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Aumentar el rendimiento de los jugadores de StarCraft con Dashboard Analytics

Aumentar el rendimiento de los jugadores de StarCraft con Dashboard Analytics

StarCraft II es un juego de estrategia en tiempo real lanzado por Blizzard. Es uno de los primeros e-sports que consolidó esta industria y cuenta con una gran comunidad. Desde 2021 hasta 2019, se han celebrado más de 15 campeonatos con una recompensa total de más de 1M de dólares en todo el mundo. Los jugadores de alto rango han tenido ganancias acumuladas de 500K, y cada año une a miles de jugadores a través de varios campeonatos alrededor del mundo.

El propio Juego de StarCraft ofrece algunas analíticas reveladoras sobre cada partida una vez terminada ésta, para dar pistas sobre el rendimiento general del juego a lo largo del tiempo en gráficos de Valor del Ejército, Trabajadores Activos y Actualizaciones a lo largo del tiempo. Además, en cuanto al rendimiento general, ofrecen métricas como recursos no consumidos, número de unidades y trabajadores creados y APM (Acciones por minuto)

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Fig1. Algunos datos que los juegos de StarCraft 2 te dan después de jugar

Hoy nos adentraremos en un análisis teniendo en cuenta el conjunto de datos elaborado por Thompson JJ et al SkillCraft1 Master Table Dataset apoyado en el paper La telemetría de videojuegos como herramienta crítica en el estudio del aprendizaje de habilidades complejas.El objetivo principal de este estudio es estudiar los datos de telemetría para comprender el desarrollo de habilidades complejas. El estudio identifica datos de procesamiento cognitivo-motor, atencional y perceptivo.

Tomando en cuenta el conjunto de datos de SkillCraft [1] podemos mejorar o proponer un nuevo dashboard de analítica que podría ayudar al jugador a conocer mejor su rendimiento en el juego, comparándolo con la liga anterior o superior para ayudar al jugador a saber en qué posición se encuentra con respecto a los demás. Este tablero podría ofrecerse al jugador al principio y al final de la liga, ofreciendo una herramienta para medir la eficiencia del jugador a lo largo de la temporada.

Atención y destreza: APM, PAC y latencia de la acción

Las acciones por minuto (APM) es una medida de la capacidad de carga de un jugador y es una de las métricas para juzgar la habilidad del jugador [2]. Idealmente, el APM incluye sólo las acciones «productivas». Sin embargo, el APM puede estar inflado artificialmente por acciones repetitivas superfluas. Como métrica aislada, el APM ofrece un valor parcial, ya que podría ser digno de estudio si es una métrica que está correlacionada con algún uso de teclas de acceso rápido (como el número de teclas de acceso rápido únicas, la asignación y la selección).

El Ciclo de Acción de la Percepción es una métrica para medir la atención dentro de StarCraft II. Según los autores del artículo Video Game Telemetry as a Critical Tool in the Study of Complex Skill Learning, cada variable pertenece a un periodo de tiempo en el que los jugadores se fijan y actúan en un lugar concreto. Dentro del juego, un conjunto predominante de acciones ocurre dentro de este ciclo de acción de percepción. Uno de los principales momentos del juego que podría estar dentro de esta definición incluye mirar el mapa en cierta ubicación y ejecutar cierto tipo de acciones, cambiando luego a otra ubicación.
En general, un número de PaCs más alto da un ejemplo de multitarea o de buena habilidad, y en última instancia establece una diferencia entre diferentes ligas.

Fig. 2. Algunos ejemplos del ciclo de acción de percepción dentro de StarCraft para cada una de las razas. El ciclo de acción de percepción mide la atención, los procesos perceptivos y la habilidad motora cognitiva

Para demostrar la importancia de estas variables a lo largo del progreso del jugador, hemos producido varios experimentos. La matriz de correlación entre el Índice de la Liga y las diferentes variables muestran datos interesantes: mayores APMs y Número de PACs se asocian a un mayor ranking en la Liga StarCraft, y menor Gap entre PACs y Latencia de Acciones se asocian a mayores ligas, lo que nos hace establecer la hipótesis de que a mayor número de acciones por segundo y número de ciclos de atención mejor puede ser el jugador, y el menor tiempo en ejecutar acciones son también un indicador de una mayor liga.

Fig. 3. Matriz de correlación para estudiar la relación entre PaCs y APMs.

Tomando otro enfoque desde la perspectiva del aprendizaje automático, hemos construido un clasificador XGBoost de la Liga de Índices para medir la importancia de las diferentes características con respecto a la clasificación en la liga utilizando el marco de explicabilidad SHAP [3].

SHAP StarCraft1
SHAP StarCraft2

Fig 4. SHAP. Se muestra en Rojo las características aque contribuyen a empujar la salida del modelo desde el valor base. En este caso, el clasificador XGBoost muestra que Latencia de la acción ,APM, los comportamientos de las teclas de acceso rápido y los huecos entre PACs influyen mucho en el modelo

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Captura de pantalla 2021 09 15 a las 16.22.10

Comparación de APM y PaCs en todas las ligas. A medida que la habilidad del jugador aumenta, también lo hace el APM y el Número de PaCs, y la Brecha entre Caps disminuye.

Análisis de cuadros de mando: Medir el rendimiento y la atención

Teniendo en cuenta el análisis de las partidas anteriores, podemos proponer el siguiente cuadro de mandos que podría entregarse al jugador al principio y al final de la temporada, teniendo en cuenta que esto podría ofrecer al jugador la oportunidad de comparar su rendimiento con el de la liga anterior y con el de la superior para mejorar el juego.
Además de eso, podemos añadir recomendaciones para mejorar la jugabilidad centrándonos en los análisis procedentes de la siguiente liga, como el número de asignaciones de teclas de acceso rápido. Para ello, tomamos los valores de la mediana y de la moda de la siguiente liga y comparamos los valores de la liga actual con el fin de compararlos.

Con estas conclusiones procedentes del análisis del conjunto de datos, podemos llegar a un cuadro de mando analítico dividido en tres categorías principales : atención, destreza y Recomendaciones. Estas tres categorías incluyen el análisis procedente de la liga anterior y de la siguiente en un conjunto de juegos distribuidos de forma equitativa entre las diferentes ligas.

[1] SkillCraft Dataset

[2] Judging player skill

[3] SHAP explainabilty dataset

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n(){!a.hasLayer(e)&&!a.hasLayer(e.__parent)||this._inZoomAnimation||(this._map.off("moveend",n,this),this.off("animationend",n,this),a.hasLayer(e)?t():e.__parent._icon&&(this.once("spiderfied",t,this),e.__parent.spiderfy()))};e._icon&&this._map.getBounds().contains(e.getLatLng())?t():e.__parent._zoom=0;a--)if(e[a]===t)return e.splice(a,1),!0},_removeFromGridUnclustered:function(e,t){for(var a=this._map,n=this._gridUnclustered,r=Math.floor(this._map.getMinZoom());t>=r&&n[t].removeObject(e,a.project(e.getLatLng(),t));t--);},_childMarkerDragStart:function(e){e.target.__dragStart=e.target._latlng},_childMarkerMoved:function(e){if(!this._ignoreMove&&!e.target.__dragStart){var t=e.target._popup&&e.target._popup.isOpen();this._moveChild(e.target,e.oldLatLng,e.latlng),t&&e.target.openPopup()}},_moveChild:function(e,t,a){e._latlng=t,this.removeLayer(e),e._latlng=a,this.addLayer(e)},_childMarkerDragEnd:function(e){var t=e.target.__dragStart;delete e.target.__dragStart,t&&this._moveChild(e.target,t,e.target._latlng)},_removeLayer:function(e,t,a){var n=this._gridClusters,r=this._gridUnclustered,i=this._featureGroup,l=this._map,o=Math.floor(this._map.getMinZoom());t&&this._removeFromGridUnclustered(e,this._maxZoom);var s,u=e.__parent,c=u._markers;for(this._arraySplice(c,e);u&&(u._childCount--,u._boundsNeedUpdate=!0,!(u._zoom"+t+"",className:"marker-cluster"+a,iconSize:new L.Point(40,40)})},_bindEvents:function(){var e=this._map,t=this.options.spiderfyOnMaxZoom,a=this.options.showCoverageOnHover,n=this.options.zoomToBoundsOnClick;(t||n)&&this.on("clusterclick",this._zoomOrSpiderfy,this),a&&(this.on("clustermouseover",this._showCoverage,this),this.on("clustermouseout",this._hideCoverage,this),e.on("zoomend",this._hideCoverage,this))},_zoomOrSpiderfy:function(e){for(var t=e.layer,a=t;1===a._childClusters.length;)a=a._childClusters[0];a._zoom===this._maxZoom&&a._childCount===t._childCount&&this.options.spiderfyOnMaxZoom?t.spiderfy():this.options.zoomToBoundsOnClick&&t.zoomToBounds(),e.originalEvent&&13===e.originalEvent.keyCode&&this._map._container.focus()},_showCoverage:function(e){var t=this._map;this._inZoomAnimation||(this._shownPolygon&&t.removeLayer(this._shownPolygon),e.layer.getChildCount()>2&&e.layer!==this._spiderfied&&(this._shownPolygon=new L.Polygon(e.layer.getConvexHull(),this.options.polygonOptions),t.addLayer(this._shownPolygon)))},_hideCoverage:function(){this._shownPolygon&&(this._map.removeLayer(this._shownPolygon),this._shownPolygon=null)},_unbindEvents:function(){var e=this.options.spiderfyOnMaxZoom,t=this.options.showCoverageOnHover,a=this.options.zoomToBoundsOnClick,n=this._map;(e||a)&&this.off("clusterclick",this._zoomOrSpiderfy,this),t&&(this.off("clustermouseover",this._showCoverage,this),this.off("clustermouseout",this._hideCoverage,this),n.off("zoomend",this._hideCoverage,this))},_zoomEnd:function(){this._map&&(this._mergeSplitClusters(),this._zoom=Math.round(this._map._zoom),this._currentShownBounds=this._getExpandedVisibleBounds())},_moveEnd:function(){if(!this._inZoomAnimation){var e=this._getExpandedVisibleBounds();this._topClusterLevel._recursivelyRemoveChildrenFromMap(this._currentShownBounds,Math.floor(this._map.getMinZoom()),this._zoom,e),this._topClusterLevel._recursivelyAddChildrenToMap(null,Math.round(this._map._zoom),e),this._currentShownBounds=e}},_generateInitialClusters:function(){var e=Math.ceil(this._map.getMaxZoom()),t=Math.floor(this._map.getMinZoom()),a=this.options.maxClusterRadius,n=a;"function"!==typeof a&&(n=function(){return a}),null!==this.options.disableClusteringAtZoom&&(e=this.options.disableClusteringAtZoom-1),this._maxZoom=e,this._gridClusters={},this._gridUnclustered={};for(var r=e;r>=t;r--)this._gridClusters[r]=new L.DistanceGrid(n(r)),this._gridUnclustered[r]=new L.DistanceGrid(n(r));this._topClusterLevel=new this._markerCluster(this,t-1)},_addLayer:function(e,t){var a,n,r=this._gridClusters,i=this._gridUnclustered,l=Math.floor(this._map.getMinZoom());for(this.options.singleMarkerMode&&this._overrideMarkerIcon(e),e.on(this._childMarkerEventHandlers,this);t>=l;t--){a=this._map.project(e.getLatLng(),t);var o=r[t].getNearObject(a);if(o)return o._addChild(e),void(e.__parent=o);if(o=i[t].getNearObject(a)){var s=o.__parent;s&&this._removeLayer(o,!1);var u=new this._markerCluster(this,t,o,e);r[t].addObject(u,this._map.project(u._cLatLng,t)),o.__parent=u,e.__parent=u;var c=u;for(n=t-1;n>s._zoom;n--)c=new this._markerCluster(this,n,c),r[n].addObject(c,this._map.project(o.getLatLng(),n));return s._addChild(c),void this._removeFromGridUnclustered(o,t)}i[t].addObject(e,a)}this._topClusterLevel._addChild(e),e.__parent=this._topClusterLevel},_refreshClustersIcons:function(){this._featureGroup.eachLayer((function(e){e instanceof L.MarkerCluster&&e._iconNeedsUpdate&&e._updateIcon()}))},_enqueue:function(e){this._queue.push(e),this._queueTimeout||(this._queueTimeout=setTimeout(L.bind(this._processQueue,this),300))},_processQueue:function(){for(var e=0;ee?(this._animationStart(),this._animationZoomOut(this._zoom,e)):this._moveEnd()},_getExpandedVisibleBounds:function(){return this.options.removeOutsideVisibleBounds?L.Browser.mobile?this._checkBoundsMaxLat(this._map.getBounds()):this._checkBoundsMaxLat(this._map.getBounds().pad(1)):this._mapBoundsInfinite},_checkBoundsMaxLat:function(e){var t=this._maxLat;return void 0!==t&&(e.getNorth()>=t&&(e._northEast.lat=1/0),e.getSouth()<=-t&&(e._southWest.lat=-1/0)),e},_animationAddLayerNonAnimated:function(e,t){if(t===e)this._featureGroup.addLayer(e);else if(2===t._childCount){t._addToMap();var a=t.getAllChildMarkers();this._featureGroup.removeLayer(a[0]),this._featureGroup.removeLayer(a[1])}else t._updateIcon()},_extractNonGroupLayers:function(e,t){var a,n=e.getLayers(),r=0;for(t=t||[];r=0;a--)l=s[a],n.contains(l._latlng)||r.removeLayer(l)})),this._forceLayout(),this._topClusterLevel._recursivelyBecomeVisible(n,t),r.eachLayer((function(e){e instanceof L.MarkerCluster||!e._icon||e.clusterShow()})),this._topClusterLevel._recursively(n,e,t,(function(e){e._recursivelyRestoreChildPositions(t)})),this._ignoreMove=!1,this._enqueue((function(){this._topClusterLevel._recursively(n,e,i,(function(e){r.removeLayer(e),e.clusterShow()})),this._animationEnd()}))},_animationZoomOut:function(e,t){this._animationZoomOutSingle(this._topClusterLevel,e-1,t),this._topClusterLevel._recursivelyAddChildrenToMap(null,t,this._getExpandedVisibleBounds()),this._topClusterLevel._recursivelyRemoveChildrenFromMap(this._currentShownBounds,Math.floor(this._map.getMinZoom()),e,this._getExpandedVisibleBounds())},_animationAddLayer:function(e,t){var a=this,n=this._featureGroup;n.addLayer(e),t!==e&&(t._childCount>2?(t._updateIcon(),this._forceLayout(),this._animationStart(),e._setPos(this._map.latLngToLayerPoint(t.getLatLng())),e.clusterHide(),this._enqueue((function(){n.removeLayer(e),e.clusterShow(),a._animationEnd()}))):(this._forceLayout(),a._animationStart(),a._animationZoomOutSingle(t,this._map.getMaxZoom(),this._zoom)))}},_animationZoomOutSingle:function(e,t,a){var n=this._getExpandedVisibleBounds(),r=Math.floor(this._map.getMinZoom());e._recursivelyAnimateChildrenInAndAddSelfToMap(n,r,t+1,a);var i=this;this._forceLayout(),e._recursivelyBecomeVisible(n,a),this._enqueue((function(){if(1===e._childCount){var l=e._markers[0];this._ignoreMove=!0,l.setLatLng(l.getLatLng()),this._ignoreMove=!1,l.clusterShow&&l.clusterShow()}else e._recursively(n,a,r,(function(e){e._recursivelyRemoveChildrenFromMap(n,r,t+1)}));i._animationEnd()}))},_animationEnd:function(){this._map&&(this._map._mapPane.className=this._map._mapPane.className.replace(" leaflet-cluster-anim","")),this._inZoomAnimation--,this.fire("animationend")},_forceLayout:function(){L.Util.falseFn(document.body.offsetWidth)}}),L.markerClusterGroup=function(e){return new L.MarkerClusterGroup(e)};var a=L.MarkerCluster=L.Marker.extend({options:L.Icon.prototype.options,initialize:function(e,t,a,n){L.Marker.prototype.initialize.call(this,a?a._cLatLng||a.getLatLng():new L.LatLng(0,0),{icon:this,pane:e.options.clusterPane}),this._group=e,this._zoom=t,this._markers=[],this._childClusters=[],this._childCount=0,this._iconNeedsUpdate=!0,this._boundsNeedUpdate=!0,this._bounds=new L.LatLngBounds,a&&this._addChild(a),n&&this._addChild(n)},getAllChildMarkers:function(e,t){e=e||[];for(var a=this._childClusters.length-1;a>=0;a--)this._childClusters[a].getAllChildMarkers(e);for(var n=this._markers.length-1;n>=0;n--)t&&this._markers[n].__dragStart||e.push(this._markers[n]);return e},getChildCount:function(){return this._childCount},zoomToBounds:function(e){for(var t,a=this._childClusters.slice(),n=this._group._map,r=n.getBoundsZoom(this._bounds),i=this._zoom+1,l=n.getZoom();a.length>0&&r>i;){i++;var o=[];for(t=0;ti?this._group._map.setView(this._latlng,i):r<=l?this._group._map.setView(this._latlng,l+1):this._group._map.fitBounds(this._bounds,e)},getBounds:function(){var e=new L.LatLngBounds;return e.extend(this._bounds),e},_updateIcon:function(){this._iconNeedsUpdate=!0,this._icon&&this.setIcon(this)},createIcon:function(){return this._iconNeedsUpdate&&(this._iconObj=this._group.options.iconCreateFunction(this),this._iconNeedsUpdate=!1),this._iconObj.createIcon()},createShadow:function(){return this._iconObj.createShadow()},_addChild:function(e,t){this._iconNeedsUpdate=!0,this._boundsNeedUpdate=!0,this._setClusterCenter(e),e instanceof L.MarkerCluster?(t||(this._childClusters.push(e),e.__parent=this),this._childCount+=e._childCount):(t||this._markers.push(e),this._childCount++),this.__parent&&this.__parent._addChild(e,!0)},_setClusterCenter:function(e){this._cLatLng||(this._cLatLng=e._cLatLng||e._latlng)},_resetBounds:function(){var e=this._bounds;e._southWest&&(e._southWest.lat=1/0,e._southWest.lng=1/0),e._northEast&&(e._northEast.lat=-1/0,e._northEast.lng=-1/0)},_recalculateBounds:function(){var e,t,a,n,r=this._markers,i=this._childClusters,l=0,o=0,s=this._childCount;if(0!==s){for(this._resetBounds(),e=0;e=0;a--)(n=r[a])._icon&&(n._setPos(t),n.clusterHide())}),(function(e){var a,n,r=e._childClusters;for(a=r.length-1;a>=0;a--)(n=r[a])._icon&&(n._setPos(t),n.clusterHide())}))},_recursivelyAnimateChildrenInAndAddSelfToMap:function(e,t,a,n){this._recursively(e,n,t,(function(r){r._recursivelyAnimateChildrenIn(e,r._group._map.latLngToLayerPoint(r.getLatLng()).round(),a),r._isSingleParent()&&a-1===n?(r.clusterShow(),r._recursivelyRemoveChildrenFromMap(e,t,a)):r.clusterHide(),r._addToMap()}))},_recursivelyBecomeVisible:function(e,t){this._recursively(e,this._group._map.getMinZoom(),t,null,(function(e){e.clusterShow()}))},_recursivelyAddChildrenToMap:function(e,t,a){this._recursively(a,this._group._map.getMinZoom()-1,t,(function(n){if(t!==n._zoom)for(var r=n._markers.length-1;r>=0;r--){var i=n._markers[r];a.contains(i._latlng)&&(e&&(i._backupLatlng=i.getLatLng(),i.setLatLng(e),i.clusterHide&&i.clusterHide()),n._group._featureGroup.addLayer(i))}}),(function(t){t._addToMap(e)}))},_recursivelyRestoreChildPositions:function(e){for(var t=this._markers.length-1;t>=0;t--){var a=this._markers[t];a._backupLatlng&&(a.setLatLng(a._backupLatlng),delete a._backupLatlng)}if(e-1===this._zoom)for(var n=this._childClusters.length-1;n>=0;n--)this._childClusters[n]._restorePosition();else for(var r=this._childClusters.length-1;r>=0;r--)this._childClusters[r]._recursivelyRestoreChildPositions(e)},_restorePosition:function(){this._backupLatlng&&(this.setLatLng(this._backupLatlng),delete this._backupLatlng)},_recursivelyRemoveChildrenFromMap:function(e,t,a,n){var r,i;this._recursively(e,t-1,a-1,(function(e){for(i=e._markers.length-1;i>=0;i--)r=e._markers[i],n&&n.contains(r._latlng)||(e._group._featureGroup.removeLayer(r),r.clusterShow&&r.clusterShow())}),(function(e){for(i=e._childClusters.length-1;i>=0;i--)r=e._childClusters[i],n&&n.contains(r._latlng)||(e._group._featureGroup.removeLayer(r),r.clusterShow&&r.clusterShow())}))},_recursively:function(e,t,a,n,r){var i,l,o=this._childClusters,s=this._zoom;if(t<=s&&(n&&n(this),r&&s===a&&r(this)),s=0;i--)(l=o[i])._boundsNeedUpdate&&l._recalculateBounds(),e.intersects(l._bounds)&&l._recursively(e,t,a,n,r)},_isSingleParent:function(){return this._childClusters.length>0&&this._childClusters[0]._childCount===this._childCount}});L.Marker.include({clusterHide:function(){var e=this.options.opacity;return this.setOpacity(0),this.options.opacity=e,this},clusterShow:function(){return this.setOpacity(this.options.opacity)}}),L.DistanceGrid=function(e){this._cellSize=e,this._sqCellSize=e*e,this._grid={},this._objectPoint={}},L.DistanceGrid.prototype={addObject:function(e,t){var a=this._getCoord(t.x),n=this._getCoord(t.y),r=this._grid,i=r[n]=r[n]||{},l=i[a]=i[a]||[],o=L.Util.stamp(e);this._objectPoint[o]=t,l.push(e)},updateObject:function(e,t){this.removeObject(e),this.addObject(e,t)},removeObject:function(e,t){var a,n,r=this._getCoord(t.x),i=this._getCoord(t.y),l=this._grid,o=l[i]=l[i]||{},s=o[r]=o[r]||[];for(delete this._objectPoint[L.Util.stamp(e)],a=0,n=s.length;a=0;a--)n=t[a],(r=this.getDistant(n,e))>0&&(o.push(n),r>i&&(i=r,l=n));return{maxPoint:l,newPoints:o}},buildConvexHull:function(e,t){var a=[],n=this.findMostDistantPointFromBaseLine(e,t);return n.maxPoint?a=(a=a.concat(this.buildConvexHull([e[0],n.maxPoint],n.newPoints))).concat(this.buildConvexHull([n.maxPoint,e[1]],n.newPoints)):[e[0]]},getConvexHull:function(e){var t,a=!1,n=!1,r=!1,i=!1,l=null,o=null,s=null,u=null,c=null,d=null;for(t=e.length-1;t>=0;t--){var p=e[t];(!1===a||p.lat>a)&&(l=p,a=p.lat),(!1===n||p.latr)&&(s=p,r=p.lng),(!1===i||p.lng=0;t--)e=a[t].getLatLng(),n.push(e);return L.QuickHull.getConvexHull(n)}}),L.MarkerCluster.include({_2PI:2*Math.PI,_circleFootSeparation:25,_circleStartAngle:0,_spiralFootSeparation:28,_spiralLengthStart:11,_spiralLengthFactor:5,_circleSpiralSwitchover:9,spiderfy:function(){if(this._group._spiderfied!==this&&!this._group._inZoomAnimation){var e,t=this.getAllChildMarkers(null,!0),a=this._group._map.latLngToLayerPoint(this._latlng);this._group._unspiderfy(),this._group._spiderfied=this,this._group.options.spiderfyShapePositions?e=this._group.options.spiderfyShapePositions(t.length,a):t.length>=this._circleSpiralSwitchover?e=this._generatePointsSpiral(t.length,a):(a.y+=10,e=this._generatePointsCircle(t.length,a)),this._animationSpiderfy(t,e)}},unspiderfy:function(e){this._group._inZoomAnimation||(this._animationUnspiderfy(e),this._group._spiderfied=null)},_generatePointsCircle:function(e,t){var a,n,r=this._group.options.spiderfyDistanceMultiplier*this._circleFootSeparation*(2+e)/this._2PI,i=this._2PI/e,l=[];for(r=Math.max(r,35),l.length=e,a=0;a=0;a--)a=0;t--)e=i[t],r.removeLayer(e),e._preSpiderfyLatlng&&(e.setLatLng(e._preSpiderfyLatlng),delete e._preSpiderfyLatlng),e.setZIndexOffset&&e.setZIndexOffset(0),e._spiderLeg&&(n.removeLayer(e._spiderLeg),delete e._spiderLeg);a.fire("unspiderfied",{cluster:this,markers:i}),a._ignoreMove=!1,a._spiderfied=null}}),L.MarkerClusterNonAnimated=L.MarkerCluster.extend({_animationSpiderfy:function(e,t){var a,n,r,i,l=this._group,o=l._map,s=l._featureGroup,u=this._group.options.spiderLegPolylineOptions;for(l._ignoreMove=!0,a=0;a=0;a--)o=c.layerPointToLatLng(t[a]),(n=e[a])._preSpiderfyLatlng=n._latlng,n.setLatLng(o),n.clusterShow&&n.clusterShow(),f&&((i=(r=n._spiderLeg)._path).style.strokeDashoffset=0,r.setStyle({opacity:v}));this.setOpacity(.3),u._ignoreMove=!1,setTimeout((function(){u._animationEnd(),u.fire("spiderfied",{cluster:s,markers:e})}),200)},_animationUnspiderfy:function(e){var t,a,n,r,i,l,o=this,s=this._group,u=s._map,c=s._featureGroup,d=e?u._latLngToNewLayerPoint(this._latlng,e.zoom,e.center):u.latLngToLayerPoint(this._latlng),p=this.getAllChildMarkers(null,!0),h=L.Path.SVG;for(s._ignoreMove=!0,s._animationStart(),this.setOpacity(1),a=p.length-1;a>=0;a--)(t=p[a])._preSpiderfyLatlng&&(t.closePopup(),t.setLatLng(t._preSpiderfyLatlng),delete t._preSpiderfyLatlng,l=!0,t._setPos&&(t._setPos(d),l=!1),t.clusterHide&&(t.clusterHide(),l=!1),l&&c.removeLayer(t),h&&(i=(r=(n=t._spiderLeg)._path).getTotalLength()+.1,r.style.strokeDashoffset=i,n.setStyle({opacity:0})));s._ignoreMove=!1,setTimeout((function(){var e=0;for(a=p.length-1;a>=0;a--)(t=p[a])._spiderLeg&&e++;for(a=p.length-1;a>=0;a--)(t=p[a])._spiderLeg&&(t.clusterShow&&t.clusterShow(),t.setZIndexOffset&&t.setZIndexOffset(0),e>1&&c.removeLayer(t),u.removeLayer(t._spiderLeg),delete t._spiderLeg);s._animationEnd(),s.fire("unspiderfied",{cluster:o,markers:p})}),200)}}),L.MarkerClusterGroup.include({_spiderfied:null,unspiderfy:function(){this._unspiderfy.apply(this,arguments)},_spiderfierOnAdd:function(){this._map.on("click",this._unspiderfyWrapper,this),this._map.options.zoomAnimation&&this._map.on("zoomstart",this._unspiderfyZoomStart,this),this._map.on("zoomend",this._noanimationUnspiderfy,this),L.Browser.touch||this._map.getRenderer(this)},_spiderfierOnRemove:function(){this._map.off("click",this._unspiderfyWrapper,this),this._map.off("zoomstart",this._unspiderfyZoomStart,this),this._map.off("zoomanim",this._unspiderfyZoomAnim,this),this._map.off("zoomend",this._noanimationUnspiderfy,this),this._noanimationUnspiderfy()},_unspiderfyZoomStart:function(){this._map&&this._map.on("zoomanim",this._unspiderfyZoomAnim,this)},_unspiderfyZoomAnim:function(e){L.DomUtil.hasClass(this._map._mapPane,"leaflet-touching")||(this._map.off("zoomanim",this._unspiderfyZoomAnim,this),this._unspiderfy(e))},_unspiderfyWrapper:function(){this._unspiderfy()},_unspiderfy:function(e){this._spiderfied&&this._spiderfied.unspiderfy(e)},_noanimationUnspiderfy:function(){this._spiderfied&&this._spiderfied._noanimationUnspiderfy()},_unspiderfyLayer:function(e){e._spiderLeg&&(this._featureGroup.removeLayer(e),e.clusterShow&&e.clusterShow(),e.setZIndexOffset&&e.setZIndexOffset(0),this._map.removeLayer(e._spiderLeg),delete e._spiderLeg)}}),L.MarkerClusterGroup.include({refreshClusters:function(e){return e?e instanceof L.MarkerClusterGroup?e=e._topClusterLevel.getAllChildMarkers():e instanceof L.LayerGroup?e=e._layers:e instanceof L.MarkerCluster?e=e.getAllChildMarkers():e instanceof L.Marker&&(e=[e]):e=this._topClusterLevel.getAllChildMarkers(),this._flagParentsIconsNeedUpdate(e),this._refreshClustersIcons(),this.options.singleMarkerMode&&this._refreshSingleMarkerModeMarkers(e),this},_flagParentsIconsNeedUpdate:function(e){var t,a;for(t in e)for(a=e[t].__parent;a;)a._iconNeedsUpdate=!0,a=a.__parent},_refreshSingleMarkerModeMarkers:function(e){var t,a;for(t in e)a=e[t],this.hasLayer(a)&&a.setIcon(this._overrideMarkerIcon(a))}}),L.Marker.include({refreshIconOptions:function(e,t){var a=this.options.icon;return 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