cesiumDemo/Source/Workers/PolygonPipeline-e486c11c.js

/* This file is automatically rebuilt by the Cesium build process. */
define(['exports', './defined-26bd4a03', './Check-da037458', './freezeObject-2d83f591', './defaultValue-f2e68450', './Math-fa6e45cb', './Cartesian2-2a723276', './WebGLConstants-497deb20', './ComponentDatatype-69643096', './GeometryAttribute-ed359d71', './EllipsoidRhumbLine-c6cdbfd3'], function (exports, defined, Check, freezeObject, defaultValue, _Math, Cartesian2, WebGLConstants, ComponentDatatype, GeometryAttribute, EllipsoidRhumbLine) { 'use strict';

    function earcut(data, holeIndices, dim) {

        dim = dim || 2;

        var hasHoles = holeIndices && holeIndices.length,
            outerLen = hasHoles ? holeIndices[0] * dim : data.length,
            outerNode = linkedList(data, 0, outerLen, dim, true),
            triangles = [];

        if (!outerNode) return triangles;

        var minX, minY, maxX, maxY, x, y, size;

        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 (var 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 size are later used to transform coords into integers for z-order calculation
            size = Math.max(maxX - minX, maxY - minY);
        }

        earcutLinked(outerNode, triangles, dim, minX, minY, size);

        return triangles;
    }

    // create a circular doubly linked list from polygon points in the specified winding order
    function linkedList(data, start, end, dim, clockwise) {
        var 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;

        var 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) return null;
                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, size, pass) {
        if (!ear) return;

        // interlink polygon nodes in z-order
        if (!pass && size) indexCurve(ear, minX, minY, size);

        var stop = ear,
            prev, next;

        // iterate through ears, slicing them one by one
        while (ear.prev !== ear.next) {
            prev = ear.prev;
            next = ear.next;

            if (size ? isEarHashed(ear, minX, minY, size) : 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 vertice 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, size, 1);

                // if this didn't work, try curing all small self-intersections locally
                } else if (pass === 1) {
                    ear = cureLocalIntersections(ear, triangles, dim);
                    earcutLinked(ear, triangles, dim, minX, minY, size, 2);

                // as a last resort, try splitting the remaining polygon into two
                } else if (pass === 2) {
                    splitEarcut(ear, triangles, dim, minX, minY, size);
                }

                break;
            }
        }
    }

    // check whether a polygon node forms a valid ear with adjacent nodes
    function isEar(ear) {
        var 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
        var 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, size) {
        var 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
        var 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;
        var minZ = zOrder(minTX, minTY, minX, minY, size),
            maxZ = zOrder(maxTX, maxTY, minX, minY, size);

        // first look for points inside the triangle in increasing z-order
        var p = ear.nextZ;

        while (p && p.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.nextZ;
        }

        // then look for points in decreasing z-order
        p = ear.prevZ;

        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;
        }

        return true;
    }

    // go through all polygon nodes and cure small local self-intersections
    function cureLocalIntersections(start, triangles, dim) {
        var p = start;
        do {
            var 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 p;
    }

    // try splitting polygon into two and triangulate them independently
    function splitEarcut(start, triangles, dim, minX, minY, size) {
        // look for a valid diagonal that divides the polygon into two
        var a = start;
        do {
            var b = a.next.next;
            while (b !== a.prev) {
                if (a.i !== b.i && isValidDiagonal(a, b)) {
                    // split the polygon in two by the diagonal
                    var 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, size);
                    earcutLinked(c, triangles, dim, minX, minY, size);
                    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) {
        var queue = [],
            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) {
            var b = splitPolygon(outerNode, hole);
            filterPoints(b, b.next);
        }
    }

    // David Eberly's algorithm for finding a bridge between hole and outer polygon
    function findHoleBridge(hole, outerNode) {
        var p = outerNode,
            hx = hole.x,
            hy = hole.y,
            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) {
                var 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.prev; // hole touches outer segment; pick lower 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

        var stop = m,
            mx = m.x,
            my = m.y,
            tanMin = Infinity,
            tan;

        p = m.next;

        while (p !== stop) {
            if (hx >= p.x && p.x >= mx &&
                    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 ((tan < tanMin || (tan === tanMin && p.x > m.x)) && locallyInside(p, hole)) {
                    m = p;
                    tanMin = tan;
                }
            }

            p = p.next;
        }

        return m;
    }

    // interlink polygon nodes in z-order
    function indexCurve(start, minX, minY, size) {
        var p = start;
        do {
            if (p.z === null) p.z = zOrder(p.x, p.y, minX, minY, size);
            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) {
        var 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) {
                        e = q;
                        q = q.nextZ;
                        qSize--;
                    } else if (qSize === 0 || !q) {
                        e = p;
                        p = p.nextZ;
                        pSize--;
                    } else if (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 size of the data bounding box
    function zOrder(x, y, minX, minY, size) {
        // coords are transformed into non-negative 15-bit integer range
        x = 32767 * (x - minX) / size;
        y = 32767 * (y - minY) / size;

        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) {
        var p = start,
            leftmost = start;
        do {
            if (p.x < leftmost.x) 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) &&
               locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b);
    }

    // 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) {
        if ((equals(p1, q1) && equals(p2, q2)) ||
            (equals(p1, q2) && equals(p2, q1))) return true;
        return area(p1, q1, p2) > 0 !== area(p1, q1, q2) > 0 &&
               area(p2, q2, p1) > 0 !== area(p2, q2, q1) > 0;
    }

    // check if a polygon diagonal intersects any polygon segments
    function intersectsPolygon(a, b) {
        var 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) {
        var p = a,
            inside = false,
            px = (a.x + b.x) / 2,
            py = (a.y + b.y) / 2;
        do {
            if (((p.y > py) !== (p.next.y > py)) && (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) {
        var 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) {
        var 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) {
        // vertice index in coordinates array
        this.i = i;

        // vertex coordinates
        this.x = x;
        this.y = y;

        // previous and next vertice 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 = function (data, holeIndices, dim, triangles) {
        var hasHoles = holeIndices && holeIndices.length;
        var outerLen = hasHoles ? holeIndices[0] * dim : data.length;

        var polygonArea = Math.abs(signedArea(data, 0, outerLen, dim));
        if (hasHoles) {
            for (var i = 0, len = holeIndices.length; i < len; i++) {
                var start = holeIndices[i] * dim;
                var end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
                polygonArea -= Math.abs(signedArea(data, start, end, dim));
            }
        }

        var trianglesArea = 0;
        for (i = 0; i < triangles.length; i += 3) {
            var a = triangles[i] * dim;
            var b = triangles[i + 1] * dim;
            var 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) {
        var sum = 0;
        for (var 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 = function (data) {
        var dim = data[0][0].length,
            result = {vertices: [], holes: [], dimensions: dim},
            holeIndex = 0;

        for (var i = 0; i < data.length; i++) {
            for (var j = 0; j < data[i].length; j++) {
                for (var 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;
    };

    /**
         * Winding order defines the order of vertices for a triangle to be considered front-facing.
         *
         * @exports WindingOrder
         */
        var WindingOrder = {
            /**
             * Vertices are in clockwise order.
             *
             * @type {Number}
             * @constant
             */
            CLOCKWISE : WebGLConstants.WebGLConstants.CW,

            /**
             * Vertices are in counter-clockwise order.
             *
             * @type {Number}
             * @constant
             */
            COUNTER_CLOCKWISE : WebGLConstants.WebGLConstants.CCW,

            /**
             * @private
             */
            validate : function(windingOrder) {
                return windingOrder === WindingOrder.CLOCKWISE ||
                       windingOrder === WindingOrder.COUNTER_CLOCKWISE;
            }
        };
    var WindingOrder$1 = freezeObject.freezeObject(WindingOrder);

    var scaleToGeodeticHeightN = new Cartesian2.Cartesian3();
        var scaleToGeodeticHeightP = new Cartesian2.Cartesian3();

        /**
         * @private
         */
        var PolygonPipeline = {};

        /**
         * @exception {DeveloperError} At least three positions are required.
         */
        PolygonPipeline.computeArea2D = function(positions) {
            //>>includeStart('debug', pragmas.debug);
            Check.Check.defined('positions', positions);
            Check.Check.typeOf.number.greaterThanOrEquals('positions.length', positions.length, 3);
            //>>includeEnd('debug');

            var length = positions.length;
            var area = 0.0;

            for ( var i0 = length - 1, i1 = 0; i1 < length; i0 = i1++) {
                var v0 = positions[i0];
                var v1 = positions[i1];

                area += (v0.x * v1.y) - (v1.x * v0.y);
            }

            return area * 0.5;
        };

        /**
         * @returns {WindingOrder} The winding order.
         *
         * @exception {DeveloperError} At least three positions are required.
         */
        PolygonPipeline.computeWindingOrder2D = function(positions) {
            var area = PolygonPipeline.computeArea2D(positions);
            return (area > 0.0) ? WindingOrder$1.COUNTER_CLOCKWISE : WindingOrder$1.CLOCKWISE;
        };

        /**
         * Triangulate a polygon.
         *
         * @param {Cartesian2[]} positions Cartesian2 array containing the vertices of the polygon
         * @param {Number[]} [holes] An array of the staring indices of the holes.
         * @returns {Number[]} Index array representing triangles that fill the polygon
         */
        PolygonPipeline.triangulate = function(positions, holes) {
            //>>includeStart('debug', pragmas.debug);
            Check.Check.defined('positions', positions);
            //>>includeEnd('debug');

            var flattenedPositions = Cartesian2.Cartesian2.packArray(positions);
            return earcut(flattenedPositions, holes, 2);
        };

        var subdivisionV0Scratch = new Cartesian2.Cartesian3();
        var subdivisionV1Scratch = new Cartesian2.Cartesian3();
        var subdivisionV2Scratch = new Cartesian2.Cartesian3();
        var subdivisionS0Scratch = new Cartesian2.Cartesian3();
        var subdivisionS1Scratch = new Cartesian2.Cartesian3();
        var subdivisionS2Scratch = new Cartesian2.Cartesian3();
        var subdivisionMidScratch = new Cartesian2.Cartesian3();

        /**
         * Subdivides positions and raises points to the surface of the ellipsoid.
         *
         * @param {Ellipsoid} ellipsoid The ellipsoid the polygon in on.
         * @param {Cartesian3[]} positions An array of {@link Cartesian3} positions of the polygon.
         * @param {Number[]} indices An array of indices that determines the triangles in the polygon.
         * @param {Number} [granularity=CesiumMath.RADIANS_PER_DEGREE] The distance, in radians, between each latitude and longitude. Determines the number of positions in the buffer.
         *
         * @exception {DeveloperError} At least three indices are required.
         * @exception {DeveloperError} The number of indices must be divisable by three.
         * @exception {DeveloperError} Granularity must be greater than zero.
         */
        PolygonPipeline.computeSubdivision = function(ellipsoid, positions, indices, granularity) {
            granularity = defaultValue.defaultValue(granularity, _Math.CesiumMath.RADIANS_PER_DEGREE);

            //>>includeStart('debug', pragmas.debug);
            Check.Check.typeOf.object('ellipsoid', ellipsoid);
            Check.Check.defined('positions', positions);
            Check.Check.defined('indices', indices);
            Check.Check.typeOf.number.greaterThanOrEquals('indices.length', indices.length, 3);
            Check.Check.typeOf.number.equals('indices.length % 3', '0', indices.length % 3, 0);
            Check.Check.typeOf.number.greaterThan('granularity', granularity, 0.0);
            //>>includeEnd('debug');

            // triangles that need (or might need) to be subdivided.
            var triangles = indices.slice(0);

            // New positions due to edge splits are appended to the positions list.
            var i;
            var length = positions.length;
            var subdividedPositions = new Array(length * 3);
            var q = 0;
            for (i = 0; i < length; i++) {
                var item = positions[i];
                subdividedPositions[q++] = item.x;
                subdividedPositions[q++] = item.y;
                subdividedPositions[q++] = item.z;
            }

            var subdividedIndices = [];

            // Used to make sure shared edges are not split more than once.
            var edges = {};

            var radius = ellipsoid.maximumRadius;
            var minDistance = _Math.CesiumMath.chordLength(granularity, radius);
            var minDistanceSqrd = minDistance * minDistance;

            while (triangles.length > 0) {
                var i2 = triangles.pop();
                var i1 = triangles.pop();
                var i0 = triangles.pop();

                var v0 = Cartesian2.Cartesian3.fromArray(subdividedPositions, i0 * 3, subdivisionV0Scratch);
                var v1 = Cartesian2.Cartesian3.fromArray(subdividedPositions, i1 * 3, subdivisionV1Scratch);
                var v2 = Cartesian2.Cartesian3.fromArray(subdividedPositions, i2 * 3, subdivisionV2Scratch);

                var s0 = Cartesian2.Cartesian3.multiplyByScalar(Cartesian2.Cartesian3.normalize(v0, subdivisionS0Scratch), radius, subdivisionS0Scratch);
                var s1 = Cartesian2.Cartesian3.multiplyByScalar(Cartesian2.Cartesian3.normalize(v1, subdivisionS1Scratch), radius, subdivisionS1Scratch);
                var s2 = Cartesian2.Cartesian3.multiplyByScalar(Cartesian2.Cartesian3.normalize(v2, subdivisionS2Scratch), radius, subdivisionS2Scratch);

                var g0 = Cartesian2.Cartesian3.magnitudeSquared(Cartesian2.Cartesian3.subtract(s0, s1, subdivisionMidScratch));
                var g1 = Cartesian2.Cartesian3.magnitudeSquared(Cartesian2.Cartesian3.subtract(s1, s2, subdivisionMidScratch));
                var g2 = Cartesian2.Cartesian3.magnitudeSquared(Cartesian2.Cartesian3.subtract(s2, s0, subdivisionMidScratch));

                var max = Math.max(g0, g1, g2);
                var edge;
                var mid;

                // if the max length squared of a triangle edge is greater than the chord length of squared
                // of the granularity, subdivide the triangle
                if (max > minDistanceSqrd) {
                    if (g0 === max) {
                        edge = Math.min(i0, i1) + ' ' + Math.max(i0, i1);

                        i = edges[edge];
                        if (!defined.defined(i)) {
                            mid = Cartesian2.Cartesian3.add(v0, v1, subdivisionMidScratch);
                            Cartesian2.Cartesian3.multiplyByScalar(mid, 0.5, mid);
                            subdividedPositions.push(mid.x, mid.y, mid.z);
                            i = subdividedPositions.length / 3 - 1;
                            edges[edge] = i;
                        }

                        triangles.push(i0, i, i2);
                        triangles.push(i, i1, i2);
                    } else if (g1 === max) {
                        edge = Math.min(i1, i2) + ' ' + Math.max(i1, i2);

                        i = edges[edge];
                        if (!defined.defined(i)) {
                            mid = Cartesian2.Cartesian3.add(v1, v2, subdivisionMidScratch);
                            Cartesian2.Cartesian3.multiplyByScalar(mid, 0.5, mid);
                            subdividedPositions.push(mid.x, mid.y, mid.z);
                            i = subdividedPositions.length / 3 - 1;
                            edges[edge] = i;
                        }

                        triangles.push(i1, i, i0);
                        triangles.push(i, i2, i0);
                    } else if (g2 === max) {
                        edge = Math.min(i2, i0) + ' ' + Math.max(i2, i0);

                        i = edges[edge];
                        if (!defined.defined(i)) {
                            mid = Cartesian2.Cartesian3.add(v2, v0, subdivisionMidScratch);
                            Cartesian2.Cartesian3.multiplyByScalar(mid, 0.5, mid);
                            subdividedPositions.push(mid.x, mid.y, mid.z);
                            i = subdividedPositions.length / 3 - 1;
                            edges[edge] = i;
                        }

                        triangles.push(i2, i, i1);
                        triangles.push(i, i0, i1);
                    }
                } else {
                    subdividedIndices.push(i0);
                    subdividedIndices.push(i1);
                    subdividedIndices.push(i2);
                }
            }

            return new GeometryAttribute.Geometry({
                attributes : {
                    position : new GeometryAttribute.GeometryAttribute({
                        componentDatatype : ComponentDatatype.ComponentDatatype.DOUBLE,
                        componentsPerAttribute : 3,
                        values : subdividedPositions
                    })
                },
                indices : subdividedIndices,
                primitiveType : GeometryAttribute.PrimitiveType.TRIANGLES
            });
        };

        var subdivisionC0Scratch = new Cartesian2.Cartographic();
        var subdivisionC1Scratch = new Cartesian2.Cartographic();
        var subdivisionC2Scratch = new Cartesian2.Cartographic();
        var subdivisionCartographicScratch = new Cartesian2.Cartographic();

        /**
         * Subdivides positions on rhumb lines and raises points to the surface of the ellipsoid.
         *
         * @param {Ellipsoid} ellipsoid The ellipsoid the polygon in on.
         * @param {Cartesian3[]} positions An array of {@link Cartesian3} positions of the polygon.
         * @param {Number[]} indices An array of indices that determines the triangles in the polygon.
         * @param {Number} [granularity=CesiumMath.RADIANS_PER_DEGREE] The distance, in radians, between each latitude and longitude. Determines the number of positions in the buffer.
         *
         * @exception {DeveloperError} At least three indices are required.
         * @exception {DeveloperError} The number of indices must be divisable by three.
         * @exception {DeveloperError} Granularity must be greater than zero.
         */
        PolygonPipeline.computeRhumbLineSubdivision = function(ellipsoid, positions, indices, granularity) {
            granularity = defaultValue.defaultValue(granularity, _Math.CesiumMath.RADIANS_PER_DEGREE);

            //>>includeStart('debug', pragmas.debug);
            Check.Check.typeOf.object('ellipsoid', ellipsoid);
            Check.Check.defined('positions', positions);
            Check.Check.defined('indices', indices);
            Check.Check.typeOf.number.greaterThanOrEquals('indices.length', indices.length, 3);
            Check.Check.typeOf.number.equals('indices.length % 3', '0', indices.length % 3, 0);
            Check.Check.typeOf.number.greaterThan('granularity', granularity, 0.0);
            //>>includeEnd('debug');

            // triangles that need (or might need) to be subdivided.
            var triangles = indices.slice(0);

            // New positions due to edge splits are appended to the positions list.
            var i;
            var length = positions.length;
            var subdividedPositions = new Array(length * 3);
            var q = 0;
            for (i = 0; i < length; i++) {
                var item = positions[i];
                subdividedPositions[q++] = item.x;
                subdividedPositions[q++] = item.y;
                subdividedPositions[q++] = item.z;
            }

            var subdividedIndices = [];

            // Used to make sure shared edges are not split more than once.
            var edges = {};

            var radius = ellipsoid.maximumRadius;
            var minDistance = _Math.CesiumMath.chordLength(granularity, radius);

            var rhumb0 = new EllipsoidRhumbLine.EllipsoidRhumbLine(undefined, undefined, ellipsoid);
            var rhumb1 = new EllipsoidRhumbLine.EllipsoidRhumbLine(undefined, undefined, ellipsoid);
            var rhumb2 = new EllipsoidRhumbLine.EllipsoidRhumbLine(undefined, undefined, ellipsoid);

            while (triangles.length > 0) {
                var i2 = triangles.pop();
                var i1 = triangles.pop();
                var i0 = triangles.pop();

                var v0 = Cartesian2.Cartesian3.fromArray(subdividedPositions, i0 * 3, subdivisionV0Scratch);
                var v1 = Cartesian2.Cartesian3.fromArray(subdividedPositions, i1 * 3, subdivisionV1Scratch);
                var v2 = Cartesian2.Cartesian3.fromArray(subdividedPositions, i2 * 3, subdivisionV2Scratch);

                var c0 = ellipsoid.cartesianToCartographic(v0, subdivisionC0Scratch);
                var c1 = ellipsoid.cartesianToCartographic(v1, subdivisionC1Scratch);
                var c2 = ellipsoid.cartesianToCartographic(v2, subdivisionC2Scratch);

                rhumb0.setEndPoints(c0, c1);
                var g0 = rhumb0.surfaceDistance;
                rhumb1.setEndPoints(c1, c2);
                var g1 = rhumb1.surfaceDistance;
                rhumb2.setEndPoints(c2, c0);
                var g2 = rhumb2.surfaceDistance;

                var max = Math.max(g0, g1, g2);
                var edge;
                var mid;
                var midHeight;
                var midCartesian3;

                // if the max length squared of a triangle edge is greater than granularity, subdivide the triangle
                if (max > minDistance) {
                    if (g0 === max) {
                        edge = Math.min(i0, i1) + ' ' + Math.max(i0, i1);

                        i = edges[edge];
                        if (!defined.defined(i)) {
                            mid = rhumb0.interpolateUsingFraction(0.5, subdivisionCartographicScratch);
                            midHeight = (c0.height + c1.height) * 0.5;
                            midCartesian3 = Cartesian2.Cartesian3.fromRadians(mid.longitude, mid.latitude, midHeight, ellipsoid, subdivisionMidScratch);
                            subdividedPositions.push(midCartesian3.x, midCartesian3.y, midCartesian3.z);
                            i = subdividedPositions.length / 3 - 1;
                            edges[edge] = i;
                        }

                        triangles.push(i0, i, i2);
                        triangles.push(i, i1, i2);
                    } else if (g1 === max) {
                        edge = Math.min(i1, i2) + ' ' + Math.max(i1, i2);

                        i = edges[edge];
                        if (!defined.defined(i)) {
                            mid = rhumb1.interpolateUsingFraction(0.5, subdivisionCartographicScratch);
                            midHeight = (c1.height + c2.height) * 0.5;
                            midCartesian3 = Cartesian2.Cartesian3.fromRadians(mid.longitude, mid.latitude, midHeight, ellipsoid, subdivisionMidScratch);
                            subdividedPositions.push(midCartesian3.x, midCartesian3.y, midCartesian3.z);
                            i = subdividedPositions.length / 3 - 1;
                            edges[edge] = i;
                        }

                        triangles.push(i1, i, i0);
                        triangles.push(i, i2, i0);
                    } else if (g2 === max) {
                        edge = Math.min(i2, i0) + ' ' + Math.max(i2, i0);

                        i = edges[edge];
                        if (!defined.defined(i)) {
                            mid = rhumb2.interpolateUsingFraction(0.5, subdivisionCartographicScratch);
                            midHeight = (c2.height + c0.height) * 0.5;
                            midCartesian3 = Cartesian2.Cartesian3.fromRadians(mid.longitude, mid.latitude, midHeight, ellipsoid, subdivisionMidScratch);
                            subdividedPositions.push(midCartesian3.x, midCartesian3.y, midCartesian3.z);
                            i = subdividedPositions.length / 3 - 1;
                            edges[edge] = i;
                        }

                        triangles.push(i2, i, i1);
                        triangles.push(i, i0, i1);
                    }
                } else {
                    subdividedIndices.push(i0);
                    subdividedIndices.push(i1);
                    subdividedIndices.push(i2);
                }
            }

            return new GeometryAttribute.Geometry({
                attributes : {
                    position : new GeometryAttribute.GeometryAttribute({
                        componentDatatype : ComponentDatatype.ComponentDatatype.DOUBLE,
                        componentsPerAttribute : 3,
                        values : subdividedPositions
                    })
                },
                indices : subdividedIndices,
                primitiveType : GeometryAttribute.PrimitiveType.TRIANGLES
            });
        };

        /**
         * Scales each position of a geometry's position attribute to a height, in place.
         *
         * @param {Number[]} positions The array of numbers representing the positions to be scaled
         * @param {Number} [height=0.0] The desired height to add to the positions
         * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the positions lie.
         * @param {Boolean} [scaleToSurface=true] <code>true</code> if the positions need to be scaled to the surface before the height is added.
         * @returns {Number[]} The input array of positions, scaled to height
         */
        PolygonPipeline.scaleToGeodeticHeight = function(positions, height, ellipsoid, scaleToSurface) {
            ellipsoid = defaultValue.defaultValue(ellipsoid, Cartesian2.Ellipsoid.WGS84);

            var n = scaleToGeodeticHeightN;
            var p = scaleToGeodeticHeightP;

            height = defaultValue.defaultValue(height, 0.0);
            scaleToSurface = defaultValue.defaultValue(scaleToSurface, true);

            if (defined.defined(positions)) {
                var length = positions.length;

                for ( var i = 0; i < length; i += 3) {
                    Cartesian2.Cartesian3.fromArray(positions, i, p);

                    if (scaleToSurface) {
                        p = ellipsoid.scaleToGeodeticSurface(p, p);
                    }

                    if (height !== 0) {
                        n = ellipsoid.geodeticSurfaceNormal(p, n);

                        Cartesian2.Cartesian3.multiplyByScalar(n, height, n);
                        Cartesian2.Cartesian3.add(p, n, p);
                    }

                    positions[i] = p.x;
                    positions[i + 1] = p.y;
                    positions[i + 2] = p.z;
                }
            }

            return positions;
        };

    exports.PolygonPipeline = PolygonPipeline;
    exports.WindingOrder = WindingOrder$1;

});