gojs/extensionsJSM/VirtualizedPackedLayout.js

/*
*  Copyright (C) 1998-2021 by Northwoods Software Corporation. All Rights Reserved.
*/
/*
* This is an extension and not part of the main GoJS library.
* Note that the API for this class may change with any version, even point releases.
* If you intend to use an extension in production, you should copy the code to your own source directory.
* Extensions can be found in the GoJS kit under the extensions or extensionsTS folders.
* See the Extensions intro page (https://gojs.net/latest/intro/extensions.html) for more information.
*/
import * as go from '../release/go-module.js';
import { Quadtree } from './Quadtree.js';
/**
 * @hidden @internal
 * Used to represent the perimeter of the currently packed
 * shape when packing rectangles. Segments are always assumed
 * to be either horizontal or vertical, and store whether or
 * not their first point is concave (this makes sense in the
 * context of representing a perimeter, as the next segment
 * will always be connected to the last).
 */
class Segment {
    /**
     * @hidden @internal
     * Constructs a new Segment. Segments are assumed to be either
     * horizontal or vertical, and the given coordinates should
     * reflect that.
     * @param x1 the x coordinate of the first point
     * @param y1 the y coordinate of the first point
     * @param x2 the x coordinate of the second point
     * @param y2 the y coordinate of the second point
     * @param p1Concave whether or not the first point is concave
     */
    constructor(x1, y1, x2, y2, p1Concave) {
        this.x1 = x1;
        this.y1 = y1;
        this.x2 = x2;
        this.y2 = y2;
        this.bounds = Segment.rectFromSegment(this);
        this.p1Concave = p1Concave;
        this.isHorizontal = Math.abs(y2 - y1) < 1e-7;
    }
    /**
     * @hidden @internal
     * Gets a rectangle representing the bounds of a given segment.
     * Used to supply bounds of segments to the quadtree.
     * @this {VirtualizedPackedLayout}
     * @param segment the segment to get a rectangle for
     */
    static rectFromSegment(segment) {
        if (Math.abs(segment.x1 - segment.x2) < 1e-7) {
            return new go.Rect(segment.x1, Math.min(segment.y1, segment.y2), 0, Math.abs(segment.y1 - segment.y2));
        }
        return new go.Rect(Math.min(segment.x1, segment.x2), segment.y1, Math.abs(segment.x1 - segment.x2), 0);
    }
}
/**
 * @hidden @internal
 * Defines the possible orientations that two adjacent
 * horizontal/vertical segments can form.
 */
var Orientation;
(function (Orientation) {
    Orientation[Orientation["NE"] = 0] = "NE";
    Orientation[Orientation["NW"] = 1] = "NW";
    Orientation[Orientation["SW"] = 2] = "SW";
    Orientation[Orientation["SE"] = 3] = "SE";
})(Orientation || (Orientation = {}));
/**
 * @hidden @internal
 * Structure for storing possible placements when packing
 * rectangles. Fits have a cost associated with them (lower
 * cost placements are preferred), and can be placed relative
 * to either one or two segments. If the fit is only placed
 * relative to one segment, s2 will be undefined. Fits placed
 * relative to multiple segments will hereafter be referred to
 * as "skip fits".
 */
class Fit {
    /**
     * @hidden @internal
     * Constructs a new Fit.
     * @param bounds the boundaries of the placement, including defined x and y coordinates
     * @param cost the cost of the placement, lower cost fits will be preferred
     * @param s1 the segment that the placement was made relative to
     * @param s2 the second segment that the placement was made relative to, if the fit is a skip fit
     */
    constructor(bounds, cost, s1, s2) {
        this.bounds = bounds;
        this.cost = cost;
        this.s1 = s1;
        this.s2 = s2;
    }
}
;
/**
 * A Custom Layout that attempts to pack nodes as close together as possible
 * without overlap.  Each node is assumed to be either rectangular or
 * circular (dictated by the {@link #hasCircularNodes} property). This layout
 * supports packing nodes into either a rectangle or an ellipse, with the
 * shape determined by the packShape property and the aspect ratio determined
 * by either the aspectRatio property or the specified width and height
 * (depending on the packMode).
 *
 * Nodes with 0 width or height cannot be packed, so they are treated by this
 * layout as having a width or height of 0.1 instead.
 *
 * Unlike other "Virtualized..." layouts, this does not inherit from {@link PackedLayout}
 * because there were a lot of internal changes that needed to be made.  That may
 * change in the future if PackedLayout's implementation is generalized.
 * @category Layout Extension
 */
export class VirtualizedPackedLayout extends go.Layout {
    constructor() {
        super(...arguments);
        // configuration defaults
        /** @hidden @internal */ this._packShape = VirtualizedPackedLayout.Elliptical;
        /** @hidden @internal */ this._packMode = VirtualizedPackedLayout.AspectOnly;
        /** @hidden @internal */ this._sortMode = VirtualizedPackedLayout.None;
        /** @hidden @internal */ this._sortOrder = VirtualizedPackedLayout.Descending;
        /** @hidden @internal */ this._comparer = undefined;
        /** @hidden @internal */ this._aspectRatio = 1;
        /** @hidden @internal */ this._size = new go.Size(500, 500);
        /** @hidden @internal */ this._defaultSize = this._size.copy();
        /** @hidden @internal */ this._fillViewport = false; // true if size is (NaN, NaN)
        /** @hidden @internal */ this._spacing = 0;
        /** @hidden @internal */ this._hasCircularNodes = false;
        /** @hidden @internal */ this._arrangesToOrigin = true;
        /**
         * @hidden @internal
         * The forced spacing value applied in the {@link VirtualizedPackedLayout.Fit}
         * and {@link VirtualizedPackedLayout.ExpandToFit} modes.
         */
        this._fixedSizeModeSpacing = 0;
        /**
         * @hidden @internal
         * The actual target aspect ratio, set from either {@link #aspectRatio}
         * or from the {@link #size}, depending on the {@link #packMode}.
         */
        this._eAspectRatio = this._aspectRatio;
        // layout state
        /** @hidden @internal */ this._center = new go.Point();
        /** @hidden @internal */ this._bounds = new go.Rect();
        /** @hidden @internal */ this._actualBounds = new go.Rect();
        /** @hidden @internal */ this._enclosingCircle = null;
        /** @hidden @internal */ this._minXSegment = null;
        /** @hidden @internal */ this._minYSegment = null;
        /** @hidden @internal */ this._maxXSegment = null;
        /** @hidden @internal */ this._maxYSegment = null;
        /** @hidden @internal */ this._tree = new Quadtree();
        // saved node bounds and segment list to use to calculate enclosing circle in the enclosingCircle getter
        /** @hidden @internal */ this._nodeBounds = [];
        /** @hidden @internal */ this._segments = new CircularDoublyLinkedList();
    }
    /**
     * Gets or sets the shape that nodes will be packed into. Valid values are
     * {@link VirtualizedPackedLayout.Elliptical}, {@link VirtualizedPackedLayout.Rectangular}, and
     * {@link VirtualizedPackedLayout.Spiral}.
     *
     * In {@link VirtualizedPackedLayout.Spiral} mode, nodes are not packed into a particular
     * shape, but rather packed consecutively one after another in a spiral fashion.
     * The {@link #aspectRatio} property is ignored in this mode, and
     * the {@link #size} property (if provided) is expected to be square.
     * If it is not square, the largest dimension given will be used. This mode
     * currently only works with circular nodes, so setting it cause the assume that
     * layout to assume that {@link #hasCircularNodes} is true.
     *
     * Note that this property sets only the shape, not the aspect ratio. The aspect
     * ratio of this shape is determined by either {@link #aspectRatio}
     * or {@link #size}, depending on the {@link #packMode}.
     *
     * When the {@link #packMode} is {@link VirtualizedPackedLayout.Fit} or
     * {@link VirtualizedPackedLayout.ExpandToFit} and this property is set to true, the
     * layout will attempt to make the diameter of the enclosing circle of the
     * layout approximately equal to the greater dimension of the given
     * {@link #size} property.
     *
     * The default value is {@link VirtualizedPackedLayout.Elliptical}.
     */
    get packShape() { return this._packShape; }
    set packShape(value) {
        if (this._packShape !== value && (value === VirtualizedPackedLayout.Elliptical || value === VirtualizedPackedLayout.Rectangular || value === VirtualizedPackedLayout.Spiral)) {
            this._packShape = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets the mode that the layout will use to determine its size. Valid values
     * are {@link VirtualizedPackedLayout.AspectOnly}, {@link VirtualizedPackedLayout.Fit}, and {@link VirtualizedPackedLayout.ExpandToFit}.
     *
     * The default value is {@link VirtualizedPackedLayout.AspectOnly}. In this mode, the layout will simply
     * grow as needed, attempting to keep the aspect ratio defined by {@link #aspectRatio}.
     */
    get packMode() { return this._packMode; }
    set packMode(value) {
        if (value === VirtualizedPackedLayout.AspectOnly || value === VirtualizedPackedLayout.Fit || value === VirtualizedPackedLayout.ExpandToFit) {
            this._packMode = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets the method by which nodes will be sorted before being packed. To change
     * the order, see {@link #sortOrder}.
     *
     * The default value is {@link VirtualizedPackedLayout.None}, in which nodes will not be sorted at all.
     */
    get sortMode() { return this._sortMode; }
    set sortMode(value) {
        if (value === VirtualizedPackedLayout.None || value === VirtualizedPackedLayout.MaxSide || value === VirtualizedPackedLayout.Area) {
            this._sortMode = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets the order that nodes will be sorted in before being packed. To change
     * the sort method, see {@link #sortMode}.
     *
     * The default value is {@link VirtualizedPackedLayout.Descending}
     */
    get sortOrder() { return this._sortOrder; }
    set sortOrder(value) {
        if (value === VirtualizedPackedLayout.Descending || value === VirtualizedPackedLayout.Ascending) {
            this._sortOrder = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets the comparison function used for sorting nodes.
     *
     * By default, the comparison function is set according to the values of {@link #sortMode}
     * and {@link #sortOrder}.
     *
     * Whether this comparison function is used is determined by the value of {@link #sortMode}.
     * Any value except {@link VirtualizedPackedLayout.None} will result in the comparison function being used.
     * ```js
     *   $(VirtualizedPackedLayout,
     *     {
     *       sortMode: VirtualizedPackedLayout.Area,
     *       comparer: function(na, nb) {
     *         var na = na.data;
     *         var nb = nb.data;
     *         if (da.someProperty < db.someProperty) return -1;
     *         if (da.someProperty > db.someProperty) return 1;
     *         return 0;
     *       }
     *     }
     *   )
     * ```
     */
    get comparer() { return this._comparer; }
    set comparer(value) {
        if (typeof value === 'function') {
            this._comparer = value;
        }
    }
    /**
     * Gets or sets the aspect ratio for the shape that nodes will be packed into.
     * The provided aspect ratio should be a nonzero postive number.
     *
     * Note that this only applies if the {@link #packMode} is
     * {@link VirtualizedPackedLayout.AspectOnly}. Otherwise, the {@link #size}
     * will determine the aspect ratio of the packed shape.
     *
     * The default value is 1.
     */
    get aspectRatio() { return this._aspectRatio; }
    set aspectRatio(value) {
        if (this.isNumeric(value) && isFinite(value) && value > 0) {
            this._aspectRatio = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets the size for the shape that nodes will be packed into.
     * To fill the viewport, set a size with a width and height of NaN. Size
     * values of 0 are considered for layout purposes to instead be 1.
     *
     * If the width and height are set to NaN (to fill the viewport), but this
     * layout has no diagram associated with it, the default value of size will
     * be used instead.
     *
     * Note that this only applies if the {@link #packMode} is
     * {@link VirtualizedPackedLayout.Fit} or {@link VirtualizedPackedLayout.ExpandToFit}.
     *
     * The default value is 500x500.
     */
    get size() { return this._size; }
    set size(value) {
        // check if both width and height are NaN, as per https://stackoverflow.com/a/16988441
        if (value.width !== value.width && value.height !== value.height) {
            this._size = value;
            this._fillViewport = true;
            this.invalidateLayout();
        }
        else if (this.isNumeric(value.width) && isFinite(value.width) && value.width >= 0
            && this.isNumeric(value.height) && isFinite(value.height) && value.height >= 0) {
            this._size = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets the spacing between nodes. This value can be set to any
     * real number (a negative spacing will compress nodes together, and a
     * positive spacing will leave space between them).
     *
     * Note that the spacing value is only respected in the {@link VirtualizedPackedLayout.Fit}
     * {@link #packMode} if it does not cause the layout to grow outside
     * of the specified bounds. In the {@link VirtualizedPackedLayout.ExpandToFit}
     * {@link #packMode}, this property does not do anything.
     *
     * The default value is 0.
     */
    get spacing() { return this._spacing; }
    set spacing(value) {
        if (this.isNumeric(value) && isFinite(value)) {
            this._spacing = value;
            this.invalidateLayout();
        }
    }
    /**
     * Gets or sets whether or not to assume that nodes are circular. This changes
     * the packing algorithm to one that is much more efficient for circular nodes.
     *
     * As this algorithm expects circles, it is assumed that if this property is set
     * to true that the given nodes will all have the same height and width. All
     * calculations are done using the width of the given nodes, so unexpected results
     * may occur if the height differs from the width.
     *
     * The default value is false.
     */
    get hasCircularNodes() { return this._hasCircularNodes; }
    set hasCircularNodes(value) {
        if (typeof (value) === typeof (true) && value !== this._hasCircularNodes) {
            this._hasCircularNodes = value;
            this.invalidateLayout();
        }
    }
    /**
     * This read-only property is the effective spacing calculated after {@link VirtualizedPackedLayout#doLayout}.
     *
     * If the {@link #packMode} is {@link VirtualizedPackedLayout.AspectOnly}, this will simply be the
     * {@link #spacing} property. However, in the {@link VirtualizedPackedLayout.Fit} and
     * {@link VirtualizedPackedLayout.ExpandToFit} modes, this property will include the forced spacing added by
     * the modes themselves.
     *
     * Note that this property will only return a valid value after a layout has been performed. Before
     * then, its behavior is undefined.
     */
    get actualSpacing() { return this.spacing + this._fixedSizeModeSpacing; }
    /**
     * This read-only property returns the actual rectangular bounds occupied by the packed nodes.
     * This property does not take into account any kind of spacing around the packed nodes.
     *
     * Note that this property will only return a valid value after a layout has been performed. Before
     * then, its behavior is undefined.
     */
    get actualBounds() { return this._actualBounds; }
    /**
     * This read-only property returns the smallest enclosing circle around the packed nodes. It makes
     * use of the {@link #hasCircularNodes} property to determine whether or not to make
     * enclosing circle calculations for rectangles or for circles. This property does not take into
     * account any kind of spacing around the packed nodes. The enclosing circle calculation is
     * performed the first time this property is retrieved, and then cached to prevent slow accesses
     * in the future.
     *
     * Note that this property will only return a valid value after a layout has been performed. Before
     * then, its behavior is undefined.
     *
     * This property is included as it may be useful for some data visualizations.
     */
    get enclosingCircle() {
        if (this._enclosingCircle === null) {
            if (this.hasCircularNodes || this.packShape === VirtualizedPackedLayout.Spiral) { // remember, spiral mode assumes hasCircularNodes
                const circles = new Array(this._nodeBounds.length);
                for (let i = 0; i < circles.length; i++) {
                    const bounds = this._nodeBounds[i];
                    const r = bounds.width / 2;
                    circles[i] = new Circle(bounds.x + r, bounds.y + r, r);
                }
                this._enclosingCircle = enclose(circles);
            }
            else {
                const points = new Array(); // TODO: make this work with segments, not the whole nodeboudns list
                let segment = this._segments.start;
                if (segment !== null) {
                    do {
                        points.push(new go.Point(segment.data.x1, segment.data.y1));
                        segment = segment.next;
                    } while (segment !== this._segments.start);
                }
                this._enclosingCircle = enclose(points);
            }
        }
        return this._enclosingCircle;
    }
    /**
     * Gets or sets whether or not to use the {@link Layout#arrangementOrigin}
     * property when placing nodes.
     *
     * The default value is true.
     */
    get arrangesToOrigin() { return this._arrangesToOrigin; }
    set arrangesToOrigin(value) {
        if (typeof (value) === typeof (true) && value !== this._arrangesToOrigin) {
            this._arrangesToOrigin = value;
            this.invalidateLayout();
        }
    }
    /**
     * Performs the VirtualizedPackedLayout.
     * @this {VirtualizedPackedLayout}
     * @param {Diagram|Group|Iterable.<Part>} coll A {@link Diagram} or a {@link Group} or a collection of {@link Part}s.
     */
    performLayout(nodes) {
        const diagram = this.diagram;
        if (diagram !== null)
            diagram.startTransaction('Layout');
        this._bounds = new go.Rect();
        this._enclosingCircle = null;
        // push all nodes in parts iterator to an array for easy sorting
        let averageSize = 0;
        let maxSize = 0;
        nodes.forEach(function (node) {
            averageSize += node.bounds.width + node.bounds.height;
            if (node.bounds.width > maxSize) {
                maxSize = node.bounds.width;
            }
            else if (node.bounds.height > maxSize) {
                maxSize = node.bounds.height;
            }
        });
        averageSize = averageSize / (nodes.length * 2);
        if (averageSize < 1) {
            averageSize = 1;
        }
        if (this.sortMode !== VirtualizedPackedLayout.None) {
            if (!this.comparer) {
                const sortOrder = this.sortOrder;
                const sortMode = this.sortMode;
                this.comparer = (a, b) => {
                    const sortVal = sortOrder === VirtualizedPackedLayout.Ascending ? 1 : -1;
                    if (sortMode === VirtualizedPackedLayout.MaxSide) {
                        const aMax = Math.max(a.bounds.width, a.bounds.height);
                        const bMax = Math.max(b.bounds.width, b.bounds.height);
                        if (aMax > bMax) {
                            return sortVal;
                        }
                        else if (bMax > aMax) {
                            return -sortVal;
                        }
                        return 0;
                    }
                    else if (sortMode === VirtualizedPackedLayout.Area) {
                        const area1 = a.bounds.width * a.bounds.height;
                        const area2 = b.bounds.width * b.bounds.height;
                        if (area1 > area2) {
                            return sortVal;
                        }
                        else if (area2 > area1) {
                            return -sortVal;
                        }
                        return 0;
                    }
                    return 0;
                };
            }
            nodes.sort(this.comparer);
        }
        let targetWidth = this.size.width !== 0 ? this.size.width : 1;
        let targetHeight = this.size.height !== 0 ? this.size.height : 1;
        if (this._fillViewport && this.diagram !== null) {
            targetWidth = this.diagram.viewportBounds.width !== 0 ? this.diagram.viewportBounds.width : 1;
            targetHeight = this.diagram.viewportBounds.height !== 0 ? this.diagram.viewportBounds.height : 1;
        }
        else if (this._fillViewport) {
            targetWidth = this._defaultSize.width !== 0 ? this._defaultSize.width : 1;
            targetHeight = this._defaultSize.height !== 0 ? this._defaultSize.height : 1;
        }
        // set the target aspect ratio using the given bounds if necessary
        if (this.packMode === VirtualizedPackedLayout.Fit || this.packMode === VirtualizedPackedLayout.ExpandToFit) {
            this._eAspectRatio = targetWidth / targetHeight;
        }
        else {
            this._eAspectRatio = this.aspectRatio;
        }
        let fits = this.hasCircularNodes || this.packShape === VirtualizedPackedLayout.Spiral ? this.fitCircles(nodes) : this.fitRects(nodes);
        // in the Fit and ExpandToFit modes, we need to run the packing another time to figure out what the correct
        // _fixedModeSpacing should be. Then the layout is run a final time with the correct spacing.
        if (this.packMode === VirtualizedPackedLayout.Fit || this.packMode === VirtualizedPackedLayout.ExpandToFit) {
            const bounds0 = this._bounds.copy();
            this._bounds = new go.Rect();
            this._fixedSizeModeSpacing = Math.floor(averageSize);
            fits = this.hasCircularNodes || this.packShape === VirtualizedPackedLayout.Spiral ? this.fitCircles(nodes) : this.fitRects(nodes);
            if ((this.hasCircularNodes || this.packShape === VirtualizedPackedLayout.Spiral) && this.packShape === VirtualizedPackedLayout.Spiral) {
                const targetDiameter = Math.max(targetWidth, targetHeight);
                const oldDiameter = targetDiameter === targetWidth ? bounds0.width : bounds0.height;
                const newDiameter = targetDiameter === targetWidth ? this._bounds.width : this._bounds.height;
                const diff = (newDiameter - oldDiameter) / this._fixedSizeModeSpacing;
                this._fixedSizeModeSpacing = (targetDiameter - oldDiameter) / diff;
            }
            else {
                const dx = (this._bounds.width - bounds0.width) / this._fixedSizeModeSpacing;
                const dy = (this._bounds.height - bounds0.height) / this._fixedSizeModeSpacing;
                const paddingX = (targetWidth - bounds0.width) / dx;
                const paddingY = (targetHeight - bounds0.height) / dy;
                this._fixedSizeModeSpacing = Math.abs(paddingX) > Math.abs(paddingY) ? paddingX : paddingY;
            }
            if (this.packMode === VirtualizedPackedLayout.Fit) {
                // make sure that the spacing is not positive in this mode
                this._fixedSizeModeSpacing = Math.min(this._fixedSizeModeSpacing, 0);
            }
            if (this._fixedSizeModeSpacing === Infinity) {
                this._fixedSizeModeSpacing = -maxSize;
            }
            this._bounds = new go.Rect();
            fits = this.hasCircularNodes || this.packShape === VirtualizedPackedLayout.Spiral ? this.fitCircles(nodes) : this.fitRects(nodes);
        }
        // move the nodes and calculate the actualBounds property
        if (this.arrangesToOrigin) {
            this._actualBounds = new go.Rect(this.arrangementOrigin.x, this.arrangementOrigin.y, 0, 0);
        }
        const nodeBounds = new Array(nodes.length);
        for (let i = 0; i < nodes.length; i++) {
            const fit = fits[i];
            const node = nodes[i];
            if (this.arrangesToOrigin) {
                // translate coordinates to respect this.arrangementOrigin
                // this.arrangementOrigin should be the top left corner of the bounding box around the layout
                fit.x = fit.x - this._bounds.x + this.arrangementOrigin.x;
                fit.y = fit.y - this._bounds.y + this.arrangementOrigin.y;
            }
            this.moveNode(node, fit.x, fit.y);
            nodeBounds[i] = node.bounds;
            this._actualBounds.unionRect(node.bounds);
        }
        this._nodeBounds = nodeBounds; // save node bounds in case we want to calculate the smallest enclosing circle later
        // can be overriden to change layout behavior, doesn't do anything by default
        this.commitLayout();
        if (diagram !== null)
            diagram.commitTransaction('Layout');
        this.isValidLayout = true;
    }
    /**
     * Cause the vertex to be moved so that its position is at (nx,ny).
     * The default implementation assumes the node.bounds is a Rect that may be modified.
     * @expose
     * @param node
     * @param nx
     * @param ny
     */
    moveNode(node, nx, ny) {
        node.bounds.x = nx;
        node.bounds.y = ny;
    }
    /**
     * This method is called at the end of {@link #doLayout}, but
     * before the layout transaction is committed. It can be overriden and
     * used to customize layout behavior. By default, the method does nothing.
     * @expose
     * @this {VirtualizedPackedLayout}
     */
    commitLayout() { }
    /**
     * @hidden @internal
     * Runs a circle packing algorithm on the given array of nodes. The
     * algorithm used is a slightly modified version of the one proposed
     * by Wang et al. in "Visualization of large hierarchical data by
     * circle packing", 2006.
     * @this {VirtualizedPackedLayout}
     * @param nodes the array of Nodes to pack
     * @return {Array<Rect>} an array of positioned rectangles corresponding to the nodes argument
     */
    fitCircles(nodes) {
        function place(a, b, c) {
            const ax = a.centerX;
            const ay = a.centerY;
            let da = (b.width + c.width) / 2;
            let db = (a.width + c.width) / 2;
            const dx = b.centerX - ax;
            const dy = b.centerY - ay;
            const dc = dx * dx + dy * dy;
            if (dc) {
                const x = 0.5 + ((db *= db) - (da *= da)) / (2 * dc);
                const y = Math.sqrt(Math.max(0, 2 * da * (db + dc) - (db -= dc) * db - da * da)) / (2 * dc);
                c.x = (ax + x * dx + y * dy) - (c.width / 2);
                c.y = (ay + x * dy - y * dx) - (c.height / 2);
            }
            else {
                c.x = ax + db;
                c.y = ay;
            }
            return c;
        }
        function intersects(a, b) {
            const ar = a.height / 2;
            const br = b.height / 2;
            const dist = Math.sqrt(a.center.distanceSquaredPoint(b.center));
            const difference = dist - (ar + br);
            return difference < -0.0000001;
        }
        const aspect = this._eAspectRatio;
        const shape = this.packShape;
        const placementCost = this.placementCost;
        function score(n) {
            const a = n.data;
            const b = n.next.data;
            const ar = a.width / 2;
            const br = b.width / 2;
            const ab = ar + br;
            const dx = (a.centerX * br + b.centerX * ar) / ab;
            const dy = (a.centerY * br + b.centerY * ar) / ab * aspect;
            return shape === VirtualizedPackedLayout.Elliptical ? dx * dx + dy * dy : Math.max(dx * dx, dy * dy);
        }
        const sideSpacing = (this.spacing + this._fixedSizeModeSpacing) / 2;
        const fits = [];
        const frontChain = new CircularDoublyLinkedList();
        if (!nodes.length)
            return fits;
        let r1 = nodes[0].bounds.copy().inflate(sideSpacing, sideSpacing);
        r1.setTo(0, 0, r1.width === 0 ? 0.1 : r1.width, r1.height === 0 ? 0.1 : r1.height);
        fits.push(r1.setTo(0, 0, r1.width, r1.height));
        this._bounds.unionRect(r1);
        if (nodes.length < 2)
            return fits;
        let r2 = nodes[1].bounds.copy().inflate(sideSpacing, sideSpacing);
        r2.setTo(0, 0, r2.width === 0 ? 0.1 : r2.width, r2.height === 0 ? 0.1 : r2.height);
        fits.push(r2.setTo(-r2.width, r1.centerY - r2.width / 2, r2.width, r2.height));
        this._bounds.unionRect(r2);
        if (nodes.length < 3)
            return fits;
        let r3 = nodes[2].bounds.copy().inflate(sideSpacing, sideSpacing);
        r3.setTo(0, 0, r3.width === 0 ? 0.1 : r3.width, r3.height === 0 ? 0.1 : r3.height);
        fits.push(place(r2, r1, r3));
        this._bounds.unionRect(r3);
        let n2 = frontChain.push(r2);
        let n3 = frontChain.push(r3);
        let n1 = frontChain.push(r1);
        pack: for (let i = 3; i < nodes.length; i++) {
            r3 = nodes[i].bounds.copy().inflate(sideSpacing, sideSpacing);
            r3.setTo(0, 0, r3.width === 0 ? 0.1 : r3.width, r3.height === 0 ? 0.1 : r3.height);
            place(n1.data, n2.data, r3);
            let j = n2.next;
            let k = n1.prev;
            let sj = n2.data.width / 2;
            let sk = n1.data.width / 2;
            do {
                if (sj <= sk) {
                    if (intersects(j.data, r3)) {
                        n2 = frontChain.removeBetween(n1, j), i--;
                        continue pack;
                    }
                    sj += j.data.width / 2, j = j.next;
                }
                else {
                    if (intersects(k.data, r3)) {
                        frontChain.removeBetween(k, n2);
                        n1 = k, i--;
                        continue pack;
                    }
                    sk += k.data.width / 2, k = k.prev;
                }
            } while (j !== k.next);
            fits.push(r3);
            this._bounds.unionRect(r3);
            n2 = n3 = frontChain.insertAfter(r3, n1);
            if (this.packShape !== VirtualizedPackedLayout.Spiral) {
                let aa = score(n1);
                while ((n3 = n3.next) !== n2) {
                    const ca = score(n3);
                    if (ca < aa) {
                        n1 = n3, aa = ca;
                    }
                }
                n2 = n1.next;
            }
        }
        return fits;
    }
    /**
     * @hidden @internal
     * Runs a rectangle packing algorithm on the given array of nodes.
     * The algorithm presented is original, and operates by maintaining
     * a representation (with segments) of the perimeter of the already
     * packed shape. The perimeter of segments is stored in both a linked
     * list (for ordered iteration) and a quadtree (for fast intersection
     * detection). Similar to the circle packing algorithm presented
     * above, this is a greedy algorithm.
     *
     * For each node, a large list of possible placements is created,
     * each one relative to a segment on the perimeter. These placements
     * are sorted according to a cost function, and then the lowest cost
     * placement with no intersections is picked. The perimeter
     * representation is then updated according to the new placement.
     *
     * However, in addition to placements made relative to a single segment
     * on the perimeter, the algorithm also attempts to make placements
     * between two nonsequential segments ("skip fits"), closing gaps in the
     * packed shape. If a placement made in this way has no intersections
     * and a lower cost than any of the original placements, it is picked
     * instead. This step occurs simultaneously to checking intersections on
     * the original placement list.
     *
     * Intersections for new placements are checked only against the current
     * perimeter of segments, rather than the entire packed shape.
     * Additionally, before the quadtree is queried at all, a few closely
     * surrounding segments to the placement are checked in case an
     * intersection can be found more quickly. The combination of these two
     * strategies enables intersection checking to take place extremely
     * quickly, when it would normally be the slowest part of the entire
     * algorithm.
     *
     * @this {VirtualizedPackedLayout}
     * @param nodes the array of Nodes to pack
     * @return {Array<Rect>} an array of positioned rectangles corresponding to the nodes argument
     */
    fitRects(nodes) {
        const sideSpacing = (this.spacing + this._fixedSizeModeSpacing) / 2;
        const fits = [];
        const segments = new CircularDoublyLinkedList();
        // reset layout state
        this._tree.clear();
        this._minXSegment = null;
        this._maxXSegment = null;
        this._minYSegment = null;
        this._maxYSegment = null;
        if (nodes.length < 1) {
            return fits;
        }
        // place first node at 0, 0
        const bounds0 = nodes[0].bounds;
        fits.push(new go.Rect(sideSpacing, sideSpacing, bounds0.width, bounds0.height));
        fits[0].inflate(sideSpacing, sideSpacing);
        fits[0].setTo(0, 0, fits[0].width === 0 ? 0.1 : fits[0].width, fits[0].height === 0 ? 0.1 : fits[0].height);
        this._bounds.unionRect(fits[0]);
        this._center = fits[0].center;
        const s1 = new Segment(0, 0, fits[0].width, 0, false);
        const s2 = new Segment(fits[0].width, 0, fits[0].width, fits[0].height, false);
        const s3 = new Segment(fits[0].width, fits[0].height, 0, fits[0].height, false);
        const s4 = new Segment(0, fits[0].height, 0, 0, false);
        this._tree.add(s1);
        this._tree.add(s2);
        this._tree.add(s3);
        this._tree.add(s4);
        segments.push(s1, s2, s3, s4);
        this.fixMissingMinMaxSegments(true);
        for (let i = 1; i < nodes.length; i++) {
            const node = nodes[i];
            const bounds = node.bounds.copy().inflate(sideSpacing, sideSpacing);
            bounds.setTo(0, 0, bounds.width === 0 ? 0.1 : bounds.width, bounds.height === 0 ? 0.1 : bounds.height);
            const possibleFits = new Array(segments.length);
            let j = 0;
            let s = segments.start;
            do {
                // make sure segment is perfectly straight (fixing some floating point error)
                const sdata = s.data;
                sdata.x1 = s.prev.data.x2;
                sdata.y1 = s.prev.data.y2;
                if (sdata.isHorizontal) {
                    sdata.y2 = sdata.y1;
                }
                else {
                    sdata.x2 = sdata.x1;
                }
                const fitBounds = this.getBestFitRect(s, bounds.width, bounds.height);
                const cost = this.placementCost(fitBounds);
                possibleFits[j] = new Fit(fitBounds, cost, s);
                s = s.next;
                j++;
            } while (s !== segments.start);
            possibleFits.sort((a, b) => {
                return a.cost - b.cost;
            });
            /* scales the cost of skip fits. a number below
             * one makes skip fits more likely to appear,
             * which is preferable because they are more
             * aesthetically pleasing and reduce the total
             * number of segments.
             */
            const skipFitScaleFactor = 0.98;
            let bestFit = null;
            let onlyCheckSkipFits = false;
            for (const fit of possibleFits) {
                if (bestFit && bestFit.cost <= fit.cost) {
                    onlyCheckSkipFits = true;
                }
                let hasIntersections = true; // set initially to true to make skip fit checking work when onlyCheckSkipFits = true
                if (!onlyCheckSkipFits) {
                    hasIntersections = this.fastFitHasIntersections(fit) || this.fitHasIntersections(fit);
                    if (!hasIntersections) {
                        bestFit = fit;
                        continue;
                    }
                }
                // check skip fits
                if (hasIntersections && !fit.s1.data.p1Concave && (fit.s1.next.data.p1Concave || fit.s1.next.next.data.p1Concave)) {
                    let [nextSegment, usePreviousSegment] = this.findNextOrientedSegment(fit, fit.s1.next);
                    let nextSegmentTouchesFit = false;
                    while (hasIntersections && nextSegment !== null) {
                        fit.bounds = this.rectAgainstMultiSegment(fit.s1, nextSegment, bounds.width, bounds.height);
                        hasIntersections = this.fastFitHasIntersections(fit) || this.fitHasIntersections(fit);
                        nextSegmentTouchesFit = this.segmentIsOnFitPerimeter(nextSegment.data, fit.bounds);
                        if (hasIntersections || !nextSegmentTouchesFit) {
                            [nextSegment, usePreviousSegment] = this.findNextOrientedSegment(fit, nextSegment);
                        }
                    }
                    if (!hasIntersections && nextSegment !== null && nextSegmentTouchesFit) {
                        fit.cost = this.placementCost(fit.bounds) * skipFitScaleFactor;
                        if (bestFit === null || fit.cost <= bestFit.cost) {
                            bestFit = fit;
                            bestFit.s2 = nextSegment;
                            if (usePreviousSegment) {
                                bestFit.s1 = bestFit.s1.prev;
                            }
                        }
                    }
                }
            }
            if (bestFit !== null) {
                this.updateSegments(bestFit, segments);
                fits.push(bestFit.bounds);
                this._bounds.unionRect(bestFit.bounds);
            }
        }
        // save segments in case we want to calculate the enclosing circle later
        this._segments = segments;
        return fits;
    }
    /**
     * @hidden @internal
     * Attempts to find a segment which can be used to create a new skip fit
     * between fit.s1 and the found segment. A number of conditions are checked
     * before returning a segment, ensuring that if the skip fit *does* intersect
     * with the already packed shape, it will do so along the perimeter (so that it
     * can be detected with only knowledge about the perimeter). Multiple oriented
     * segments can be found for a given fit, so this function starts searching at
     * the segment after the given lastSegment parameter.
     *
     * Oriented segments can be oriented with either fit.s1, or fit.s1.prev. The
     * second return value (usePreviousSegment) indicates which the found segment is.
     *
     * @this {VirtualizedPackedLayout}
     * @param fit the fit to search for a new segment for
     * @param lastSegment the last segment found.
     */
    findNextOrientedSegment(fit, lastSegment) {
        lastSegment = lastSegment.next;
        const orientation = this.segmentOrientation(fit.s1.prev.data, fit.s1.data);
        const targetOrientation = (orientation + 1) % 4;
        while (!this.segmentIsMinOrMax(lastSegment.data)) {
            const usePreviousSegment = lastSegment.data.isHorizontal === fit.s1.data.isHorizontal;
            let lastOrientation;
            if (usePreviousSegment) {
                lastOrientation = this.segmentOrientation(lastSegment.data, lastSegment.next.data);
                if (lastSegment.next.data.p1Concave) {
                    lastOrientation = (lastOrientation + 1) % 4;
                }
            }
            else {
                lastOrientation = this.segmentOrientation(lastSegment.prev.data, lastSegment.data);
                if (lastSegment.data.p1Concave) {
                    lastOrientation = (lastOrientation + 1) % 4;
                }
            }
            const validLastOrientation = lastOrientation === targetOrientation;
            const exceededPrimaryDimension = fit.s1.data.isHorizontal ?
                Math.abs(lastSegment.data.y1 - fit.s1.data.y1) + 1e-7 > fit.bounds.height :
                Math.abs(lastSegment.data.x1 - fit.s1.data.x1) + 1e-7 > fit.bounds.width;
            let validCornerPlacement;
            let exceededSecondaryDimension;
            switch (orientation) {
                case Orientation.NE:
                    validCornerPlacement = fit.s1.data.x1 < lastSegment.data.x1;
                    exceededSecondaryDimension = usePreviousSegment ? fit.s1.data.y1 - fit.bounds.height >= lastSegment.data.y1 : fit.s1.data.y2 + fit.bounds.height <= lastSegment.data.y1;
                    break;
                case Orientation.NW:
                    validCornerPlacement = fit.s1.data.y1 > lastSegment.data.y1;
                    exceededSecondaryDimension = usePreviousSegment ? fit.s1.data.x1 - fit.bounds.width >= lastSegment.data.x1 : fit.s1.data.x2 + fit.bounds.width <= lastSegment.data.x1;
                    break;
                case Orientation.SW:
                    validCornerPlacement = fit.s1.data.x1 > lastSegment.data.x1;
                    exceededSecondaryDimension = usePreviousSegment ? fit.s1.data.y1 + fit.bounds.height <= lastSegment.data.y1 : fit.s1.data.y2 - fit.bounds.height >= lastSegment.data.y1;
                    break;
                case Orientation.SE:
                    validCornerPlacement = fit.s1.data.y1 < lastSegment.data.y1;
                    exceededSecondaryDimension = usePreviousSegment ? fit.s1.data.x1 + fit.bounds.width <= lastSegment.data.x1 : fit.s1.data.x2 - fit.bounds.width >= lastSegment.data.x1;
                    break;
                default:
                    throw new Error('Unknown orientation ' + orientation);
            }
            if (!exceededPrimaryDimension && !exceededSecondaryDimension && validCornerPlacement && validLastOrientation) {
                return [lastSegment, usePreviousSegment];
            }
            lastSegment = lastSegment.next;
        }
        return [null, false];
    }
    /**
     * @hidden @internal
     * Returns the orientation of two adjacent segments. s2
     * is assumed to start at the end of s1.
     * @this {VirtualizedPackedLayout}
     * @param s1 the first segment
     * @param s2 the second segment
     */
    segmentOrientation(s1, s2) {
        if (s1.isHorizontal) {
            if (s1.x1 < s2.x1) {
                return s2.p1Concave ? Orientation.SE : Orientation.NE;
            }
            else {
                return s2.p1Concave ? Orientation.NW : Orientation.SW;
            }
        }
        else {
            if (s1.y1 < s2.y1) {
                return s2.p1Concave ? Orientation.SW : Orientation.SE;
            }
            else {
                return s2.p1Concave ? Orientation.NE : Orientation.NW;
            }
        }
    }
    /**
     * @hidden @internal
     * Fits a rectangle between two segments (used for skip fits). This is an operation
     * related more to corners than segments, so fit.s1 should always be supplied for
     * segment a (even if usePreviousSegment was true in the return value for
     * {@link #findNextOrientedSegment}).
     *
     * @this {VirtualizedPackedLayout}
     * @param a the first segment to fit between, should always be fit.s1
     * @param b the second segment to fit between, found with {@link #findNextOrientedSegment}
     * @param width the width of the rectangle, should be fit.width
     * @param height the height of the rectangle, should be fit.height
     */
    rectAgainstMultiSegment(a, b, width, height) {
        switch (this.segmentOrientation(a.prev.data, a.data)) {
            case Orientation.NE:
                if (a.data.y1 > b.data.y2) {
                    return new go.Rect(b.data.x1 - width, a.data.y1 - height, width, height);
                }
                else {
                    return new go.Rect(a.data.x1, b.data.y1 - height, width, height);
                }
            case Orientation.NW:
                if (a.data.x1 > b.data.x2) {
                    return new go.Rect(a.data.x1 - width, b.data.y1, width, height);
                }
                else {
                    return new go.Rect(b.data.x1 - width, a.data.y1 - height, width, height);
                }
            case Orientation.SW:
                if (a.data.y1 < b.data.y2) {
                    return new go.Rect(b.data.x1, a.data.y1, width, height);
                }
                else {
                    return new go.Rect(a.data.x1 - width, b.data.y1, width, height);
                }
            case Orientation.SE:
                if (a.data.x1 < b.data.x2) {
                    return new go.Rect(a.data.x1, b.data.y1 - height, width, height);
                }
                else {
                    return new go.Rect(b.data.x1, a.data.y1, width, height);
                }
        }
    }
    /**
     * @hidden @internal
     * Gets the rectangle placed against the given segment with the lowest
     * placement cost. Rectangles can be placed against a segment either at
     * the top/left side, the bottom/right side, or at the center coordinate
     * of the entire packed shape (if the segment goes through either the x
     * or y coordinate of the center).
     * @this {VirtualizedPackedLayout}
     * @param s the segment to place against
     * @param width the width of the fit, fit.width
     * @param height the height of the fit, fit.height
     */
    getBestFitRect(s, width, height) {
        let x1 = s.data.x1;
        let y1 = s.data.y1;
        let x2 = s.data.x2;
        let y2 = s.data.y2;
        let dir = this.segmentOrientation(s.prev.data, s.data);
        if (s.data.p1Concave) {
            dir = (dir + 3) % 4;
        }
        const coordIsX = dir === Orientation.NW || dir === Orientation.SE;
        if (dir === Orientation.NE) {
            y2 -= height;
        }
        else if (dir === Orientation.SE) {
            x1 -= width;
        }
        else if (dir === Orientation.SW) {
            x1 -= width;
            y1 -= height;
            x2 -= width;
        }
        else if (dir === Orientation.NW) {
            y1 -= height;
            x2 -= width;
            y2 -= height;
        }
        const r = new go.Rect(x1, y1, width, height);
        const cost1 = this.placementCost(r);
        const cost2 = this.placementCost(r.setTo(x2, y2, width, height));
        let cost3 = Infinity;
        if (coordIsX && (this._center.x - (x1 + width / 2)) * (this._center.x - (x2 + width / 2)) < 0) {
            cost3 = this.placementCost(r.setTo(this._center.x - width / 2, y1, width, height));
        }
        else if (!coordIsX && (this._center.y - (y1 + height / 2)) * (this._center.y - (y2 + height / 2)) < 0) {
            cost3 = this.placementCost(r.setTo(x1, this._center.y - height / 2, width, height));
        }
        return cost3 < cost2 && cost3 < cost1 ? r
            : (cost2 < cost1 ? r.setTo(x2, y2, width, height)
                : r.setTo(x1, y1, width, height));
    }
    /**
     * @hidden @internal
     * Checks if a segment is on the perimeter of the given fit bounds.
     * Also returns true if the segment is within the rect, but that
     * shouldn't matter for any of the cases where this function is used.
     * @this {VirtualizedPackedLayout}
     * @param s the segment to test
     * @param bounds the fit bounds
     */
    segmentIsOnFitPerimeter(s, bounds) {
        const xCoordinatesTogether = this.numberIsBetween(s.x1, bounds.left, bounds.right)
            || this.numberIsBetween(s.x2, bounds.left, bounds.right)
            || this.numberIsBetween(bounds.left, s.x1, s.x2)
            || this.numberIsBetween(bounds.right, s.x1, s.x2);
        const yCoordinatesTogether = this.numberIsBetween(s.y1, bounds.top, bounds.bottom)
            || this.numberIsBetween(s.y2, bounds.top, bounds.bottom)
            || this.numberIsBetween(bounds.top, s.y1, s.y2)
            || this.numberIsBetween(bounds.bottom, s.y1, s.y2);
        return (s.isHorizontal && (this.approxEqual(s.y1, bounds.top) || this.approxEqual(s.y1, bounds.bottom)) && xCoordinatesTogether)
            || (!s.isHorizontal && (this.approxEqual(s.x1, bounds.left) || this.approxEqual(s.x1, bounds.right)) && yCoordinatesTogether);
    }
    /**
     * @hidden @internal
     * Checks if a point is on the perimeter of the given fit bounds.
     * Also returns true if the point is within the rect, but that
     * shouldn't matter for any of the cases where this function is used.
     * @this {VirtualizedPackedLayout}
     * @param x the x coordinate of the point to test
     * @param y the y coordinate of the point to test
     * @param bounds the fit bounds
     */
    pointIsOnFitPerimeter(x, y, bounds) {
        return (x >= bounds.left - 1e-7 && x <= bounds.right + 1e-7 && y >= bounds.top - 1e-7 && y <= bounds.bottom + 1e-7);
    }
    /**
     * @hidden @internal
     * Checks if a point is on the corner of the given fit bounds.
     * @this {VirtualizedPackedLayout}
     * @param x the x coordinate of the point to test
     * @param y the y coordinate of the point to test
     * @param bounds the fit bounds
     */
    pointIsFitCorner(x, y, bounds) {
        return (this.approxEqual(x, bounds.left) && this.approxEqual(y, bounds.top)) ||
            (this.approxEqual(x, bounds.right) && this.approxEqual(y, bounds.top)) ||
            (this.approxEqual(x, bounds.left) && this.approxEqual(y, bounds.bottom)) ||
            (this.approxEqual(x, bounds.right) && this.approxEqual(y, bounds.bottom));
    }
    /**
     * @hidden @internal
     * Updates the representation of the perimeter of segments after
     * a new placement is made. This modifies the given segments list,
     * as well as the quadtree class variable {@link #_tree}.
     * Also updates the minimum/maximum segments if they have changed as
     * a result of the new placement.
     * @this {VirtualizedPackedLayout}
     * @param fit the fit to add
     * @param segments the list of segments to update
     */
    updateSegments(fit, segments) {
        let s0 = fit.s1;
        while (this.pointIsOnFitPerimeter(s0.data.x1, s0.data.y1, fit.bounds)) {
            s0 = s0.prev;
        }
        if (!this.segmentIsMinOrMax(s0.data) || !this.segmentIsMinOrMax(s0.prev.data)) {
            let sTest = s0.prev.prev; // test for conflicting segments
            let sFound = null;
            let minMaxCount = 0;
            while (minMaxCount < 2) {
                if (this.segmentIsOnFitPerimeter(sTest.data, fit.bounds)) {
                    sFound = sTest;
                }
                sTest = sTest.prev;
                if (this.segmentIsMinOrMax(sTest.next.data)) {
                    minMaxCount++;
                }
            }
            if (sFound !== null) {
                while (this.pointIsOnFitPerimeter(sFound.data.x1, sFound.data.y1, fit.bounds)) {
                    sFound = sFound.prev;
                }
                this.removeBetween(segments, sFound, s0);
                s0 = sFound;
            }
        }
        let nextConvexCornerOrientation;
        let lastConvexCornerOrientation;
        let testOrientation = this.segmentOrientation(s0.prev.data, s0.data);
        if (s0.data.p1Concave) {
            testOrientation = (testOrientation + 3) % 4;
        }
        let [cornerX, cornerY] = this.cornerFromRect(testOrientation, fit.bounds);
        const extended0 = this.approxEqual(cornerX, s0.data.x2) && this.approxEqual(cornerY, s0.data.y2);
        let shortened0Precond;
        let [cornerX2, cornerY2] = this.cornerFromRect((testOrientation + 1) % 4, fit.bounds);
        if (s0.data.isHorizontal) {
            shortened0Precond = this.numberIsBetween(cornerX2, s0.data.x1, s0.data.x2) && this.approxEqual(cornerY2, s0.data.y1);
        }
        else {
            shortened0Precond = this.numberIsBetween(cornerY2, s0.data.y1, s0.data.y2) && this.approxEqual(cornerX2, s0.data.x1);
        }
        const shortened0 = !extended0 && this.pointIsFitCorner(s0.data.x2, s0.data.y2, fit.bounds)
            || !this.pointIsOnFitPerimeter(s0.data.x2, s0.data.y2, fit.bounds)
            || (this.pointIsOnFitPerimeter(s0.data.x2, s0.data.y2, fit.bounds)
                && !this.pointIsOnFitPerimeter(s0.data.x1, s0.data.y1, fit.bounds)
                && shortened0Precond);
        if (extended0) {
            // extend s0
            [s0.data.x2, s0.data.y2] = this.cornerFromRect((testOrientation + 3) % 4, fit.bounds);
            this._tree.setTo(s0.data, Segment.rectFromSegment(s0.data));
            nextConvexCornerOrientation = (testOrientation + 3) % 4;
            this.updateMinMaxSegments(s0.data);
        }
        else {
            if (shortened0) {
                [s0.data.x2, s0.data.y2] = this.cornerFromRect((testOrientation + 1) % 4, fit.bounds);
                this._tree.setTo(s0.data, Segment.rectFromSegment(s0.data));
            }
            const newSegment = new Segment(s0.data.x2, s0.data.y2, cornerX, cornerY, true);
            s0 = segments.insertAfter(newSegment, s0);
            this._tree.add(newSegment);
            nextConvexCornerOrientation = testOrientation;
            this.updateMinMaxSegments(newSegment);
        }
        let sNext = fit.s2 ? fit.s2 : s0;
        while (this.pointIsOnFitPerimeter(sNext.data.x2, sNext.data.y2, fit.bounds)) {
            sNext = sNext.next;
        }
        if (!this.segmentIsMinOrMax(sNext.data) || !this.segmentIsMinOrMax(sNext.next.data)) {
            let sTest = sNext.next.next; // test for conflicting segments
            let sFound = null;
            let minMaxCount = 0;
            while (minMaxCount < 2) {
                if (this.segmentIsOnFitPerimeter(sTest.data, fit.bounds)) {
                    sFound = sTest;
                }
                sTest = sTest.next;
                if (this.segmentIsMinOrMax(sTest.prev.data)) {
                    minMaxCount++;
                }
            }
            if (sFound !== null) {
                sNext = sFound;
                while (this.pointIsOnFitPerimeter(sNext.data.x2, sNext.data.y2, fit.bounds)) {
                    sNext = sNext.next;
                }
            }
        }
        testOrientation = this.segmentOrientation(sNext.data, sNext.next.data);
        if (sNext.data.p1Concave) {
            testOrientation = (testOrientation + 2) % 4;
        }
        if (sNext.next.data.p1Concave) {
            testOrientation = (testOrientation + 1) % 4;
        }
        [cornerX2, cornerY2] = this.cornerFromRect((testOrientation + 3) % 4, fit.bounds);
        if (sNext.data.isHorizontal && this.numberIsBetween(cornerX2, sNext.data.x1, sNext.data.x2) && this.approxEqual(cornerY2, sNext.data.y1)
            || (!sNext.data.isHorizontal && this.numberIsBetween(cornerY2, sNext.data.y1, sNext.data.y2) && this.approxEqual(cornerX2, sNext.data.x1))
            || (sNext.data.isHorizontal && this.numberIsBetween(fit.bounds.left, sNext.data.x1, sNext.data.x2) && this.numberIsBetween(fit.bounds.right, sNext.data.x1, sNext.data.x2)
                && (this.approxEqual(fit.bounds.top, sNext.data.y1) || this.approxEqual(fit.bounds.bottom, sNext.data.y1)))
            || (!sNext.data.isHorizontal && this.numberIsBetween(fit.bounds.top, sNext.data.y1, sNext.data.y2) && this.numberIsBetween(fit.bounds.bottom, sNext.data.y1, sNext.data.y2)
                && (this.approxEqual(fit.bounds.left, sNext.data.x1) || this.approxEqual(fit.bounds.right, sNext.data.x1)))) {
            sNext = sNext.next;
            testOrientation = this.segmentOrientation(sNext.data, sNext.next.data);
            if (sNext.data.p1Concave) {
                testOrientation = (testOrientation + 2) % 4;
            }
            if (sNext.next.data.p1Concave) {
                testOrientation = (testOrientation + 1) % 4;
            }
        }
        this.removeBetween(segments, s0, sNext);
        [cornerX, cornerY] = this.cornerFromRect(testOrientation, fit.bounds);
        if (this.approxEqual(cornerX, sNext.data.x1) && this.approxEqual(cornerY, sNext.data.y1)) {
            // extend sNext
            if (s0.data.isHorizontal === sNext.data.isHorizontal && (s0.data.isHorizontal ? this.approxEqual(s0.data.y1, sNext.data.y1) : this.approxEqual(s0.data.x1, sNext.data.x1))) {
                s0.data.x2 = sNext.data.x2;
                s0.data.y2 = sNext.data.y2;
                this.removeSegmentFromLayoutState(sNext);
                segments.remove(sNext);
                this._tree.setTo(s0.data, Segment.rectFromSegment(s0.data));
                lastConvexCornerOrientation = nextConvexCornerOrientation; // no additional segments need to be added
                this.updateMinMaxSegments(s0.data);
            }
            else {
                [sNext.data.x1, sNext.data.y1] = this.cornerFromRect((testOrientation + 1) % 4, fit.bounds);
                this._tree.setTo(sNext.data, Segment.rectFromSegment(sNext.data));
                lastConvexCornerOrientation = (testOrientation + 1) % 4;
                this.updateMinMaxSegments(sNext.data);
            }
        }
        else if (extended0 && (s0.data.isHorizontal ?
            this.approxEqual(s0.data.y1, sNext.data.y1) && this.numberIsBetween(sNext.data.x1, s0.data.x1, s0.data.x2) :
            this.approxEqual(s0.data.x1, sNext.data.x1) && this.numberIsBetween(sNext.data.y1, s0.data.y1, s0.data.y2))) {
            if (s0.data.isHorizontal) {
                s0.data.x2 = sNext.data.x1;
            }
            else {
                s0.data.y2 = sNext.data.y1;
            }
            this._tree.setTo(s0.data, Segment.rectFromSegment(s0.data));
            lastConvexCornerOrientation = nextConvexCornerOrientation;
            sNext.data.p1Concave = true;
            this.updateMinMaxSegments(s0.data);
        }
        else if (!this.pointIsFitCorner(sNext.data.x1, sNext.data.y1, fit.bounds)) {
            // add concave segment
            const newSegment = new Segment(cornerX, cornerY, sNext.data.x1, sNext.data.y1, false);
            if (this.pointIsOnFitPerimeter(sNext.data.x1, sNext.data.y1, fit.bounds)) {
                sNext.data.p1Concave = true;
            }
            else {
                newSegment.p1Concave = true;
            }
            if (this.approxEqual(sNext.prev.data.x1, cornerX) && this.approxEqual(sNext.prev.data.y1, cornerY) && newSegment.isHorizontal === sNext.prev.data.isHorizontal) {
                sNext.prev.data.x2 = sNext.data.x1;
                sNext.prev.data.y2 = sNext.data.y1;
                this._tree.setTo(sNext.prev.data, Segment.rectFromSegment(sNext.prev.data));
                lastConvexCornerOrientation = nextConvexCornerOrientation;
            }
            else {
                segments.insertAfter(newSegment, sNext.prev);
                this._tree.add(newSegment);
                lastConvexCornerOrientation = testOrientation;
                this.updateMinMaxSegments(newSegment);
            }
        }
        else { // if (this.pointIsOnFitPerimeter(sNext.data.x1, sNext.data.y1, fit.bounds))
            // shorten existing segment
            [sNext.data.x1, sNext.data.y1] = this.cornerFromRect((testOrientation + 3) % 4, fit.bounds);
            sNext.data.p1Concave = true;
            this._tree.setTo(sNext.data, Segment.rectFromSegment(sNext.data));
            lastConvexCornerOrientation = (testOrientation + 3) % 4;
        }
        while (nextConvexCornerOrientation !== lastConvexCornerOrientation) {
            [cornerX, cornerY] = this.cornerFromRect((nextConvexCornerOrientation + 3) % 4, fit.bounds);
            const newSegment = new Segment(s0.data.x2, s0.data.y2, cornerX, cornerY, false);
            s0 = segments.insertAfter(newSegment, s0);
            this._tree.add(newSegment);
            nextConvexCornerOrientation = (nextConvexCornerOrientation + 3) % 4;
            this.updateMinMaxSegments(newSegment);
        }
        this.fixMissingMinMaxSegments();
    }
    /**
     * @hidden @internal
     * Finds the new minimum and maximum segments in the packed shape if
     * any of them have been deleted. To do this quickly, the quadtree
     * is used.
     * @this{VirtualizedPackedLayout}
     * @param force whether or not to force an update based on the quadtree even if none of the segments were deleted
     */
    fixMissingMinMaxSegments(force = false) {
        if (!this._minXSegment || !this._maxXSegment || !this._minYSegment || !this._maxYSegment || force) {
            [this._minXSegment, this._maxXSegment, this._minYSegment, this._maxYSegment] = this._tree.findExtremeObjects();
        }
    }
    /**
     * @hidden @internal
     * Updates the minimum or maximum segments with a new segment if that
     * segment is a new minimum or maximum.
     * @this {VirtualizedPackedLayout}
     * @param s the new segment to test
     */
    updateMinMaxSegments(s) {
        const centerX = (s.x1 + s.x2) / 2;
        const centerY = (s.y1 + s.y2) / 2;
        if (this._minXSegment && centerX < (this._minXSegment.x1 + this._minXSegment.x2) / 2) {
            this._minXSegment = s;
        }
        if (this._minYSegment && centerY < (this._minYSegment.y1 + this._minYSegment.y2) / 2) {
            this._minYSegment = s;
        }
        if (this._maxXSegment && centerX > (this._maxXSegment.x1 + this._maxXSegment.x2) / 2) {
            this._maxXSegment = s;
        }
        if (this._maxYSegment && centerY > (this._maxYSegment.y1 + this._maxYSegment.y2) / 2) {
            this._maxYSegment = s;
        }
    }
    /**
     * @hidden @internal
     * Gets the x and y coordinates of a corner of a given rectangle.
     * @this {VirtualizedPackedLayout}
     * @param orientation the orientation of the corner to get
     * @param bounds the bounds of the rectangle to get the corner from
     */
    cornerFromRect(orientation, bounds) {
        let x = bounds.x;
        let y = bounds.y;
        if (orientation === Orientation.NE || orientation === Orientation.SE) {
            x = bounds.right;
        }
        if (orientation === Orientation.SW || orientation === Orientation.SE) {
            y = bounds.bottom;
        }
        return [x, y];
    }
    /**
     * @hidden @internal
     * Tests if a number is in between two other numbers, with included
     * allowance for some floating point error with the supplied values.
     * The order of the given boundaries does not matter.
     * @this {VirtualizedPackedLayout}
     * @param n the number to test
     * @param b1 the first boundary
     * @param b2 the second boundary
     */
    numberIsBetween(n, b1, b2) {
        const tmp = b1;
        b1 = Math.min(b1, b2);
        b2 = Math.max(tmp, b2);
        return n + 1e-7 >= b1 && n - 1e-7 <= b2;
    }
    /**
     * @hidden @internal
     * Tests whether or not a given segment is a minimum or maximum segment.
     * @this {VirtualizedPackedLayout}
     * @param s the segment to test
     */
    segmentIsMinOrMax(s) {
        return s === this._minXSegment || s === this._minYSegment || s === this._maxXSegment || s === this._maxYSegment;
    }
    /**
     * @hidden @internal
     * Removes a segment from the layout state. This includes removing it
     * from the quadtree, as well as setting the corresponding minimum or
     * maximum segment to null if the given segment is a minimum or
     * maximum.
     * @this {VirtualizedPackedLayout}
     * @param s the segment to remove
     */
    removeSegmentFromLayoutState(s) {
        if (s.data === this._minXSegment) {
            this._minXSegment = null;
        }
        if (s.data === this._maxXSegment) {
            this._maxXSegment = null;
        }
        if (s.data === this._minYSegment) {
            this._minYSegment = null;
        }
        if (s.data === this._maxYSegment) {
            this._maxYSegment = null;
        }
        this._tree.remove(s.data);
    }
    /**
     * @hidden @internal
     * Removes all segments between the two given segments (exclusive).
     * This includes removing them from the layout state, as well as
     * the given segment list.
     * @this {VirtualizedPackedLayout}
     * @param segments the full list of segments
     * @param s1 the first segment
     * @param s2 the second segment
     */
    removeBetween(segments, s1, s2) {
        if (s1 === s2)
            return;
        let last = s1.next;
        let count = 0;
        while (last !== s2) {
            if (last === segments.start) {
                segments.start = s2;
            }
            this.removeSegmentFromLayoutState(last);
            count++;
            last = last.next;
        }
        s1.next = s2;
        s2.prev = s1;
        segments.length -= count;
    }
    /**
     * @hidden @internal
     * Calculates the cost of a given fit placement, depending on the
     * {@link #packShape} and {@link #_eAspectRatio}.
     * @this {VirtualizedPackedLayout}
     * @param fit the fit to calculate the cost of
     */
    placementCost(fit) {
        if (this.packShape === VirtualizedPackedLayout.Rectangular) {
            if (this._bounds.containsRect(fit)) {
                return 0;
            }
            return Math.max(Math.abs(this._center.x - fit.center.x), Math.abs(this._center.y - fit.center.y) * this._eAspectRatio);
        }
        else { // if (this.packShape === VirtualizedPackedLayout.Elliptical)
            return Math.pow((fit.center.x - this._center.x) / this._eAspectRatio, 2) + Math.pow(fit.center.y - this._center.y, 2);
        }
    }
    /**
     * @hidden @internal
     * Uses the quadtree to determine if the given fit has any
     * intersections anywhere along the perimeter.
     * @this {VirtualizedPackedLayout}
     * @param fit the fit to check
     */
    fitHasIntersections(fit) {
        return this._tree.intersecting(fit.bounds).length > 0;
    }
    /**
     * @hidden @internal
     * Checks if a few nearby segments intersect with the given fit,
     * producing faster interesection detection than a complete check
     * with the quadtree in many cases. However, since it doesn't check
     * the entire perimeter, this function is susceptible to false
     * negatives and should only be used with a more comprehensive check.
     * @this {VirtualizedPackedLayout}
     * @param fit the fit to check
     */
    fastFitHasIntersections(fit) {
        let sNext = fit.s1.next;
        let sPrev = fit.s1.prev;
        for (let i = 0; i < 2; i++) {
            if (this.segmentIntersectsRect(sNext.data, fit.bounds)) {
                return true;
            }
            if (this.segmentIntersectsRect(sPrev.data, fit.bounds)) {
                return true;
            }
            sNext = sNext.next;
            sPrev = sPrev.prev;
        }
        return false;
    }
    /**
     * @hidden @internal
     * Checks whether or not a segment intersects with a given rect.
     * Used for {@link #fastFitHasIntersections}.
     * @this {VirtualizedPackedLayout}
     * @param s the segment to test
     * @param r the rectangle to test
     */
    segmentIntersectsRect(s, r) {
        const left = Math.min(s.x1, s.x2);
        const right = Math.max(s.x1, s.x2);
        const top = Math.min(s.y1, s.y2);
        const bottom = Math.min(s.y1, s.y2);
        return !(left + 1e-7 >= r.right || right - 1e-7 <= r.left || top + 1e-7 >= r.bottom || bottom - 1e-7 <= r.top);
    }
    /**
     * @hidden @internal
     * Checks if two numbers are approximately equal, used for
     * eliminating mistakes caused by floating point error.
     * @this {VirtualizedPackedLayout}
     * @param x the first number
     * @param y the second number
     */
    approxEqual(x, y) {
        return Math.abs(x - y) < 1e-7;
    }
    /**
     * @hidden @internal
     * Checks if a value is a number, used for parameter validation
     * @this {VirtualizedPackedLayout}
     * @param value the value to check
     */
    isNumeric(value) {
        return !isNaN(Number(value.toString()));
    }
    /**
     * @hidden @internal
     * Copies properties to a cloned Layout.
     * @this {VirtualizedPackedLayout}
     * @param {?} copy
     */
    cloneProtected(copy) {
        copy._packShape = this._packShape;
        copy._packMode = this._packMode;
        copy._sortMode = this._sortMode;
        copy._sortOrder = this._sortOrder;
        copy._comparer = this._comparer;
        copy._aspectRatio = this._aspectRatio;
        copy._size = this._size;
        copy._spacing = this._spacing;
        copy._hasCircularNodes = this._hasCircularNodes;
        copy._arrangesToOrigin = this._arrangesToOrigin;
    }
}
/********************** Configuration constants **********************/
// These values determine the shape of the final layout
/**
 * This value for {@link #packShape} causes nodes to be packed
 * into an ellipse.
 *
 * The aspect ratio of this ellipse is determined by either
 * {@link #aspectRatio} or {@link #size}.
 * @constant
 */
VirtualizedPackedLayout.Elliptical = 0;
/**
 * Causes nodes to be packed into a rectangle; this value is used for
 * {@link #packShape}.
 *
 * The aspect ratio of this rectangle is determined by either
 * {@link #aspectRatio} or {@link #size}.
 * @constant
 */
VirtualizedPackedLayout.Rectangular = 1;
/**
 * Causes nodes to be packed into a spiral shape; this value is used
 * for {@link #packShape}.
 *
 * The {@link #aspectRatio} property is ignored in this mode, the
 * {@link #size} is expected to be square, and {@link #hasCircularNodes}
 * will be assumed 'true'. Please see {@link #packShape} for more details.
 */
VirtualizedPackedLayout.Spiral = 2;
// These values determine the size of the layout
/**
 * Nodes will be packed using the {@link #aspectRatio} property, with
 * no size considerations; this value is used for {@link #packMode}.
 *
 * The {@link #spacing} property will be respected in this mode.
 * @constant
 */
VirtualizedPackedLayout.AspectOnly = 10;
/**
 * Nodes will be compressed if necessary (using negative spacing) to fit the given
 * {@link #size}. However, if the {@link #size} is bigger
 * than the packed shape (with 0 spacing), it will not expand to fit it. This value
 * is used for {@link #packMode}.
 *
 * The {@link #spacing} property will be respected in this mode, but only
 * if it does not cause the layout to grow larger than the {@link #size}.
 * @constant
 */
VirtualizedPackedLayout.Fit = 11;
/**
 * Nodes will be either compressed or spaced evenly to fit the given
 * {@link #size}; this value is used for {@link #packMode}.
 *
 * The {@link #spacing} property will not be respected in this mode, and
 * will not do anything if set.
 * @constant
 */
VirtualizedPackedLayout.ExpandToFit = 12;
// These values specify an optional method by which to sort nodes before packing
/**
 * Nodes will not be sorted before packing; this value is used for {@link #sortMode}.
 * @constant
 */
VirtualizedPackedLayout.None = 20;
/**
 * Nodes will be sorted by their maximum side length before packing; this value is
 * used for {@link #sortMode}.
 * @constant
 */
VirtualizedPackedLayout.MaxSide = 21;
/**
 * Nodes will be sorted by their area; this value is used for {@link #sortMode}.
 * @constant
 */
VirtualizedPackedLayout.Area = 22;
// These values specify the order that nodes will be sorted, if applicable
/**
 * Nodes will be sorted in descending order; this value is used for {@link #sortOrder}.
 *
 * Does nothing if {@link #sortMode} is set to {@link VirtualizedPackedLayout.None}.
 * @constant
 */
VirtualizedPackedLayout.Descending = 30;
/**
 * Nodes will be sorted in ascending order; this value is used for {@link #sortOrder}.
 *
 * Does nothing if {@link #sortMode} is set to {@link VirtualizedPackedLayout.None}.
 * @constant
 */
VirtualizedPackedLayout.Ascending = 31;
/**
 * @hidden @internal
 * Class for a node in a {{@link CircularDoublyLinkedList}.
 * Stores a pointer to the previous and next node.
 */
class ListNode {
    constructor(data, prev, next) {
        this.data = data;
        this.prev = prev !== undefined ? prev : this;
        this.next = next !== undefined ? next : this;
    }
}
/**
 * @hidden @internal
 * A Circular doubly linked list, used by {@link VirtualizedPackedLayout} to
 * efficiently store {@link Segment}s with fast insertion and
 * deletion time.
 */
class CircularDoublyLinkedList {
    /**
     * Constructs a new list with an optional list of values
     * @param vals values to create the list with
     */
    constructor(...vals) {
        /**
         * The start of the list, null when the list is empty.
         */
        this.start = null;
        /**
         * The length of the list.
         */
        this.length = 0;
        if (vals.length > 0) {
            this.push(...vals);
        }
    }
    /**
     * Inserts the given value directly after the given node
     * @this {CircularDoublyLinkedList}
     * @param val the value to insert
     * @param node the node to insert after
     * @return {ListNode<T>} the new node
     */
    insertAfter(val, node) {
        if (node === null) {
            const newnode = new ListNode(val);
            newnode.prev = newnode;
            newnode.next = newnode;
            this.length = 1;
            return this.start = newnode;
        }
        const tmp = node.next;
        node.next = new ListNode(val, node, tmp);
        tmp.prev = node.next;
        this.length++;
        return node.next;
    }
    /**
     * Inserts the given value or values at the end of the list
     * @this {CircularDoublyLinkedList}
     * @param vals the value(s) to insert
     * @return {ListNode<T>} the node for the last value inserted (a list of values is inserted sequentially)
     */
    push(...vals) {
        if (vals.length === 0) {
            throw new Error('You must push at least one element!');
        }
        const sp = this.start !== null ? this.start.prev : null;
        let last = this.insertAfter(vals[0], sp);
        for (let i = 1; i < vals.length; i++) {
            last = this.insertAfter(vals[i], last);
        }
        return last;
    }
    /**
     * Removes the given node from the list
     * @this {CircularDoublyLinkedList}
     * @param node the node to remove
     */
    remove(node) {
        this.length--;
        if (this.length) {
            node.prev.next = node.next;
            node.next.prev = node.prev;
            if (node === this.start) {
                this.start = node.next;
            }
        }
        else {
            this.start = null;
        }
    }
    /**
     * Removes all nodes between the given start and end point (exclusive).
     * Returns the given end node.
     * @this {CircularDoublyLinkedList}
     * @param start node to start removing after
     * @param end node to stop removing at
     * @return {ListNode<T>} the end node
     */
    removeBetween(start, end) {
        if (start !== end) {
            let last = start.next;
            let count = 0;
            while (last !== end) {
                if (last === this.start) {
                    this.start = end;
                }
                count++;
                last = last.next;
            }
            start.next = end;
            end.prev = start;
            this.length -= count;
            return end;
        }
        return start;
    }
}
/**
 * The following is a BSD-licensed implementation of the
 * Matousek-Sharir-Welzl algorithm for finding the smallest
 * enclosing circle around a given set of circles. The
 * original algorithm was adapted to support enclosing points
 * by assuming that the radius of a point is 0.
 */
/**
 * Copyright 2010-2016 Mike Bostock
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without modification,
 * are permitted provided that the following conditions are met:
 *
 * * Redistributions of source code must retain the above copyright notice, this
 *   list of conditions and the following disclaimer.
 *
 * * Redistributions in binary form must reproduce the above copyright notice,
 *   this list of conditions and the following disclaimer in the documentation
 *   and/or other materials provided with the distribution.
 *
 * * Neither the name of the author nor the names of contributors may be used to
 *   endorse or promote products derived from this software without specific prior
 *   written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
/**
 * @hidden @internal
 * Represents a circle for the purposes of the smallest-enclosing
 * circle algorithm. The x and y values represent the center of
 * the circle.
 */
class Circle extends go.Point {
    constructor(x, y, r) {
        super(x, y);
        this.r = r;
    }
}
/**
 * @hidden @internal
 * @param circles array of circles of points to find the enclosing circle for
 */
function enclose(circles) {
    let i = 0;
    const n = (circles = shuffle(circles.slice())).length;
    let B = new Array();
    let p;
    let e = null;
    while (i < n) {
        p = circles[i];
        if (e !== null && enclosesWeak(e, p))
            ++i;
        else
            e = encloseBasis(B = extendBasis(B, p)), i = 0;
    }
    if (e !== null) {
        return circleToRect(e);
    }
    else { // this will never happen, but needs to be here for strict TypeScript compilation
        throw new Error('Assertion error');
    }
}
/**
 * @hidden @internal
 * Converts a Circle to a go.Rect object
 * @param c the Circle to convert
 */
function circleToRect(c) {
    return new go.Rect(c.x - c.r, c.y - c.r, c.r * 2, c.r * 2);
}
/**
 * @hidden @internal
 */
function extendBasis(B, p) {
    if (enclosesWeakAll(p, B))
        return [p];
    // If we get here then B must have at least one element.
    for (let i = 0; i < B.length; ++i) {
        if (enclosesNot(p, B[i])
            && enclosesWeakAll(encloseBasis2(B[i], p), B)) {
            return [B[i], p];
        }
    }
    // If we get here then B must have at least two elements.
    for (let i = 0; i < B.length - 1; ++i) {
        for (let j = i + 1; j < B.length; ++j) {
            if (enclosesNot(encloseBasis2(B[i], B[j]), p)
                && enclosesNot(encloseBasis2(B[i], p), B[j])
                && enclosesNot(encloseBasis2(B[j], p), B[i])
                && enclosesWeakAll(encloseBasis3(B[i], B[j], p), B)) {
                return [B[i], B[j], p];
            }
        }
    }
    // If we get here then something is very wrong.
    throw new Error('Assertion error');
}
/**
 * @hidden @internal
 */
function enclosesNot(a, b) {
    const ar = a instanceof Circle ? a.r : 0;
    const br = b instanceof Circle ? b.r : 0;
    const dr = ar - br;
    const dx = b.x - a.x;
    const dy = b.y - a.y;
    return dr < 0 || dr * dr < dx * dx + dy * dy;
}
/**
 * @hidden @internal
 */
function enclosesWeak(a, b) {
    const ar = a instanceof Circle ? a.r : 0;
    const br = b instanceof Circle ? b.r : 0;
    const dr = ar - br + 1e-6;
    const dx = b.x - a.x;
    const dy = b.y - a.y;
    return dr > 0 && dr * dr > dx * dx + dy * dy;
}
/**
 * @hidden @internal
 */
function enclosesWeakAll(a, B) {
    for (let i = 0; i < B.length; ++i) {
        if (!enclosesWeak(a, B[i])) {
            return false;
        }
    }
    return true;
}
/**
 * @hidden @internal
 */
function encloseBasis(B) {
    switch (B.length) {
        case 2: return encloseBasis2(B[0], B[1]);
        case 3: return encloseBasis3(B[0], B[1], B[2]);
        default: return encloseBasis1(B[0]); // case 1
    }
}
/**
 * @hidden @internal
 */
function encloseBasis1(a) {
    const ar = a instanceof Circle ? a.r : 0;
    return new Circle(a.x, a.y, ar);
}
/**
 * @hidden @internal
 */
function encloseBasis2(a, b) {
    const ar = a instanceof Circle ? a.r : 0;
    const br = b instanceof Circle ? b.r : 0;
    const x1 = a.x;
    const y1 = a.y;
    const r1 = ar;
    const x2 = b.x;
    const y2 = b.y;
    const r2 = br;
    const x21 = x2 - x1;
    const y21 = y2 - y1;
    const r21 = r2 - r1;
    const l = Math.sqrt(x21 * x21 + y21 * y21);
    return new Circle((x1 + x2 + x21 / l * r21) / 2, (y1 + y2 + y21 / l * r21) / 2, (l + r1 + r2) / 2);
}
/**
 * @hidden @internal
 */
function encloseBasis3(a, b, c) {
    const ar = a instanceof Circle ? a.r : 0;
    const br = b instanceof Circle ? b.r : 0;
    const cr = c instanceof Circle ? c.r : 0;
    const x1 = a.x;
    const y1 = a.y;
    const r1 = ar;
    const x2 = b.x;
    const y2 = b.y;
    const r2 = br;
    const x3 = c.x;
    const y3 = c.y;
    const r3 = cr;
    const a2 = x1 - x2;
    const a3 = x1 - x3;
    const b2 = y1 - y2;
    const b3 = y1 - y3;
    const c2 = r2 - r1;
    const c3 = r3 - r1;
    const d1 = x1 * x1 + y1 * y1 - r1 * r1;
    const d2 = d1 - x2 * x2 - y2 * y2 + r2 * r2;
    const d3 = d1 - x3 * x3 - y3 * y3 + r3 * r3;
    const ab = a3 * b2 - a2 * b3;
    const xa = (b2 * d3 - b3 * d2) / (ab * 2) - x1;
    const xb = (b3 * c2 - b2 * c3) / ab;
    const ya = (a3 * d2 - a2 * d3) / (ab * 2) - y1;
    const yb = (a2 * c3 - a3 * c2) / ab;
    const A = xb * xb + yb * yb - 1;
    const B = 2 * (r1 + xa * xb + ya * yb);
    const C = xa * xa + ya * ya - r1 * r1;
    const r = -(A ? (B + Math.sqrt(B * B - 4 * A * C)) / (2 * A) : C / B);
    return new Circle(x1 + xa + xb * r, y1 + ya + yb * r, r);
}
/**
 * @hidden @internal
 * Shuffles array in place.
 * @param {Array} a items An array containing the items.
 */
function shuffle(a) {
    let j;
    let x;
    let i;
    for (i = a.length - 1; i > 0; i--) {
        j = Math.floor(Math.random() * (i + 1));
        x = a[i];
        a[i] = a[j];
        a[j] = x;
    }
    return a;
}