/**
* Port from https://github.com/mapbox/earcut (v2.2.2)
*/
const Earcut = {
triangulate: function ( data, holeIndices, 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, len, start, end, 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 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, 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,
mx = m.x,
my = m.y;
let tanMin = Infinity, 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 ) && // doesn'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,
inside = false;
const px = ( a.x + b.x ) / 2,
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;
}
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;
}
export { Earcut };
