/** * 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 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 ) && // 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, 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 };