/lib/flare/vis/axis/Axis.as

package flare.vis.axis {

	import flare.animate.Transitioner;

	import flare.display.TextSprite;

	import flare.scale.IScaleMap;

	import flare.scale.LinearScale;

	import flare.scale.Scale;

	import flare.scale.ScaleType;

	import flare.util.Sort;

	import flare.util.Stats;

	import flare.util.Strings;

	import flare.util.Vectors;



	import flash.display.DisplayObject;

	import flash.display.Sprite;

	import flash.geom.Point;

	import flash.text.TextFormat;

	import flash.utils.Dictionary;



	/**

	 * A metric data axis consisting of axis labels and gridlines.

	 * 

	 * <p>Axis labels can be configured both in terms of text formatting,

	 * orientation, and position. Use the <code>labelOffsetX</code> or

	 * <code>labelOffsetY</code> property to adjust label positioning. For

	 * example, <code>labelOffsetX = -10;</code> places the anchor point for

	 * the label ten pixels to the left of the data bounds, whereas

	 * <code>labelOffsetX = 10;</code> will place the point 10 pixels to the

	 * right of the data bounds. One could simultaneously adjust the

	 * <code>horizontalAnchor</code> property to align the labels as desired.

	 * </p>

	 * 

	 * <p>Similarly, axis gridlines can also be configured. The

	 * <code>lineCapX1</code>, <code>lineCapX2</code>, <code>lineCapY1</code>,

	 * and <code>lineCapY2</code> properties determine by how much the

	 * grid lines should exceed the data bounds. For example,

	 * <code>lineCapX1 = 5</code> causes the grid line to extend an extra

	 * 5 pixels to the left. Each of these values should be greater than or

	 * equal to zero.</p>

	 */

	public class Axis extends Sprite implements IScaleMap

	{

		// children indices

		protected static const TITLE:uint = 2;

		protected static const LABELS:uint = 1;

        protected static const GRIDLINES:uint = 0;

		

		// axis scale

		protected var _prevScale:Scale;

		// axis settings

		protected var _xa:Number=0, _ya:Number=0;   // start of the axis

		protected var _xb:Number=0, _yb:Number=0;   // end of the axis

		protected var _xaP:Number=0, _yaP:Number=0; // previous start of the axis

		protected var _xbP:Number=0, _ybP:Number=0; // previous end of the axis

		protected var _xd:int, _yd:int;             // axis directions (1 or -1)

		protected var _xlo:Number, _ylo:Number;     // label offsets

		// gridline settings

		protected var _lineColor:uint = 0xd8d8d8;

		protected var _lineWidth:Number = 0;

		// label settings

		protected var _numLabels:int = -1;

		protected var _anchorH:int = TextSprite.LEFT;

		protected var _anchorV:int = TextSprite.TOP;

		protected var _labelAngle:Number = 0;

		protected var _labelColor:uint = 0;

		protected var _labelFormat:String = null;

		protected var _labelTextMode:int = TextSprite.BITMAP;

		protected var _labelTextFormat:TextFormat = new TextFormat("Arial",12,0);

		// title settings

		protected var _axisTitleText:String;

		protected var _titleTextMode:int = TextSprite.BITMAP;

		protected var _titleTextFormat:TextFormat = new TextFormat("Arial",14,0);

		

		// temporary variables

		protected var _point:Point = new Point();

		

		// -- Properties ------------------------------------------------------

		

		/** Sprite containing the axis labels. */

		public function get labels():Sprite { return getChildAt(LABELS) as Sprite; }

		/** Sprite containing the axis grid lines. */

		public function get gridLines():Sprite { return getChildAt(GRIDLINES) as Sprite; }

		/** Sprite containing the axis title. */

		public function get title():TextSprite { return getChildAt(TITLE) as TextSprite; }

		

		/** @inheritDoc */

		public function get x1():Number { return _xa; }

		public function set x1(x:Number):void { _xa = x; }

		

		/** @inheritDoc */

		public function get y1():Number { return _ya; }

		public function set y1(y:Number):void { _ya = y; }

		

		/** @inheritDoc */

		public function get x2():Number { return _xb; }

		public function set x2(x:Number):void { _xb = x; }

		

		/** @inheritDoc */

		public function get y2():Number { return _yb; }

		public function set y2(y:Number):void { _yb = y; }



		/** The Scale used to map values to this axis. */

		public var axisScale:Scale;

		

		/** Flag indicating if axis labels should be shown. */

		public var showLabels:Boolean = true;

		

		/** Flag indicating if labels should be removed in case of overlap. */

		public var fixLabelOverlap:Boolean = true;

		

		/** Flag indicating if axis grid lines should be shown. */

		public var showLines:Boolean = true;

		

		/** X length of axis gridlines. */

		public var lineLengthX:Number = 0;

		

		/** Y length of axis gridlines. */

		public var lineLengthY:Number = 0;	

			

		/** X offset for axis gridlines at the lower end of the axis. */

		public var lineCapX1:Number = 0;

		

		/** X offset for axis gridlines at the upper end of the axis. */

		public var lineCapX2:Number = 0;

		

		/** Y offset for axis gridlines at the lower end of the axis. */

		public var lineCapY1:Number = 0;

		

		/** Y offset for axis gridlines at the upper end of the axis. */

		public var lineCapY2:Number = 0;

		

		/** X-dimension offset value for axis labels. If negative or zero, this

		 *  value indicates how much to offset to the left of the data bounds.

		 *  If positive, the offset is made to the right of the data bounds. */

		public var labelOffsetX:Number = 0;	

			

		/** Y-dimension offset value for axis labels. If negative or zero, this

		 *  value indicates how much to offset above the data bounds.

		 *  If positive, the offset is made beneath the data bounds.*/

		public var labelOffsetY:Number = 0;

		

		/** X-dimension offset value for axis title. If negative or zero, this

		 *  value indicates how much to offset to the left of the label offset.

		 *  If positive, the offset is made to the right of the label offset. */

		public var titleOffsetX:Number = 0;

		

		/** Y-dimension offset value for axis title. If negative or zero, this

		 *  value indicates how much to offset above the label offset.

		 *  If positive, the offset is made beneath the label offset.*/

		public var titleOffsetY:Number = 0;

		

		/** The line color of axis grid lines. */

		public function get lineColor():uint { return _lineColor; }

		public function set lineColor(c:uint):void { _lineColor = c; updateGridLines(); }

		

		/** The line width of axis grid lines. */

		public function get lineWidth():Number { return _lineWidth; }

		public function set lineWidth(w:Number):void { _lineWidth = w; updateGridLines(); }

		

		/** The color of axis label text. */

		public function get labelColor():uint { return _labelColor; }

		public function set labelColor(c:uint):void { _labelColor = c; updateLabels(); }

		

		/** The angle (orientation) of axis label text. */

		public function get labelAngle():Number { return _labelAngle; }

		public function set labelAngle(a:Number):void { _labelAngle = a; updateLabels(); }

		

		/** TextFormat (font, size, style) for axis label text. */

		public function get labelTextFormat():TextFormat { return _labelTextFormat; }

		public function set labelTextFormat(f:TextFormat):void { _labelTextFormat = f; updateLabels(); }

		

		/** The text rendering mode to use for label TextSprites.

		 *  @see flare.display.TextSprite. */

		public function get labelTextMode():int { return _labelTextMode; }

		public function set labelTextMode(m:int):void { _labelTextMode = m; updateLabels(); }

		

		/** String formatting pattern used for axis labels, overwrites any

		 *  formatting pattern used by the <code>axisScale</code>. If null,

		 *  the formatting pattern for the <code>axisScale</code> is used. */

		public function get labelFormat():String {

			return _labelFormat==null ? null 

					: _labelFormat.substring(3, _labelFormat.length-1);

		}

		public function set labelFormat(fmt:String):void {

			_labelFormat = "{0:"+fmt+"}"; updateLabels();

		}

		

		/** The number of labels and gridlines to generate by default. If this

		 *  number is zero or less (default -1), the number of labels will be

		 *  automatically determined from the current scale and size. */

		public function get numLabels():int {

			// if set positive, return number

			if (_numLabels > 0) return _numLabels;

			// if ordinal return all labels

			if (ScaleType.isOrdinal(axisScale.scaleType)) return -1;

			// otherwise determine based on axis size (random hack...)

			var lx:Number = _xb-_xa; if (lx<0) lx = -lx;

			var ly:Number = _yb-_ya; if (ly<0) ly = -ly;

			lx = (lx > ly ? lx : ly);

			return lx > 200 ? 10 : lx < 20 ? 1 : int(lx/20);

		}

		public function set numLabels(n:int):void { _numLabels = n; }

		

		/** TextFormat (font, size, style) for axis title text. */

		public function get axisTitle():String { return _axisTitleText; }

		public function set axisTitle(t:String):void { _axisTitleText = t; updateLabels(); }

		

		/** TextFormat (font, size, style) for axis title text. */

		public function get titleTextFormat():TextFormat { return _titleTextFormat; }

		public function set titleTextFormat(f:TextFormat):void { _titleTextFormat = f; updateLabels(); }

		

		/** The text rendering mode to use for title TextSprite.

		 *  @see flare.display.TextSprite. */

		public function get titleTextMode():int { return _titleTextMode; }

		public function set titleTextMode(m:int):void { _titleTextMode = m; updateLabels(); }

		

		

		/** The horizontal anchor point for axis labels.

		 *  @see flare.display.TextSprite. */

		public function get horizontalAnchor():int { return _anchorH; }

		public function set horizontalAnchor(a:int):void { _anchorH = a; updateLabels(); }

		

		/** The vertical anchor point for axis labels.

		 *  @see flare.display.TextSprite. */

		public function get verticalAnchor():int { return _anchorV; }

		public function set verticalAnchor(a:int):void { _anchorV = a; updateLabels(); }		

		

		/** The x-coordinate of the axis origin. */

		public function get originX():Number {

			return (ScaleType.isQuantitative(axisScale.scaleType) ? X(0) : x1);

		}

		/** The y-coordinate of the axis origin. */

		public function get originY():Number {

			return (ScaleType.isQuantitative(axisScale.scaleType) ? Y(0) : y1);

		}

		

		// -- Initialization --------------------------------------------------

		

		/**

		 * Creates a new Axis.

		 * @param axisScale the axis scale to use. If null, a linear scale

		 *  is assumed.

		 */

		public function Axis(axisScale:Scale=null)

        {

            this.axisScale = axisScale ? axisScale : new LinearScale();

            _prevScale = this.axisScale;

            initializeChildren();

        }



		/**

		 * Initializes the child container sprites for labels and grid lines.

		 */

        protected function initializeChildren():void

        {

            addChild(new Sprite()); // add gridlines

            addChild(new Sprite()); // add labels

            addChild(new TextSprite()); // add title

        }

		

		// -- Updates ---------------------------------------------------------

		

		/**

		 * Updates this axis, performing filtering and layout as needed.

		 * @param trans a Transitioner for collecting value updates

		 * @return the input transitioner.

		 */

		public function update(trans:Transitioner):Transitioner

        {

        	var t:Transitioner = (trans!=null ? trans : Transitioner.DEFAULT);

        	

        	// compute directions and offsets

        	_xd  = lineLengthX < 0 ? -1 : 1;

        	_yd  = lineLengthY < 0 ? -1 : 1;

        	_xlo =  _xd*labelOffsetX + (labelOffsetX>0 ? lineLengthX : 0);

        	_ylo = -_yd*labelOffsetY + (labelOffsetY<0 ? lineLengthY : 0);

        	

        	// run updates

            filter(t);

            layout(t);

            updateLabels(); // TODO run through transitioner?

            updateGridLines(); // TODO run through transitioner?

            updateTitle();

            return trans;

        }

		

		// -- Lookups ---------------------------------------------------------

		

		/**

		 * Returns the horizontal offset along the axis for the input value.

		 * @param value an input data value

		 * @return the horizontal offset along the axis corresponding to the

		 *  input value. This is the x-position minus <code>x1</code>.

		 */

		public function offsetX(value:Object):Number

        {

        	return axisScale.interpolate(value) * (_xb - _xa);

        }

        

        /**

		 * Returns the vertical offset along the axis for the input value.

		 * @param value an input data value

		 * @return the vertical offset along the axis corresponding to the

		 *  input value. This is the y-position minus <code>y1</code>.

		 */

        public function offsetY(value:Object):Number

        {

        	return axisScale.interpolate(value) * (_yb - _ya);

        }



		/** @inheritDoc */

		public function X(value:Object):Number

        {

        	return _xa + offsetX(value);

        }

        

        /** @inheritDoc */

        public function Y(value:Object):Number

        {

        	return _ya + offsetY(value);

        }

        

        /** @inheritDoc */

        public function value(x:Number, y:Number, stayInBounds:Boolean=true):Object

        {

        	// project the input point onto the axis line

        	// (P-A).(B-A) / |B-A|^2 == fractional projection onto axis line

        	var dx:Number = (_xb-_xa);

        	var dy:Number = (_yb-_ya);

        	var f:Number = ((x-_xa)*dx + (y-_ya)*dy) / (dx*dx + dy*dy);

        	// correct bounds, if desired

        	if (stayInBounds) {

        		if (f < 0) f = 0;

        		if (f > 1) f = 1;

        	}

        	// lookup and return value

        	return axisScale.lookup(f);

        }

		

		/**

		 * Clears the previous axis scale used, if cached.

		 */

		public function clearPreviousScale():void

		{

			_prevScale = axisScale;

		}

		

		// -- Filter ----------------------------------------------------------

		

		/**

		 * Performs filtering, determining which axis labels and grid lines

		 * should be visible.

		 * @param trans a Transitioner for collecting value updates.

		 */

		protected function filter(trans:Transitioner) : void

		{

			var ordinal:uint = 0, i:uint, idx:int = -1, val:Object;

			var label:AxisLabel = null;

			var gline:AxisGridLine = null;

			var nl:uint = labels.numChildren;

			var ng:uint = gridLines.numChildren;

			

			var keepLabels:Vector.<Boolean> = new Vector.<Boolean>(nl);

			var keepLines:Vector.<Boolean> = new Vector.<Boolean>(ng);

			var values:Vector.<Object> = axisScale.values(numLabels);

			

			if (showLabels) { // process labels

				for (i=0, ordinal=0; i<values.length; ++i) {

					val = values[i];

					if ((idx = findLabel(val, nl)) < 0) {

						label = createLabel(val);

					} else {

						label = labels.getChildAt(idx) as AxisLabel;

						keepLabels[idx] = true;

					}

					label.ordinal = ordinal++;

				}

			}

			if (showLines) { // process gridlines

				for (i=0, ordinal=0; i<values.length; ++i) {

					val = values[i];

					if ((idx = findGridLine(val, ng)) < 0) {

						gline = createGridLine(val);

					} else {

						gline = gridLines.getChildAt(idx) as AxisGridLine;

						keepLines[idx] = true;

					}

					gline.ordinal = ordinal++;

				}

			}

			markRemovals(trans, keepLabels, labels);

			markRemovals(trans, keepLines, gridLines);

		}

		

		/**

		 * Marks all items slated for removal from this axis.

		 * @param trans a Transitioner for collecting value updates.

		 * @param keep a Boolean vector indicating which items to keep

		 * @param con a container Sprite whose contents should be marked

		 *  for removal

		 */

		protected function markRemovals(trans:Transitioner, keep:Vector.<Boolean>, con:Sprite) : void

		{

			for (var i:uint = keep.length; --i >= 0; ) {

				if (!keep[i]) trans.removeChild(con.getChildAt(i));

			}

		}

		

		// -- Layout ----------------------------------------------------------

		

		/**

		 * Performs layout, setting the position of labels and grid lines.

		 * @param trans a Transitioner for collecting value updates.

		 */

		protected function layout(trans:Transitioner) : void

		{

			var i:uint, label:AxisLabel, gline:AxisGridLine, p:Point;

			var _lab:Sprite = this.labels;

			var _gls:Sprite = this.gridLines;

			var o:Object;

			

			// layout labels

			for (i=0; i<_lab.numChildren; ++i) {

				label = _lab.getChildAt(i) as AxisLabel;

				p = positionLabel(label, axisScale);

				

				o = trans.$(label);

				o.x = p.x;

				o.y = p.y;

				o.alpha = trans.willRemove(label) ? 0 : 1;

			}

			// fix label overlap

			if (fixLabelOverlap) fixOverlap(trans);

			// layout gridlines

			for (i=0; i<_gls.numChildren; ++i) {

				gline = _gls.getChildAt(i) as AxisGridLine;

				p = positionGridLine(gline, axisScale);

				

				o = trans.$(gline);

				o.x1 = p.x;

				o.y1 = p.y;

				o.x2 = p.x + lineLengthX + _xd*(lineCapX1+lineCapX2);

				o.y2 = p.y + lineLengthY + _yd*(lineCapY1+lineCapY2);

				o.alpha = trans.willRemove(gline) ? 0 : 1;

			}

			// update previous scale

			_prevScale = axisScale.clone(); // clone scale

			_xaP = _xa; _yaP = _ya; _xbP = _xb; _ybP = _yb;

		}

		

		// -- Label Overlap ---------------------------------------------------

		

		/**

		 * Eliminates overlap between labels along an axis. 

		 * @param trans a transitioner, potentially storing label positions

		 */		

		protected function fixOverlap(trans:Transitioner):void

		{

			var labs:Vector.<Object> = new Vector.<Object>(), d:DisplayObject, i:int;

			// collect and sort labels

			for (i=0; i<labels.numChildren; ++i) {

				var s:AxisLabel = AxisLabel(labels.getChildAt(i));

				if (!trans.willRemove(s)) labs.push(s);

			}

			if (labs.length == 0) return;

			//labs.sortOn("ordinal", Array.NUMERIC);

			labs.sort(Sort.$("ordinal"));

			

			// stores the labels to remove

			var rem:Dictionary = new Dictionary();

			

			if (axisScale.scaleType == ScaleType.LOG) {

				fixLogOverlap(labs, rem, trans, axisScale);

			}

			

			// maintain min and max if we get down to two

			i = labs.length;

			var min:Object = labs[0];

			var max:Object = labs[i-1];

			var mid:Object = (i&1) ? labs[(i>>1)] : null;



			// fix overlap with an iterative optimization

			// remove every other label with each iteration

			while (hasOverlap(labs, trans)) {

				// reduce labels

				i = labs.length;

				if (mid && i>3 && i<8) { // use min, med, max if we can

					for each (d in labs) rem[d] = d;

					if (rem[min]) delete rem[min];

					if (rem[max]) delete rem[max];

					if (rem[mid]) delete rem[mid];

					var v:Vector.<Object> = new Vector.<Object>();

					v.push(min); v.push(mid); v.push(max);

					labs = v;

				}

				else if (i < 4) { // use min and max if we're down to two

					if (rem[min]) delete rem[min];

					if (rem[max]) delete rem[max];

					for each (d in labs) {

						if (d != min && d != max) rem[d] = d;

					}

					break;

				}

				else { // else remove every odd element

					i = i - (i&1 ? 2 : 1);

					for (; i>0; i-=2) {

						rem[labs[i]] = labs[i];

						labs.splice(i, 1); // remove from array

					}

				}

			}

			

			// remove the deleted labels

			for each (d in rem) {

				trans.$(d).alpha = 0;

				trans.removeChild(d, true);

			}

		}

		

		protected static function fixLogOverlap(labs:Vector.<Object>, rem:Dictionary,

			trans:Transitioner, scale:Scale):void

		{

				var base:int = int(Object(scale).base), i:int, j:int, zidx:int;

				if (!hasOverlap(labs, trans)) return;

				

				// find zero

				zidx = Vectors.binarySearch(labs, 0, "value");

				var neg:Boolean = Number(scale.min) < 0;

				var pos:Boolean = Number(scale.max) > 0;

				

				// if includes negative, traverse backwards from zero/end

				if (neg) {

					i = (zidx<0 ? labs.length : zidx) - (pos ? 1 : 2);

					for (j=pos?1:2; i>=0; ++j, --i) {

						if (j == base) {

							j = 1;

						} else {

							rem[labs[i]] = labs[i];

							labs.splice(i, 1); --zidx;

						}

					}

				}

				// if includes positive, traverse forwards from zero/start

				if (pos) {

					i = (zidx<0 ? 0 : zidx+1) + (neg ? 0 : 1);

					for (j=neg?1:2; i<labs.length; ++j) {

						if (j == base) {

							j = 1; ++i;

						} else {

							rem[labs[i]] = labs[i];

							labs.splice(i, 1);

						}

					}

				}

		}

		

		private static function hasOverlap(labs:Vector.<Object>, trans:Transitioner):Boolean

		{

			var d:DisplayObject = labs[0] as DisplayObject, e:DisplayObject;

			for (var i:int=1; i<labs.length; ++i) {

				if (overlaps(trans, d, (e=labs[i] as DisplayObject))) return true;

				d = e;

			}

			return false;

		}

		

		/**

		 * Indicates if two display objects overlap, sensitive to any target

		 * values stored in a transitioner.

		 * @param trans a Transitioner, potentially with target values

		 * @param l1 a display object

		 * @param l2 a display object

		 * @return true if the objects overlap (considering values in the

		 *  transitioner, if appropriate), false otherwise

		 */

		private static function overlaps(trans:Transitioner,

			l1:DisplayObject, l2:DisplayObject):Boolean

		{

			if (trans.immediate) return l1.hitTestObject(l2);

			// get original co-ordinates

			var xa:Number = l1.x, ya:Number = l1.y;

			var xb:Number = l2.x, yb:Number = l2.y;

			var o:Object;

			// set to target co-ordinates

			o = trans.$(l1); l1.x = o.x; l1.y = o.y;

			o = trans.$(l2); l2.x = o.x; l2.y = o.y;

			// compute overlap

			var b:Boolean = l1.hitTestObject(l2);

			// reset to original coordinates

			l1.x = xa; l1.y = ya; l2.x = xb; l2.y = yb;

			return b;

		}

		

		// -- Axis Label Helpers ----------------------------------------------

		

		/**

		 * Creates a new axis label.

		 * @param val the value to create the label for

		 * @return an AxisLabel

		 */		

		protected function createLabel(val:Object) : AxisLabel

		{

			var label:AxisLabel = new AxisLabel();

			var f:Number = _prevScale.interpolate(val);

			label.alpha = 0;

			label.value = val;

			label.x = _xlo + _xaP + f*(_xbP - _xaP);

			label.y = _ylo + _yaP + f*(_ybP - _yaP);

			updateLabel(label);

			labels.addChild(label);

			return label;

		}

		

		/**

		 * Computes the position of an axis label.

		 * @param label the axis label to layout

		 * @param scale the scale used to map values to the axis

		 * @return a Point with x,y coordinates for the axis label

		 */

		protected function positionLabel(label:AxisLabel, scale:Scale) : Point

		{

			var f:Number = scale.interpolate(label.value);

			_point.x = _xlo + _xa + f*(_xb-_xa);

			_point.y = _ylo + _ya + f*(_yb-_ya);

			return _point;

		}

		

		/**

		 * Updates an axis label's settings

		 * @param label the label to update

		 */		

		protected function updateLabel(label:AxisLabel) : void

		{

			label.textFormat = _labelTextFormat;

			label.horizontalAnchor = _anchorH;

			label.verticalAnchor = _anchorV;

			label.rotation = (180/Math.PI) * _labelAngle;

			label.textMode = _labelTextMode;

			label.text = _labelFormat==null ? axisScale.label(label.value)

					   : Strings.format(_labelFormat, label.value);

		}

		

		

		protected function updateTitle() : void

		{

			//set and format title

			var titleSprite:TextSprite = getChildAt(TITLE) as TextSprite;

			titleSprite.textFormat = _titleTextFormat;

			titleSprite.horizontalAnchor = TextSprite.CENTER;

			titleSprite.verticalAnchor = TextSprite.TOP;

			titleSprite.textMode = _titleTextMode;

			titleSprite.text = _axisTitleText;

			//position title 

			titleSprite.x = (_xb - _xa) / 2 + _xa + _xlo + titleOffsetX; 

			titleSprite.y = (_yb - _ya) / 2 + _ya + _ylo + titleOffsetY;

			

		}

		

		/**

		 * Updates all axis labels.

		 */		

		protected function updateLabels() : void

		{

			var _labels:Sprite = this.labels;

			for (var i:uint = 0; i<_labels.numChildren; ++i) {

				updateLabel(_labels.getChildAt(i) as AxisLabel);

			}

		}

		

		/**

		 * Returns the index of a label in the label's container sprite for a

		 * given data value.

		 * @param val the data value to find

		 * @param len the number of labels to check

		 * @return the index of a label with matching value, or -1 if no label

		 *  was found

		 */		

		protected function findLabel(val:Object, len:uint) : int

		{

			var _labels:Sprite = this.labels;

			for (var i:uint = 0; i < len; ++i) {

				// TODO: make this robust to repeated values

				if (Stats.equal((_labels.getChildAt(i) as AxisLabel).value, val)) {

					return i;

				}

			}

			return -1;

		}

		

		// -- Axis GridLine Helpers -------------------------------------------

		

		/**

		 * Creates a new axis grid line.

		 * @param val the value to create the grid lines for

		 * @return an AxisGridLine

		 */	

		protected function createGridLine(val:Object) : AxisGridLine

		{

			var gline:AxisGridLine = new AxisGridLine();

			var f:Number = _prevScale.interpolate(val);

			gline.alpha = 0;

			gline.value = val;

			gline.x1 = _xaP + f*(_xbP-_xaP) - _xd*lineCapX1;

			gline.y1 = _yaP + f*(_ybP-_yaP) - _yd*lineCapY1;

			gline.x2 = gline.x1 + lineLengthX + _xd*(lineCapX1 + lineCapX2)

			gline.y2 = gline.y1 + lineLengthY + _yd*(lineCapY1 + lineCapY2);

			updateGridLine(gline);

			gridLines.addChild(gline);

			return gline;

		}

		

		/**

		 * Computes the position of an axis grid line.

		 * @param gline the axis grid line to layout

		 * @param scale the scale used to map values to the axis

		 * @return a Point with x,y coordinates for the axis grid line

		 */

		protected function positionGridLine(gline:AxisGridLine, scale:Scale) : Point

		{

			var f:Number = scale.interpolate(gline.value);

			_point.x = _xa + f*(_xb-_xa) - _xd*lineCapX1;

			_point.y = _ya + f*(_yb-_ya) - _yd*lineCapY1;

			return _point;

		}

		

		/**

		 * Updates an axis grid line's settings

		 * @param gline the grid line to update

		 */

		protected function updateGridLine(gline:AxisGridLine) : void

		{

			gline.lineColor = _lineColor;

			gline.lineWidth = _lineWidth;

		}

		

		/**

		 * Updates all grid lines.

		 */

		protected function updateGridLines() : void

		{

			var _glines:Sprite = this.gridLines;

			for (var i:uint = 0; i<_glines.numChildren; ++i) {

				updateGridLine(_glines.getChildAt(i) as AxisGridLine);

			}

		}

		

		/**

		 * Returns the index of a grid lines in the line's container sprite

		 * for a given data value.

		 * @param val the data value to find

		 * @param len the number of grid lines to check

		 * @return the index of a grid line with matching value, or -1 if no

		 *  grid line was found

		 */	

		protected function findGridLine(val:Object, len:uint) : int

		{

			var _glines:Sprite = this.gridLines;

			for (var i:uint = 0; i<len; ++i) {

				// TODO: make this robust to repeated values

				if (Stats.equal((_glines.getChildAt(i) as AxisGridLine).value, val)) {

					return i;

				}

			}

			return -1;

		}

		

	} // end of class Axis

}