangles.push(prev.i / dim);
triangles.push(ear.i / dim);
triangles.push(next.i / dim);
removeNode(ear);
// skipping the next vertex leads to less sliver triangles
ear = next.next;
stop = next.next;
continue;
}
ear = next;
// if we looped through the whole remaining polygon and can't find any more ears
if (ear === stop) {
// try filtering points and slicing again
if (!pass) {
earcutLinked(filterPoints(ear), triangles, dim, minX, minY, invSize, 1);
// if this didn't work, try curing all small self-intersections locally
}
else if (pass === 1) {
ear = cureLocalIntersections(filterPoints(ear), triangles, dim);
earcutLinked(ear, triangles, dim, minX, minY, invSize, 2);
// as a last resort, try splitting the remaining polygon into two
}
else if (pass === 2) {
splitEarcut(ear, triangles, dim, minX, minY, invSize);
}
break;
}
}
}
// check whether a polygon node forms a valid ear with adjacent nodes
function isEar(ear) {
const a = ear.prev, b = ear, c = ear.next;
if (area(a, b, c) >= 0)
return false; // reflex, can't be an ear
// now make sure we don't have other points inside the potential ear
let p = ear.next.next;
while (p !== ear.prev) {
if (pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) && area(p.prev, p, p.next) >= 0)
return false;
p = p.next;
}
return true;
}
function isEarHashed(ear, minX, minY, invSize) {
const a = ear.prev, b = ear, c = ear.next;
if (area(a, b, c) >= 0)
return false; // reflex, can't be an ear
// triangle bbox; min & max are calculated like this for speed
const minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : b.x < c.x ? b.x : c.x, minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : b.y < c.y ? b.y : c.y, maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : b.x > c.x ? b.x : c.x, maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : b.y > c.y ? b.y : c.y;
// z-order range for the current triangle bbox;
const minZ = zOrder(minTX, minTY, minX, minY, invSize), maxZ = zOrder(maxTX, maxTY, minX, minY, invSize);
let p = ear.prevZ, n = ear.nextZ;
// look for points inside the triangle in both directions
while (p && p.z >= minZ && n && n.z <= maxZ) {
if (p !== ear.prev &&
p !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0)
return false;
p = p.prevZ;
if (n !== ear.prev &&
n !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&
area(n.prev, n, n.next) >= 0)
return false;
n = n.nextZ;
}
// look for remaining points in decreasing z-order
while (p && p.z >= minZ) {
if (p !== ear.prev &&
p !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0)
return false;
p = p.prevZ;
}
// look for remaining points in increasing z-order
while (n && n.z <= maxZ) {
if (n !== ear.prev &&
n !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&
area(n.prev, n, n.next) >= 0)
return false;
n = n.nextZ;
}
return true;
}
// go through all polygon nodes and cure small local self-intersections
function cureLocalIntersections(start, triangles, dim) {
let p = start;
do {
const a = p.prev, b = p.next.next;
if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) {
triangles.push(a.i / dim);
triangles.push(p.i / dim);
triangles.push(b.i / dim);
// remove two nodes involved
removeNode(p);
removeNode(p.next);
p = start = b;
}
p = p.next;
} while (p !== start);
return filterPoints(p);
}
// try splitting polygon into two and triangulate them independently
function splitEarcut(start, triangles, dim, minX, minY, invSize) {
// look for a valid diagonal that divides the polygon into two
let a = start;
do {
let b = a.next.next;
while (b !== a.prev) {
if (a.i !== b.i && isValidDiagonal(a, b)) {
// split the polygon in two by the diagonal
let c = splitPolygon(a, b);
// filter colinear points around the cuts
a = filterPoints(a, a.next);
c = filterPoints(c, c.next);
// run earcut on each half
earcutLinked(a, triangles, dim, minX, minY, invSize);
earcutLinked(c, triangles, dim, minX, minY, invSize);
return;
}
b = b.next;
}
a = a.next;
} while (a !== start);
}
// link every hole into the outer loop, producing a single-ring polygon without holes
function eliminateHoles(data, holeIndices, outerNode, dim) {
const queue = [];
let i;
let len;
let start;
let end;
let list;
for (i = 0, len = holeIndices.length; i < len; i++) {
start = holeIndices[i] * dim;
end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
list = linkedList(data, start, end, dim, false);
if (list === list.next)
list.steiner = true;
queue.push(getLeftmost(list));
}
queue.sort(compareX);
// process holes from left to right
for (i = 0; i < queue.length; i++) {
eliminateHole(queue[i], outerNode);
outerNode = filterPoints(outerNode, outerNode.next);
}
return outerNode;
}
function compareX(a, b) {
return a.x - b.x;
}
// find a bridge between vertices that connects hole with an outer ring and and link it
function eliminateHole(hole, outerNode) {
outerNode = findHoleBridge(hole, outerNode);
if (outerNode) {
const b = splitPolygon(outerNode, hole);
// filter collinear points around the cuts
filterPoints(outerNode, outerNode.next);
filterPoints(b, b.next);
}
}
// David Eberly's algorithm for finding a bridge between hole and outer polygon
function findHoleBridge(hole, outerNode) {
let p = outerNode;
const hx = hole.x;
const hy = hole.y;
let qx = -Infinity;
let m;
// find a segment intersected by a ray from the hole's leftmost point to the left;
// segment's endpoint with lesser x will be potential connection point
do {
if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) {
const x = p.x + ((hy - p.y) * (p.next.x - p.x)) / (p.next.y - p.y);
if (x <= hx && x > qx) {
qx = x;
if (x === hx) {
if (hy === p.y)
return p;
if (hy === p.next.y)
return p.next;
}
m = p.x < p.next.x ? p : p.next;
}
}
p = p.next;
} while (p !== outerNode);
if (!m)
return null;
if (hx === qx)
return m; // hole touches outer segment; pick leftmost endpoint
// look for points inside the triangle of hole point, segment intersection and endpoint;
// if there are no points found, we have a valid connection;
// otherwise choose the point of the minimum angle with the ray as connection point
const stop = m;
const mx = m.x;
const my = m.y;
let tanMin = Infinity;
let tan;
p = m;
do {
if (hx >= p.x &&
p.x >= mx &&
hx !== p.x &&
pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) {
tan = Math.abs(hy - p.y) / (hx - p.x); // tangential
if (locallyInside(p, hole) &&
(tan < tanMin || (tan === tanMin && (p.x > m.x || (p.x === m.x && sectorContainsSector(m, p)))))) {
m = p;
tanMin = tan;
}
}
p = p.next;
} while (p !== stop);
return m;
}
// whether sector in vertex m contains sector in vertex p in the same coordinates
function sectorContainsSector(m, p) {
return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0;
}
// interlink polygon nodes in z-order
function indexCurve(start, minX, minY, invSize) {
let p = start;
do {
if (p.z === null)
p.z = zOrder(p.x, p.y, minX, minY, invSize);
p.prevZ = p.prev;
p.nextZ = p.next;
p = p.next;
} while (p !== start);
p.prevZ.nextZ = null;
p.prevZ = null;
sortLinked(p);
}
// Simon Tatham's linked list merge sort algorithm
// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
function sortLinked(list) {
let i, p, q, e, tail, numMerges, pSize, qSize, inSize = 1;
do {
p = list;
list = null;
tail = null;
numMerges = 0;
while (p) {
numMerges++;
q = p;
pSize = 0;
for (i = 0; i < inSize; i++) {
pSize++;
q = q.nextZ;
if (!q)
break;
}
qSize = inSize;
while (pSize > 0 || (qSize > 0 && q)) {
if (pSize !== 0 && (qSize === 0 || !q || p.z <= q.z)) {
e = p;
p = p.nextZ;
pSize--;
}
else {
e = q;
q = q.nextZ;
qSize--;
}
if (tail)
tail.nextZ = e;
else
list = e;
e.prevZ = tail;
tail = e;
}
p = q;
}
tail.nextZ = null;
inSize *= 2;
} while (numMerges > 1);
return list;
}
// z-order of a point given coords and inverse of the longer side of data bbox
function zOrder(x, y, minX, minY, invSize) {
// coords are transformed into non-negative 15-bit integer range
x = 32767 * (x - minX) * invSize;
y = 32767 * (y - minY) * invSize;
x = (x | (x << 8)) & 0x00ff00ff;
x = (x | (x << 4)) & 0x0f0f0f0f;
x = (x | (x << 2)) & 0x33333333;
x = (x | (x << 1)) & 0x55555555;
y = (y | (y << 8)) & 0x00ff00ff;
y = (y | (y << 4)) & 0x0f0f0f0f;
y = (y | (y << 2)) & 0x33333333;
y = (y | (y << 1)) & 0x55555555;
return x | (y << 1);
}
// find the leftmost node of a polygon ring
function getLeftmost(start) {
let p = start, leftmost = start;
do {
if (p.x < leftmost.x || (p.x === leftmost.x && p.y < leftmost.y))
leftmost = p;
p = p.next;
} while (p !== start);
return leftmost;
}
// check if a point lies within a convex triangle
function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
return ((cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
(ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
(bx - px) * (cy - py) - (cx - px) * (by - py) >= 0);
}
// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
function isValidDiagonal(a, b) {
return (a.next.i !== b.i &&
a.prev.i !== b.i &&
!intersectsPolygon(a, b) && // dones't intersect other edges
((locallyInside(a, b) &&
locallyInside(b, a) &&
middleInside(a, b) && // locally visible
(area(a.prev, a, b.prev) || area(a, b.prev, b))) || // does not create opposite-facing sectors
(equals(a, b) && area(a.prev, a, a.next) > 0 && area(b.prev, b, b.next) > 0))); // special zero-length case
}
// signed area of a triangle
function area(p, q, r) {
return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
}
// check if two points are equal
function equals(p1, p2) {
return p1.x === p2.x && p1.y === p2.y;
}
// check if two segments intersect
function intersects(p1, q1, p2, q2) {
const o1 = sign(area(p1, q1, p2));
const o2 = sign(area(p1, q1, q2));
const o3 = sign(area(p2, q2, p1));
const o4 = sign(area(p2, q2, q1));
if (o1 !== o2 && o3 !== o4)
return true; // general case
if (o1 === 0 && onSegment(p1, p2, q1))
return true; // p1, q1 and p2 are collinear and p2 lies on p1q1
if (o2 === 0 && onSegment(p1, q2, q1))
return true; // p1, q1 and q2 are collinear and q2 lies on p1q1
if (o3 === 0 && onSegment(p2, p1, q2))
return true; // p2, q2 and p1 are collinear and p1 lies on p2q2
if (o4 === 0 && onSegment(p2, q1, q2))
return true; // p2, q2 and q1 are collinear and q1 lies on p2q2
return false;
}
// for collinear points p, q, r, check if point q lies on segment pr
function onSegment(p, q, r) {
return (q.x <= Math.max(p.x, r.x) && q.x >= Math.min(p.x, r.x) && q.y <= Math.max(p.y, r.y) && q.y >= Math.min(p.y, r.y));
}
function sign(num) {
return num > 0 ? 1 : num < 0 ? -1 : 0;
}
// check if a polygon diagonal intersects any polygon segments
function intersectsPolygon(a, b) {
let p = a;
do {
if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i && intersects(p, p.next, a, b))
return true;
p = p.next;
} while (p !== a);
return false;
}
// check if a polygon diagonal is locally inside the polygon
function locallyInside(a, b) {
return area(a.prev, a, a.next) < 0
? area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0
: area(a, b, a.prev) < 0 || area(a, a.next, b) < 0;
}
// check if the middle point of a polygon diagonal is inside the polygon
function middleInside(a, b) {
let p = a;
let inside = false;
const px = (a.x + b.x) / 2;
const py = (a.y + b.y) / 2;
do {
if (p.y > py !== p.next.y > py && p.next.y !== p.y && px < ((p.next.x - p.x) * (py - p.y)) / (p.next.y - p.y) + p.x)
inside = !inside;
p = p.next;
} while (p !== a);
return inside;
}
// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two;
// if one belongs to the outer ring and another to a hole, it merges it into a single ring
function splitPolygon(a, b) {
const a2 = new Node(a.i, a.x, a.y), b2 = new Node(b.i, b.x, b.y), an = a.next, bp = b.prev;
a.next = b;
b.prev = a;
a2.next = an;
an.prev = a2;
b2.next = a2;
a2.prev = b2;
bp.next = b2;
b2.prev = bp;
return b2;
}
// create a node and optionally link it with previous one (in a circular doubly linked list)
function insertNode(i, x, y, last) {
const p = new Node(i, x, y);
if (!last) {
p.prev = p;
p.next = p;
}
else {
p.next = last.next;
p.prev = last;
last.next.prev = p;
last.next = p;
}
return p;
}
function removeNode(p) {
p.next.prev = p.prev;
p.prev.next = p.next;
if (p.prevZ)
p.prevZ.nextZ = p.nextZ;
if (p.nextZ)
p.nextZ.prevZ = p.prevZ;
}
function Node(i, x, y) {
// vertex index in coordinates array
this.i = i;
// vertex coordinates
this.x = x;
this.y = y;
// previous and next vertex nodes in a polygon ring
this.prev = null;
this.next = null;
// z-order curve value
this.z = null;
// previous and next nodes in z-order
this.prevZ = null;
this.nextZ = null;
// indicates whether this is a steiner point
this.steiner = false;
}
// return a percentage difference between the polygon area and its triangulation area;
// used to verify correctness of triangulation
earcut.deviation = (data, holeIndices, dim, triangles) => {
const hasHoles = holeIndices && holeIndices.length;
const outerLen = hasHoles ? holeIndices[0] * dim : data.length;
let polygonArea = Math.abs(signedArea(data, 0, outerLen, dim));
if (hasHoles) {
for (var i = 0, len = holeIndices.length; i < len; i++) {
const start = holeIndices[i] * dim;
const end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
polygonArea -= Math.abs(signedArea(data, start, end, dim));
}
}
let trianglesArea = 0;
for (i = 0; i < triangles.length; i += 3) {
const a = triangles[i] * dim;
const b = triangles[i + 1] * dim;
const c = triangles[i + 2] * dim;
trianglesArea += Math.abs((data[a] - data[c]) * (data[b + 1] - data[a + 1]) - (data[a] - data[b]) * (data[c + 1] - data[a + 1]));
}
return polygonArea === 0 && trianglesArea === 0 ? 0 : Math.abs((trianglesArea - polygonArea) / polygonArea);
};
function signedArea(data, start, end, dim) {
let sum = 0;
for (let i = start, j = end - dim; i < end; i += dim) {
sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
j = i;
}
return sum;
}
// turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts
earcut.flatten = data => {
const dim = data[0][0].length;
const result = { vertices: [], holes: [], dimensions: dim };
let holeIndex = 0;
for (let i = 0; i < data.length; i++) {
for (let j = 0; j < data[i].length; j++) {
for (let d = 0; d < dim; d++)
result.vertices.push(data[i][j][d]);
}
if (i > 0) {
holeIndex += data[i - 1].length;
result.holes.push(holeIndex);
}
}
return result;
};
exports.default = earcut;
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