/*
 * Paper.js
 *
 * This file is part of Paper.js, a JavaScript Vector Graphics Library,
 * based on Scriptographer.org and designed to be largely API compatible.
 * http://paperjs.org/
 * http://scriptographer.org/
 *
 * Copyright (c) 2011, Juerg Lehni & Jonathan Puckey
 * http://lehni.org/ & http://jonathanpuckey.com/
 *
 * Distributed under the MIT license. See LICENSE file for details.
 *
 * All rights reserved.
 */

/**
 * @name Path
 *
 * @class The Path item represents a path in a Paper.js project.
 *
 * @extends PathItem
 */
// DOCS: Explain that path matrix is always applied with each transformation.
var Path = this.Path = PathItem.extend(/** @lends Path# */{
	/**
	 * Creates a new Path item and places it at the top of the active layer.
	 *
	 * @param {Segment[]} [segments] An array of segments (or points to be
	 * converted to segments) that will be added to the path.
	 *
	 * @example
	 * // Create an empty path and add segments to it:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(30, 30));
	 * path.add(new Point(100, 100));
	 *
	 * @example
	 * // Create a path with two segments:
	 * var segments = [new Point(30, 30), new Point(100, 100)];
	 * var path = new Path(segments);
	 * path.strokeColor = 'black';
	 */
	initialize: function(segments) {
		this.base();
		this._closed = false;
		this._selectedSegmentState = 0;
		// Support both passing of segments as array or arguments
		// If it is an array, it can also be a description of a point, so
		// check its first entry for object as well
		this.setSegments(!segments || !Array.isArray(segments)
				|| typeof segments[0] !== 'object' ? arguments : segments);
	},

	clone: function() {
		var copy = this._clone(new Path(this._segments));
		copy._closed = this._closed;
		if (this._clockwise !== undefined)
			copy._clockwise = this._clockwise;
		return copy;
	},

	_changed: function(flags) {
		// Don't use base() for reasons of performance.
		Item.prototype._changed.call(this, flags);
		if (flags & ChangeFlag.GEOMETRY) {
			delete this._length;
			// Clockwise state becomes undefined as soon as geometry changes.
			delete this._clockwise;
			// Curves are no longer valid
			if (this._curves != null) {
				for (var i = 0, l = this._curves.length; i < l; i++) {
					this._curves[i]._changed(Change.GEOMETRY);
				}
			}
		} else if (flags & ChangeFlag.STROKE) {
			// TODO: We could preserve the purely geometric bounds that are not
			// affected by stroke: _bounds.bounds and _bounds.handleBounds
			delete this._bounds;
		}
	},

	/**
	 * The segments contained within the path.
	 *
	 * @type Segment[]
	 * @bean
	 */
	getSegments: function() {
		return this._segments;
	},

	setSegments: function(segments) {
		if (!this._segments) {
			this._segments = [];
		} else {
			this._selectedSegmentState = 0;
			this._segments.length = 0;
			// Make sure new curves are calculated next time we call getCurves()
			if (this._curves)
				delete this._curves;
		}
		this._add(Segment.readAll(segments));
	},

	/**
	 * The first Segment contained within the path.
	 *
	 * @type Segment
	 * @bean
	 */
	getFirstSegment: function() {
		return this._segments[0];
	},

	/**
	 * The last Segment contained within the path.
	 *
	 * @type Segment
	 * @bean
	 */
	getLastSegment: function() {
		return this._segments[this._segments.length - 1];
	},

	/**
	 * The curves contained within the path.
	 *
	 * @type Curve[]
	 * @bean
	 */
	getCurves: function() {
		if (!this._curves) {
			var segments = this._segments,
				length = segments.length;
			// Reduce length by one if it's an open path:
			if (!this._closed && length > 0)
				length--;
			this._curves = new Array(length);
			for (var i = 0; i < length; i++)
				this._curves[i] = Curve.create(this, segments[i],
					// Use first segment for segment2 of closing curve
					segments[i + 1] || segments[0]);
		}
		return this._curves;
	},

	/**
	 * The first Curve contained within the path.
	 *
	 * @type Curve
	 * @bean
	 */
	getFirstCurve: function() {
		return this.getCurves()[0];
	},

	/**
	 * The last Curve contained within the path.
	 *
	 * @type Curve
	 * @bean
	 */
	getLastCurve: function() {
		var curves = this.getCurves();
		return curves[curves.length - 1];
	},

	/**
	 * Specifies whether the path is closed. If it is closed, Paper.js connects
	 * the first and last segments.
	 *
	 * @type Boolean
	 * @bean
	 *
	 * @example {@paperscript}
	 * var myPath = new Path();
	 * myPath.strokeColor = 'black';
	 * myPath.add(new Point(50, 75));
	 * myPath.add(new Point(100, 25));
	 * myPath.add(new Point(150, 75));
	 *
	 * // Close the path:
	 * myPath.closed = true;
	 */
	getClosed: function() {
		return this._closed;
	},

	setClosed: function(closed) {
		// On-the-fly conversion to boolean:
		if (this._closed != (closed = !!closed)) {
			this._closed = closed;
			// Update _curves length
			if (this._curves) {
				var length = this._segments.length,
					i;
				// Reduce length by one if it's an open path:
				if (!closed && length > 0)
					length--;
				this._curves.length = length;
				// If we were closing this path, we need to add a new curve now
				if (closed)
					this._curves[i = length - 1] = Curve.create(this,
						this._segments[i], this._segments[0]);
			}
			this._changed(Change.GEOMETRY);
		}
	},

	// TODO: Consider adding getSubPath(a, b), returning a part of the current
	// path, with the added benefit that b can be < a, and closed looping is
	// taken into account.

	// DOCS: Explain that path matrix is always applied with each transformation.
	transform: function(matrix) {
		return this.base(matrix, true);
	},

	getMatrix: function() {
		// Override matrix getter to always return null, since Paths act as if
		// they do not have a matrix, and always directly apply transformations
		// to their segment points.
		return null;
	},

	setMatrix: function(matrix) {
		// Do nothing for the same reason as above.
	},

	isEmpty: function() {
		return this._segments.length == 0;
	},

	_apply: function(matrix) {
		var coords = new Array(6);
		for (var i = 0, l = this._segments.length; i < l; i++) {
			this._segments[i]._transformCoordinates(matrix, coords, true);
		}
		// See #draw() for an explanation of why we can access _style properties
		// directly here:
		var style = this._style,
			fillColor = style._fillColor,
			strokeColor = style._strokeColor;
		// Try calling transform on colors in case they are GradientColors.
		if (fillColor && fillColor.transform)
			fillColor.transform(matrix);
		if (strokeColor && strokeColor.transform)
			strokeColor.transform(matrix);
		return true;
	},

	/**
	 * Private method that adds a segment to the segment list. It assumes that
	 * the passed object is a segment already and does not perform any checks.
	 * If a curves list was requested, it will kept in sync with the segments
	 * list automatically.
	 */
	_add: function(segs, index) {
		// Local short-cuts:
		var segments = this._segments,
			curves = this._curves,
			amount = segs.length,
			append = index == null,
			index = append ? segments.length : index,
			fullySelected = this.isFullySelected();
		// Scan through segments to add first, convert if necessary and set
		// _path and _index references on them.
		for (var i = 0; i < amount; i++) {
			var segment = segs[i];
			// If the segments belong to another path already, clone them before
			// adding:
			if (segment._path) {
				segment = segs[i] = new Segment(segment);
			}
			segment._path = this;
			segment._index = index + i;
			// Select newly added segments if path was fully selected before
			if (fullySelected)
				segment._selectionState = SelectionState.POINT;
			// If parts of this segment are selected, adjust the internal
			// _selectedSegmentState now
			if (segment._selectionState)
				this._updateSelection(segment, 0, segment._selectionState);
		}
		if (append) {
			// Append them all at the end by using push
			segments.push.apply(segments, segs);
		} else {
			// Insert somewhere else
			segments.splice.apply(segments, [index, 0].concat(segs));
			// Adjust the indices of the segments above.
			for (var i = index + amount, l = segments.length; i < l; i++) {
				segments[i]._index = i;
			}
		}
		// Keep the curves list in sync all the time in case it as requested
		// already. We need to step one index down from the inserted segment to
		// get its curve:
		if (curves && --index >= 0) {
			// Insert a new curve as well and update the curves above
			curves.splice(index, 0, Curve.create(this, segments[index],
				segments[index + 1]));
			// Adjust segment1 now for the curves above the inserted one
			var curve = curves[index + amount];
			if (curve) {
				curve._segment1 = segments[index + amount];
			}
		}
		this._changed(Change.GEOMETRY);
		return segs;
	},

	// PORT: Add support for adding multiple segments at once to Scriptographer
	// DOCS: find a way to document the variable segment parameters of Path#add
	/**
	 * Adds one or more segments to the end of the {@link #segments} array of
	 * this path.
	 *
	 * @param {Segment|Point} segment the segment or point to be added.
	 * @return {Segment} the added segment. This is not necessarily the same
	 * object, e.g. if the segment to be added already belongs to another path.
	 * @operator none
	 *
	 * @example {@paperscript}
	 * // Adding segments to a path using point objects:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 *
	 * // Add a segment at {x: 30, y: 75}
	 * path.add(new Point(30, 75));
	 *
	 * // Add two segments in one go at {x: 100, y: 20}
	 * // and {x: 170, y: 75}:
	 * path.add(new Point(100, 20), new Point(170, 75));
	 *
	 * @example {@paperscript}
	 * // Adding segments to a path using arrays containing number pairs:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 *
	 * // Add a segment at {x: 30, y: 75}
	 * path.add([30, 75]);
	 *
	 * // Add two segments in one go at {x: 100, y: 20}
	 * // and {x: 170, y: 75}:
	 * path.add([100, 20], [170, 75]);
	 *
	 * @example {@paperscript}
	 * // Adding segments to a path using objects:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 *
	 * // Add a segment at {x: 30, y: 75}
	 * path.add({x: 30, y: 75});
	 *
	 * // Add two segments in one go at {x: 100, y: 20}
	 * // and {x: 170, y: 75}:
	 * path.add({x: 100, y: 20}, {x: 170, y: 75});
	 *
	 * @example {@paperscript}
	 * // Adding a segment with handles to a path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 *
	 * path.add(new Point(30, 75));
	 *
	 * // Add a segment with handles:
	 * var point = new Point(100, 20);
	 * var handleIn = new Point(-50, 0);
	 * var handleOut = new Point(50, 0);
	 * var added = path.add(new Segment(point, handleIn, handleOut));
	 *
	 * // Select the added segment, so we can see its handles:
	 * added.selected = true;
	 *
	 * path.add(new Point(170, 75));
	 */
	add: function(segment1 /*, segment2, ... */) {
		return arguments.length > 1 && typeof segment1 !== 'number'
			// addSegments
			? this._add(Segment.readAll(arguments))
			// addSegment
			: this._add([ Segment.read(arguments) ])[0];
	},

	// PORT: Add support for adding multiple segments at once to Scriptographer
	/**
	 * Inserts one or more segments at a given index in the list of this path's
	 * segments.
	 *
	 * @param {Number} index the index at which to insert the segment.
	 * @param {Segment|Point} segment the segment or point to be inserted.
	 * @return {Segment} the added segment. This is not necessarily the same
	 * object, e.g. if the segment to be added already belongs to another path.
	 *
	 * @example {@paperscript}
	 * // Inserting a segment:
	 * var myPath = new Path();
	 * myPath.strokeColor = 'black';
	 * myPath.add(new Point(50, 75));
	 * myPath.add(new Point(150, 75));
	 *
	 * // Insert a new segment into myPath at index 1:
	 * myPath.insert(1, new Point(100, 25));
	 *
	 * // Select the segment which we just inserted:
	 * myPath.segments[1].selected = true;
	 *
	 * @example {@paperscript}
	 * // Inserting multiple segments:
	 * var myPath = new Path();
	 * myPath.strokeColor = 'black';
	 * myPath.add(new Point(50, 75));
	 * myPath.add(new Point(150, 75));
	 *
	 * // Insert two segments into myPath at index 1:
	 * myPath.insert(1, [80, 25], [120, 25]);
	 *
	 * // Select the segments which we just inserted:
	 * myPath.segments[1].selected = true;
	 * myPath.segments[2].selected = true;
	 */
	insert: function(index, segment1 /*, segment2, ... */) {
		return arguments.length > 2 && typeof segment1 !== 'number'
			// insertSegments
			? this._add(Segment.readAll(arguments, 1), index)
			// insertSegment
			: this._add([ Segment.read(arguments, 1) ], index)[0];
	},

	// PORT: Add to Scriptographer
	addSegment: function(segment) {
		return this._add([ Segment.read(arguments) ])[0];
	},

	// PORT: Add to Scriptographer
	insertSegment: function(index, segment) {
		return this._add([ Segment.read(arguments, 1) ], index)[0];
	},

	// PORT: Add to Scriptographer
	/**
	 * Adds an array of segments (or types that can be converted to segments)
	 * to the end of the {@link #segments} array.
	 *
	 * @param {Segment[]} segments
	 * @return {Segment[]} an array of the added segments. These segments are
	 * not necessarily the same objects, e.g. if the segment to be added already
	 * belongs to another path.
	 *
	 * @example {@paperscript}
	 * // Adding an array of Point objects:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * var points = [new Point(30, 50), new Point(170, 50)];
	 * path.addSegments(points);
	 *
	 * @example {@paperscript}
	 * // Adding an array of [x, y] arrays:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * var array = [[30, 75], [100, 20], [170, 75]];
	 * path.addSegments(array);
	 *
	 * @example {@paperscript}
	 * // Adding segments from one path to another:
	 *
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.addSegments([[30, 75], [100, 20], [170, 75]]);
	 *
	 * var path2 = new Path();
	 * path2.strokeColor = 'red';
	 *
	 * // Add the second and third segments of path to path2:
	 * path2.add(path.segments[1], path.segments[2]);
	 *
	 * // Move path2 30pt to the right:
	 * path2.position.x += 30;
	 */
	addSegments: function(segments) {
		return this._add(Segment.readAll(segments));
	},

	// PORT: Add to Scriptographer
	/**
	 * Inserts an array of segments at a given index in the path's
	 * {@link #segments} array.
	 *
	 * @param {Number} index the index at which to insert the segments.
	 * @param {Segment[]} segments the segments to be inserted.
	 * @return {Segment[]} an array of the added segments. These segments are
	 * not necessarily the same objects, e.g. if the segment to be added already
	 * belongs to another path.
	 */
	insertSegments: function(index, segments) {
		return this._add(Segment.readAll(segments), index);
	},

	// PORT: Add to Scriptographer
	/**
	 * Removes the segment at the specified index of the path's
	 * {@link #segments} array.
	 *
	 * @param {Number} index the index of the segment to be removed
	 * @return {Segment} the removed segment
	 *
	 * @example {@paperscript}
	 * // Removing a segment from a path:
	 *
	 * // Create a circle shaped path at { x: 80, y: 50 }
	 * // with a radius of 35:
	 * var path = new Path.Circle(new Point(80, 50), 35);
	 * path.strokeColor = 'black';
	 *
	 * // Remove its second segment:
	 * path.removeSegment(1);
	 *
	 * // Select the path, so we can see its segments:
	 * path.selected = true;
	 */
	removeSegment: function(index) {
		var segments = this.removeSegments(index, index + 1);
		return segments[0] || null;
	},

	// PORT: Add to Scriptographer
	/**
	 * Removes all segments from the path's {@link #segments} array.
	 *
	 * @name Path#removeSegments
	 * @function
	 * @return {Segment[]} an array containing the removed segments
	 */
	/**
	 * Removes the segments from the specified {@code from} index to the
	 * {@code to} index from the path's {@link #segments} array.
	 *
	 * @param {Number} from the beginning index, inclusive
	 * @param {Number} [to=segments.length] the ending index, exclusive
	 * @return {Segment[]} an array containing the removed segments
	 *
	 * @example {@paperscript}
	 * // Removing segments from a path:
	 *
	 * // Create a circle shaped path at { x: 80, y: 50 }
	 * // with a radius of 35:
	 * var path = new Path.Circle(new Point(80, 50), 35);
	 * path.strokeColor = 'black';
	 *
	 * // Remove the segments from index 1 till index 2:
	 * path.removeSegments(1, 2);
	 *
	 * // Select the path, so we can see its segments:
	 * path.selected = true;
	 */
	removeSegments: function(from, to) {
		from = from || 0;
		to = Base.pick(to, this._segments.length);
		var segments = this._segments,
			curves = this._curves,
			last = to >= segments.length,
			removed = segments.splice(from, to - from),
			amount = removed.length;
		if (!amount)
			return removed;
		// Update selection state accordingly
		for (var i = 0; i < amount; i++) {
			var segment = removed[i];
			if (segment._selectionState)
				this._updateSelection(segment, segment._selectionState, 0);
			// Clear the indices and path references of the removed segments
			removed._index = removed._path = undefined;
		}
		// Adjust the indices of the segments above.
		for (var i = from, l = segments.length; i < l; i++)
			segments[i]._index = i;
		// Keep curves in sync
		if (curves) {
			curves.splice(from, amount);
			// Adjust segments for the curves before and after the removed ones
			var curve;
			if (curve = curves[from - 1])
				curve._segment2 = segments[from];
			if (curve = curves[from])
				curve._segment1 = segments[from];
			// If the last segment of a closing path was removed, we need to
			// readjust the last curve of the list now.
			if (last && this._closed && (curve = curves[curves.length - 1]))
				curve._segment2 = segments[0];
		}
		this._changed(Change.GEOMETRY);
		return removed;
	},

	/**
	 * Specifies whether an path is selected and will also return {@code true}
	 * if the path is partially selected, i.e. one or more of its segments is
	 * selected.
	 *
	 * Paper.js draws the visual outlines of selected items on top of your
	 * project. This can be useful for debugging, as it allows you to see the
	 * construction of paths, position of path curves, individual segment points
	 * and bounding boxes of symbol and raster items.
	 *
	 * @type Boolean
	 * @bean
	 * @see Project#selectedItems
	 * @see Segment#selected
	 * @see Point#selected
	 *
	 * @example {@paperscript}
	 * // Selecting an item:
	 * var path = new Path.Circle(new Size(80, 50), 35);
	 * path.selected = true; // Select the path
	 *
	 * @example {@paperscript}
	 * // A path is selected, if one or more of its segments is selected:
	 * var path = new Path.Circle(new Size(80, 50), 35);
	 *
	 * // Select the second segment of the path:
	 * path.segments[1].selected = true;
	 *
	 * // If the path is selected (which it is), set its fill color to red:
	 * if (path.selected) {
	 * 	path.fillColor = 'red';
	 * }
	 *
	 */
	/**
	 * Specifies whether the path and all its segments are selected.
	 *
	 * @type Boolean
	 * @bean
	 *
	 * @example {@paperscript}
	 * // A path is fully selected, if all of its segments are selected:
	 * var path = new Path.Circle(new Size(80, 50), 35);
	 * path.fullySelected = true;
	 *
	 * var path2 = new Path.Circle(new Size(180, 50), 35);
	 * path2.fullySelected = true;
	 *
	 * // Deselect the second segment of the second path:
	 * path2.segments[1].selected = false;
	 *
	 * // If the path is fully selected (which it is),
	 * // set its fill color to red:
	 * if (path.fullySelected) {
	 * 	path.fillColor = 'red';
	 * }
	 *
	 * // If the second path is fully selected (which it isn't, since we just
	 * // deselected its second segment),
	 * // set its fill color to red:
	 * if (path2.fullySelected) {
	 * 	path2.fillColor = 'red';
	 * }
	 */
	isFullySelected: function() {
		return this._selected && this._selectedSegmentState
				== this._segments.length * SelectionState.POINT;
	},

	setFullySelected: function(selected) {
		var length = this._segments.length;
		this._selectedSegmentState = selected
				? length * SelectionState.POINT : 0;
		for (var i = 0; i < length; i++)
			this._segments[i]._selectionState = selected
					? SelectionState.POINT : 0;
		// No need to pass true for noChildren since Path has none anyway.
		this.setSelected(selected);
	},

	_updateSelection: function(segment, oldState, newState) {
		segment._selectionState = newState;
		var total = this._selectedSegmentState += newState - oldState;
		// Set this path as selected in case we have selected segments. Do not
		// unselect if we're down to 0, as the path itself can still remain
		// selected even when empty.
		if (total > 0)
			this.setSelected(true);
	},

	/**
	 * Converts the curves in a path to straight lines with an even distribution
	 * of points. The distance between the produced segments is as close as
	 * possible to the value specified by the {@code maxDistance} parameter.
	 *
	 * @param {Number} maxDistance the maximum distance between the points
	 *
	 * @example {@paperscript}
	 * // Flattening a circle shaped path:
	 *
	 * // Create a circle shaped path at { x: 80, y: 50 }
	 * // with a radius of 35:
	 * var path = new Path.Circle(new Size(80, 50), 35);
	 *
	 * // Select the path, so we can inspect its segments:
	 * path.selected = true;
	 *
	 * // Create a copy of the path and move it 150 points to the right:
	 * var copy = path.clone();
	 * copy.position.x += 150;
	 *
	 * // Convert its curves to points, with a max distance of 20:
	 * copy.flatten(20);
	 *
	 * // Select the copy, so we can inspect its segments:
	 * copy.selected = true;
	 */
	flatten: function(maxDistance) {
		var flattener = new PathFlattener(this),
			pos = 0,
			// Adapt step = maxDistance so the points distribute evenly.
			step = flattener.length / Math.ceil(flattener.length / maxDistance),
			// Add/remove half of step to end, so imprecisions are ok too.
			// For closed paths, remove it, because we don't want to add last
			// segment again
			end = flattener.length + (this._closed ? -step : step) / 2;
		// Iterate over path and evaluate and add points at given offsets
		var segments = [];
		while (pos <= end) {
			segments.push(new Segment(flattener.evaluate(pos, 0)));
			pos += step;
		}
		this.setSegments(segments);
	},

	/**
	 * Smooths a path by simplifying it. The {@link Path#segments} array is
	 * analyzed and replaced by a more optimal set of segments, reducing memory
	 * usage and speeding up drawing.
	 *
	 * @param {Number} [tolerance=2.5]
	 *
	 * @example {@paperscript height=300}
	 * // Click and drag below to draw to draw a line, when you release the
	 * // mouse, the is made smooth using path.simplify():
	 *
	 * var path;
	 * function onMouseDown(event) {
	 * 	// If we already made a path before, deselect it:
	 * 	if (path) {
	 * 		path.selected = false;
	 * 	}
	 *
	 * 	// Create a new path and add the position of the mouse
	 * 	// as its first segment. Select it, so we can see the
	 * 	// segment points:
	 * 	path = new Path();
	 * 	path.strokeColor = 'black';
	 * 	path.add(event.point);
	 * 	path.selected = true;
	 * }
	 *
	 * function onMouseDrag(event) {
	 * 	// On every drag event, add a segment to the path
	 * 	// at the position of the mouse:
	 * 	path.add(event.point);
	 * }
	 *
	 * function onMouseUp(event) {
	 * 	// When the mouse is released, simplify the path:
	 * 	path.simplify();
	 * 	path.selected = true;
	 * }
	 */
	simplify: function(tolerance) {
		if (this._segments.length > 2) {
			var fitter = new PathFitter(this, tolerance || 2.5);
			this.setSegments(fitter.fit());
		}
	},

	// TODO: reduceSegments([flatness])
	// TODO: split(offset) / split(location) / split(index[, parameter])

	/**
	 * Specifies whether the path is oriented clock-wise.
	 *
	 * @type Boolean
	 * @bean
	 */
	isClockwise: function() {
		if (this._clockwise !== undefined)
			return this._clockwise;
		var sum = 0,
			xPre, yPre;
		function edge(x, y) {
			if (xPre !== undefined)
				sum += (xPre - x) * (y + yPre);
			xPre = x;
			yPre = y;
		}
		// Method derived from:
		// http://stackoverflow.com/questions/1165647
		// We treat the curve points and handles as the outline of a polygon of
		// which we determine the orientation using the method of calculating
		// the sum over the edges. This will work even with non-convex polygons,
		// telling you whether it's mostly clockwise
		for (var i = 0, l = this._segments.length; i < l; i++) {
			var seg1 = this._segments[i],
				seg2 = this._segments[i + 1 < l ? i + 1 : 0],
				point1 = seg1._point,
				handle1 = seg1._handleOut,
				handle2 = seg2._handleIn,
				point2 = seg2._point;
			edge(point1._x, point1._y);
			edge(point1._x + handle1._x, point1._y + handle1._y);
			edge(point2._x + handle2._x, point2._y + handle2._y);
			edge(point2._x, point2._y);
		}
		return sum > 0;
	},

	setClockwise: function(clockwise) {
		// On-the-fly conversion to boolean:
		if (this.isClockwise() != (clockwise = !!clockwise)) {
			// Only revers the path if its clockwise orientation is not the same
			// as what it is now demanded to be.
			this.reverse();
			this._clockwise = clockwise;
		}
	},

	/**
	 * Reverses the segments of the path.
	 */
	reverse: function() {
		this._segments.reverse();
		// Reverse the handles:
		for (var i = 0, l = this._segments.length; i < l; i++) {
			var segment = this._segments[i];
			var handleIn = segment._handleIn;
			segment._handleIn = segment._handleOut;
			segment._handleOut = handleIn;
			segment._index = i;
		}
		// Flip clockwise state if it's defined
		if (this._clockwise !== undefined)
			this._clockwise = !this._clockwise;
	},

	// DOCS: document Path#join in more detail.
	/**
	 * Joins the path with the specified path, which will be removed in the
	 * process.
	 *
	 * @param {Path} path
	 *
	 * @example {@paperscript}
	 * // Joining two paths:
	 * var path = new Path([30, 25], [30, 75]);
	 * path.strokeColor = 'black';
	 *
	 * var path2 = new Path([200, 25], [200, 75]);
	 * path2.strokeColor = 'black';
	 *
	 * // Join the paths:
	 * path.join(path2);
	 *
	 * @example {@paperscript}
	 * // Joining two paths that share a point at the start or end of their
	 * // segments array:
	 * var path = new Path([30, 25], [30, 75]);
	 * path.strokeColor = 'black';
	 *
	 * var path2 = new Path([30, 25], [80, 25]);
	 * path2.strokeColor = 'black';
	 *
	 * // Join the paths:
	 * path.join(path2);
	 *
	 * // After joining, path with have 3 segments, since it
	 * // shared its first segment point with the first
	 * // segment point of path2.
	 *
	 * // Select the path to show that they have joined:
	 * path.selected = true;
	 *
	 * @example {@paperscript}
	 * // Joining two paths that connect at two points:
	 * var path = new Path([30, 25], [80, 25], [80, 75]);
	 * path.strokeColor = 'black';
	 *
	 * var path2 = new Path([30, 25], [30, 75], [80, 75]);
	 * path2.strokeColor = 'black';
	 *
	 * // Join the paths:
	 * path.join(path2);
	 *
	 * // Because the paths were joined at two points, the path is closed
	 * // and has 4 segments.
	 *
	 * // Select the path to show that they have joined:
	 * path.selected = true;
	 */
	join: function(path) {
		if (path) {
			var segments = path._segments,
				last1 = this.getLastSegment(),
				last2 = path.getLastSegment();
			if (last1._point.equals(last2._point))
				path.reverse();
			var first2 = path.getFirstSegment();
			if (last1._point.equals(first2._point)) {
				last1.setHandleOut(first2._handleOut);
				this._add(segments.slice(1));
			} else {
				var first1 = this.getFirstSegment();
				if (first1._point.equals(first2._point))
					path.reverse();
				last2 = path.getLastSegment();
				if (first1._point.equals(last2._point)) {
					first1.setHandleIn(last2._handleIn);
					// Prepend all segments from path except the last one
					this._add(segments.slice(0, segments.length - 1), 0);
				} else {
					this._add(segments.slice(0));
				}
			}
			path.remove();
			// Close if they touch in both places
			var first1 = this.getFirstSegment();
			last1 = this.getLastSegment();
			if (last1._point.equals(first1._point)) {
				first1.setHandleIn(last1._handleIn);
				last1.remove();
				this.setClosed(true);
			}
			this._changed(Change.GEOMETRY);
			return true;
		}
		return false;
	},

	/**
	 * The length of the perimeter of the path.
	 *
	 * @type Number
	 * @bean
	 */
	getLength: function() {
		if (this._length == null) {
			var curves = this.getCurves();
			this._length = 0;
			for (var i = 0, l = curves.length; i < l; i++)
				this._length += curves[i].getLength();
		}
		return this._length;
	},

	_getOffset: function(location) {
		var index = location && location.getIndex();
		if (index != null) {
			var curves = this.getCurves(),
				offset = 0;
			for (var i = 0; i < index; i++)
				offset += curves[i].getLength();
			var curve = curves[index];
			return offset + curve.getLength(0, location.getParameter());
		}
		return null;
	},

	getLocation: function(point) {
		var curves = this.getCurves();
		for (var i = 0, l = curves.length; i < l; i++) {
			var curve = curves[i];
			var t = curve.getParameter(point);
			if (t != null)
				return new CurveLocation(curve, t);
		}
		return null;
	},

	// PORT: Rename functions and add new isParameter argument in Scriptographer
	// DOCS: document Path#getLocationAt
	/**
	 * {@grouptitle Positions on Paths and Curves}
	 *
	 * @param {Number} offset
	 * @param {Boolean} [isParameter=false]
	 * @return {CurveLocation}
	 */
	getLocationAt: function(offset, isParameter) {
		var curves = this.getCurves(),
			length = 0;
		if (isParameter) {
			// offset consists of curve index and curve parameter, before and
			// after the fractional digit.
			var index = ~~offset; // = Math.floor()
			return new CurveLocation(curves[index], offset - index);
		}
		for (var i = 0, l = curves.length; i < l; i++) {
			var start = length,
				curve = curves[i];
			length += curve.getLength();
			if (length >= offset) {
				// Found the segment within which the length lies
				return new CurveLocation(curve,
						curve.getParameterAt(offset - start));
			}
		}
		// It may be that through impreciseness of getLength, that the end
		// of the curves was missed:
		if (offset <= this.getLength())
			return new CurveLocation(curves[curves.length - 1], 1);
		return null;
	},

	/**
	 * Get the point on the path at the given offset.
	 *
	 * @param {Number} offset
	 * @param {Boolean} [isParameter=false]
	 * @return {Point} the point at the given offset
	 *
	 * @example {@paperscript height=150}
	 * // Finding the point on a path at a given offset:
	 *
	 * // Create an arc shaped path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(40, 100));
	 * path.arcTo(new Point(150, 100));
	 *
	 * // We're going to be working with a third of the length
	 * // of the path as the offset:
	 * var offset = path.length / 3;
	 *
	 * // Find the point on the path:
	 * var point = path.getPointAt(offset);
	 *
	 * // Create a small circle shaped path at the point:
	 * var circle = new Path.Circle(point, 3);
	 * circle.fillColor = 'red';
	 *
	 * @example {@paperscript height=150}
	 * // Iterating over the length of a path:
	 *
	 * // Create an arc shaped path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(40, 100));
	 * path.arcTo(new Point(150, 100));
	 *
	 * var amount = 5;
	 * var length = path.length;
	 * for (var i = 0; i < amount + 1; i++) {
	 * 	var offset = i / amount * length;
	 *
	 * 	// Find the point on the path at the given offset:
	 * 	var point = path.getPointAt(offset);
	 *
	 * 	// Create a small circle shaped path at the point:
	 * 	var circle = new Path.Circle(point, 3);
	 * 	circle.fillColor = 'red';
	 * }
	 */
	getPointAt: function(offset, isParameter) {
		var loc = this.getLocationAt(offset, isParameter);
		return loc && loc.getPoint();
	},

	/**
	 * Get the tangent to the path at the given offset as a vector
	 * point.
	 *
	 * @param {Number} offset
	 * @param {Boolean} [isParameter=false]
	 * @return {Point} the tangent vector at the given offset
	 *
	 * @example {@paperscript height=150}
	 * // Working with the tangent vector at a given offset:
	 *
	 * // Create an arc shaped path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(40, 100));
	 * path.arcTo(new Point(150, 100));
	 *
	 * // We're going to be working with a third of the length
	 * // of the path as the offset:
	 * var offset = path.length / 3;
	 *
	 * // Find the point on the path:
	 * var point = path.getPointAt(offset);
	 *
	 * // Find the tangent vector at the given offset:
	 * var tangent = path.getTangentAt(offset);
	 *
	 * // Make the tangent vector 60pt long:
	 * tangent.length = 60;
	 *
	 * var path = new Path();
	 * path.strokeColor = 'red';
	 * path.add(point);
	 * path.add(point + tangent);
	 *
	 * @example {@paperscript height=200}
	 * // Iterating over the length of a path:
	 *
	 * // Create an arc shaped path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(40, 100));
	 * path.arcTo(new Point(150, 100));
	 *
	 * var amount = 6;
	 * var length = path.length;
	 * for (var i = 0; i < amount + 1; i++) {
	 * 	var offset = i / amount * length;
	 *
	 * 	// Find the point on the path at the given offset:
	 * 	var point = path.getPointAt(offset);
	 *
	 * 	// Find the normal vector on the path at the given offset:
	 * 	var tangent = path.getTangentAt(offset);
	 *
	 * 	// Make the tangent vector 60pt long:
	 * 	tangent.length = 60;
	 *
	 * 	var line = new Path();
	 * 	line.strokeColor = 'red';
	 * 	line.add(point);
	 * 	line.add(point + tangent);
	 * }
	 */
	getTangentAt: function(offset, isParameter) {
		var loc = this.getLocationAt(offset, isParameter);
		return loc && loc.getTangent();
	},

	/**
	 * Get the normal to the path at the given offset as a vector point.
	 *
	 * @param {Number} offset
	 * @param {Boolean} [isParameter=false]
	 * @return {Point} the normal vector at the given offset
	 *
	 * @example {@paperscript height=150}
	 * // Working with the normal vector at a given offset:
	 *
	 * // Create an arc shaped path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(40, 100));
	 * path.arcTo(new Point(150, 100));
	 *
	 * // We're going to be working with a third of the length
	 * // of the path as the offset:
	 * var offset = path.length / 3;
	 *
	 * // Find the point on the path:
	 * var point = path.getPointAt(offset);
	 *
	 * // Find the normal vector at the given offset:
	 * var normal = path.getNormalAt(offset);
	 *
	 * // Make the normal vector 30pt long:
	 * normal.length = 30;
	 *
	 * var path = new Path();
	 * path.strokeColor = 'red';
	 * path.add(point);
	 * path.add(point + normal);
	 *
	 * @example {@paperscript height=200}
	 * // Iterating over the length of a path:
	 *
	 * // Create an arc shaped path:
	 * var path = new Path();
	 * path.strokeColor = 'black';
	 * path.add(new Point(40, 100));
	 * path.arcTo(new Point(150, 100));
	 *
	 * var amount = 10;
	 * var length = path.length;
	 * for (var i = 0; i < amount + 1; i++) {
	 * 	var offset = i / amount * length;
	 *
	 * 	// Find the point on the path at the given offset:
	 * 	var point = path.getPointAt(offset);
	 *
	 * 	// Find the normal vector on the path at the given offset:
	 * 	var normal = path.getNormalAt(offset);
	 *
	 * 	// Make the normal vector 30pt long:
	 * 	normal.length = 30;
	 *
	 * 	var line = new Path();
	 * 	line.strokeColor = 'red';
	 * 	line.add(point);
	 * 	line.add(point + normal);
	 * }
	 */
	getNormalAt: function(offset, isParameter) {
		var loc = this.getLocationAt(offset, isParameter);
		return loc && loc.getNormal();
	},

	/**
	 * Returns the nearest location on the path to the specified point.
	 *
	 * @name Path#getNearestLocation
	 * @function
	 * @param point {Point} The point for which we search the nearest location
	 * @return {CurveLocation} The location on the path that's the closest to
	 * the specified point
	 */
	getNearestLocation: function(point) {
		var curves = this.getCurves(),
			minDist = Infinity,
			minLoc = null;
		for (var i = 0, l = curves.length; i < l; i++) {
			var loc = curves[i].getNearestLocation(point);
			if (loc._distance < minDist) {
				minDist = loc._distance;
				minLoc = loc;
			}
		}
		return minLoc;
	},

	/**
	 * Returns the nearest point on the path to the specified point.
	 *
	 * @name Path#getNearestPoint
	 * @function
	 * @param point {Point} The point for which we search the nearest point
	 * @return {Point} The point on the path that's the closest to the specified
	 * point
	 */
	getNearestPoint: function(point) {
		return this.getNearestLocation(point).getPoint();
	},

	contains: function(point) {
		point = Point.read(arguments);
		// Note: This only works correctly with even-odd fill rule, or paths
		// that do not overlap with themselves.
		// TODO: Find out how to implement the "Point In Polygon" problem for
		// non-zero fill rule.
		if (!this._closed || !this.getRoughBounds()._containsPoint(point))
			return false;
		// Use the crossing number algorithm, by counting the crossings of the
		// beam in right y-direction with the shape, and see if it's an odd
		// number, meaning the starting point is inside the shape.
		// http://en.wikipedia.org/wiki/Point_in_polygon
		var curves = this.getCurves(),
			crossings = 0,
			// Reuse one array for root-finding, give garbage collector a break
			roots = [];
		for (var i = 0, l = curves.length; i < l; i++)
			crossings += curves[i].getCrossings(point, roots);
		return (crossings & 1) == 1;
	},

	_hitTest: function(point, options) {
		// See #draw() for an explanation of why we can access _style properties
		// directly here:
		var style = this._style,
			tolerance = options.tolerance || 0,
			radius = (options.stroke && style._strokeColor
					? style._strokeWidth / 2 : 0) + tolerance,
			loc,
			res;
		// If we're asked to query for segments, ends or handles, do all that
		// before stroke or fill.
		var coords = [],
			that = this;
		function checkPoint(seg, pt, name) {
			// TODO: We need to transform the point back to the coordinate
			// system of the DOM level on which the inquiry was started!
			if (point.getDistance(pt) < tolerance)
				return new HitResult(name, that, { segment: seg, point: pt });
		}
		function checkSegment(seg, ends) {
			var point = seg._point;
			// Note, when checking for ends, we don't also check for handles,
			// since this will happen afterwards in a separate loop, see below.
			return (ends || options.segments)
					&& checkPoint(seg, point, 'segment')
				|| (!ends && options.handles) && (
					checkPoint(seg, point.add(seg._handleIn), 'handle-in') ||
					checkPoint(seg, point.add(seg._handleOut), 'handle-out'));
		}
		if (options.ends && !options.segments && !this._closed) {
			if (res = checkSegment(this.getFirstSegment(), true)
					|| checkSegment(this.getLastSegment(), true))
				return res;
		} else if (options.segments || options.handles) {
			for (var i = 0, l = this._segments.length; i < l; i++) {
				if (res = checkSegment(this._segments[i]))
					return res;
			}
		}
		// If we're querying for stroke, perform that before fill
		if (options.stroke && radius > 0)
			loc = this.getNearestLocation(point);
		// Don't process loc yet, as we also need to query for stroke after fill
		// in some cases. Simply skip fill query if we already have a matching
		// stroke.
		if (!(loc && loc._distance <= radius) && options.fill
				&& style._fillColor && this.contains(point))
			return new HitResult('fill', this);
		// Now query stroke if we haven't already
		if (!loc && options.stroke && radius > 0)
			loc = this.getNearestLocation(point);
		if (loc && loc._distance <= radius)
			// TODO: Do we need to transform the location back to the coordinate
			// system of the DOM level on which the inquiry was started?
			return options.stroke
					? new HitResult('stroke', this, { location: loc })
					: new HitResult('fill', this);
	}

	// TODO: intersects(item)
	// TODO: contains(item)
	// TODO: intersect(item)
	// TODO: unite(item)
	// TODO: exclude(item)
	// TODO: getIntersections(path)
}, new function() { // Scope for drawing

	// Note that in the code below we're often accessing _x and _y on point
	// objects that were read from segments. This is because the SegmentPoint
	// class overrides the plain x / y properties with getter / setters and
	// stores the values in these private properties internally. To avoid
	// calling of getter functions all the time we directly access these private
	// properties here. The distinction between normal Point objects and
	// SegmentPoint objects maybe seem a bit tedious but is worth the benefit in
	// performance.

	function drawHandles(ctx, segments, matrix) {
		var coords = new Array(6);
		for (var i = 0, l = segments.length; i < l; i++) {
			var segment = segments[i];
			segment._transformCoordinates(matrix, coords, false);
			var state = segment._selectionState,
				selected = state & SelectionState.POINT,
				pX = coords[0],
				pY = coords[1];

			function drawHandle(index) {
				var hX = coords[index],
					hY = coords[index + 1];
				if (pX != hX || pY != hY) {
					ctx.beginPath();
					ctx.moveTo(pX, pY);
					ctx.lineTo(hX, hY);
					ctx.stroke();
					ctx.beginPath();
					ctx.arc(hX, hY, 1.75, 0, Math.PI * 2, true);
					ctx.fill();
				}
			}

			if (selected || (state & SelectionState.HANDLE_IN))
				drawHandle(2);
			if (selected || (state & SelectionState.HANDLE_OUT))
				drawHandle(4);
			// Draw a rectangle at segment.point:
			ctx.save();
			ctx.beginPath();
			ctx.rect(pX - 2, pY - 2, 4, 4);
			ctx.fill();
			// If the point is not selected, draw a white square that is 1 px
			// smaller on all sides:
			if (!selected) {
				ctx.beginPath();
				ctx.rect(pX - 1, pY - 1, 2, 2);
				ctx.fillStyle = '#ffffff';
				ctx.fill();
			}
			ctx.restore();
		}
	}

	function drawSegments(ctx, path, matrix) {
		var segments = path._segments,
			length = segments.length,
			coords = new Array(6),
			first = true,
			curX, curY,
			prevX, prevY,
			inX, inY,
			outX, outY;

		function drawSegment(i) {
			var segment = segments[i];
			// Optimise code when no matrix is provided by accessing semgent
			// points hand handles directly, since this is the default when
			// drawing paths. Matrix is only used for drawing selections.
			if (matrix) {
				segment._transformCoordinates(matrix, coords, false);
				curX = coords[0];
				curY = coords[1];
			} else {
				var point = segment._point;
				curX = point._x;
				curY = point._y;
			}
			if (first) {
				ctx.moveTo(curX, curY);
				first = false;
			} else {
				if (matrix) {
					inX = coords[2];
					inY = coords[3];
				} else {
					var handle = segment._handleIn;
					inX = curX + handle._x;
					inY = curY + handle._y;
				}
				if (inX == curX && inY == curY && outX == prevX && outY == prevY) {
					ctx.lineTo(curX, curY);
				} else {
					ctx.bezierCurveTo(outX, outY, inX, inY, curX, curY);
				}
			}
			prevX = curX;
			prevY = curY;
			if (matrix) {
				outX = coords[4];
				outY = coords[5];
			} else {
				var handle = segment._handleOut;
				outX = prevX + handle._x;
				outY = prevY + handle._y;
			}
		}

		for (var i = 0; i < length; i++)
			drawSegment(i);
		// Close path by drawing first segment again
		if (path._closed && length > 1)
			drawSegment(0);
	}

	return {
		draw: function(ctx, param) {
			if (!param.compound)
				ctx.beginPath();

			// We can access styles directly on the internal _styles object,
			// since Path items do not have children, thus do not need style
			// accessors for merged styles.
			var style = this._style,
				fillColor = style._fillColor,
				strokeColor = style._strokeColor,
				dashArray = style._dashArray,
				hasDash = strokeColor && dashArray && dashArray.length;

			// Prepare the canvas path if we have any situation that requires it
			// to be defined.
			if (param.compound || this._clipMask || fillColor
					|| strokeColor && !hasDash) {
				drawSegments(ctx, this);
			}

			if (this._closed)
				ctx.closePath();

			if (this._clipMask) {
				ctx.clip();
			} else if (!param.compound && (fillColor || strokeColor)) {
				// If the path is part of a compound path or doesn't have a fill
				// or stroke, there is no need to continue.
				ctx.save();
				this._setStyles(ctx);
				if (fillColor)
					ctx.fill();
				if (strokeColor) {
					if (hasDash) {
						// We cannot use the path created by drawSegments above
						// Use CurveFlatteners to draw dashed paths:
						ctx.beginPath();
						var flattener = new PathFlattener(this),
							from = style._dashOffset, to,
							i = 0;
						while (from < flattener.length) {
							to = from + dashArray[(i++) % dashArray.length];
							flattener.drawPart(ctx, from, to);
							from = to + dashArray[(i++) % dashArray.length];
						}
					}
					ctx.stroke();
				}
				ctx.restore();
			}
		},

		drawSelected: function(ctx, matrix) {
			ctx.beginPath();
			drawSegments(ctx, this, matrix);
			// Now stroke it and draw its handles:
			ctx.stroke();
			drawHandles(ctx, this._segments, matrix);
			// If the path has no selected segments, draw its bounds too
			if (this._selectedSegmentState == 0) {
				Item.drawSelectedBounds(this.getBounds(), ctx, matrix);
			}
		}
	};
}, new function() { // Path Smoothing

	/**
	 * Solves a tri-diagonal system for one of coordinates (x or y) of first
	 * bezier control points.
	 *
	 * @param rhs right hand side vector.
	 * @return Solution vector.
	 */
	function getFirstControlPoints(rhs) {
		var n = rhs.length,
			x = [], // Solution vector.
			tmp = [], // Temporary workspace.
			b = 2;
		x[0] = rhs[0] / b;
		// Decomposition and forward substitution.
		for (var i = 1; i < n; i++) {
			tmp[i] = 1 / b;
			b = (i < n - 1 ? 4 : 2) - tmp[i];
			x[i] = (rhs[i] - x[i - 1]) / b;
		}
		// Back-substitution.
		for (var i = 1; i < n; i++) {
			x[n - i - 1] -= tmp[n - i] * x[n - i];
		}
		return x;
	};

	return {
		// Note: Documentation for smooth() is in PathItem
		smooth: function() {
			// This code is based on the work by Oleg V. Polikarpotchkin,
			// http://ov-p.spaces.live.com/blog/cns!39D56F0C7A08D703!147.entry
			// It was extended to support closed paths by averaging overlapping
			// beginnings and ends. The result of this approach is very close to
			// Polikarpotchkin's closed curve solution, but reuses the same
			// algorithm as for open paths, and is probably executing faster as
			// well, so it is preferred.
			var segments = this._segments,
				size = segments.length,
				n = size,
				// Add overlapping ends for averaging handles in closed paths
				overlap;

			if (size <= 2)
				return;

			if (this._closed) {
				// Overlap up to 4 points since averaging beziers affect the 4
				// neighboring points
				overlap = Math.min(size, 4);
				n += Math.min(size, overlap) * 2;
			} else {
				overlap = 0;
			}
			var knots = [];
			for (var i = 0; i < size; i++)
				knots[i + overlap] = segments[i]._point;
			if (this._closed) {
				// If we're averaging, add the 4 last points again at the
				// beginning, and the 4 first ones at the end.
				for (var i = 0; i < overlap; i++) {
					knots[i] = segments[i + size - overlap]._point;
					knots[i + size + overlap] = segments[i]._point;
				}
			} else {
				n--;
			}
			// Calculate first Bezier control points
			// Right hand side vector
			var rhs = [];

			// Set right hand side X values
			for (var i = 1; i < n - 1; i++)
				rhs[i] = 4 * knots[i]._x + 2 * knots[i + 1]._x;
			rhs[0] = knots[0]._x + 2 * knots[1]._x;
			rhs[n - 1] = 3 * knots[n - 1]._x;
			// Get first control points X-values
			var x = getFirstControlPoints(rhs);

			// Set right hand side Y values
			for (var i = 1; i < n - 1; i++)
				rhs[i] = 4 * knots[i]._y + 2 * knots[i + 1]._y;
			rhs[0] = knots[0]._y + 2 * knots[1]._y;
			rhs[n - 1] = 3 * knots[n - 1]._y;
			// Get first control points Y-values
			var y = getFirstControlPoints(rhs);

			if (this._closed) {
				// Do the actual averaging simply by linearly fading between the
				// overlapping values.
				for (var i = 0, j = size; i < overlap; i++, j++) {
					var f1 = (i / overlap);
					var f2 = 1 - f1;
					// Beginning
					x[j] = x[i] * f1 + x[j] * f2;
					y[j] = y[i] * f1 + y[j] * f2;
					// End
					var ie = i + overlap, je = j + overlap;
					x[je] = x[ie] * f2 + x[je] * f1;
					y[je] = y[ie] * f2 + y[je] * f1;
				}
				n--;
			}
			var handleIn = null;
			// Now set the calculated handles
			for (var i = overlap; i <= n - overlap; i++) {
				var segment = segments[i - overlap];
				if (handleIn)
					segment.setHandleIn(handleIn.subtract(segment._point));
				if (i < n) {
					segment.setHandleOut(
							Point.create(x[i], y[i]).subtract(segment._point));
					if (i < n - 1)
						handleIn = Point.create(
								2 * knots[i + 1]._x - x[i + 1],
								2 * knots[i + 1]._y - y[i + 1]);
					else
						handleIn = Point.create(
								(knots[n]._x + x[n - 1]) / 2,
								(knots[n]._y + y[n - 1]) / 2);
				}
			}
			if (this._closed && handleIn) {
				var segment = this._segments[0];
				segment.setHandleIn(handleIn.subtract(segment._point));
			}
		}
	};
}, new function() { // PostScript-style drawing commands
	/**
	 * Helper method that returns the current segment and checks if a moveTo()
	 * command is required first.
	 */
	function getCurrentSegment(that) {
		var segments = that._segments;
		if (segments.length == 0)
			throw new Error('Use a moveTo() command first');
		return segments[segments.length - 1];
	}

	return {
		// Note: Documentation for these methods is found in PathItem, as they
		// are considered abstract methods of PathItem and need to be defined in
		// all implementing classes.
		moveTo: function(point) {
			// Let's not be picky about calling moveTo() when not at the
			// beginning of a path, just bail out:
			if (!this._segments.length)
				this._add([ new Segment(Point.read(arguments)) ]);
		},

		moveBy: function(point) {
			throw new Error('moveBy() is unsupported on Path items.');
		},

		lineTo: function(point) {
			// Let's not be picky about calling moveTo() first:
			this._add([ new Segment(Point.read(arguments)) ]);
		},

		cubicCurveTo: function(handle1, handle2, to) {
			var _handle1 = Point.read(arguments);
				_handle2 = Point.read(arguments);
				_to = Point.read(arguments);
			// First modify the current segment:
			var current = getCurrentSegment(this);
			// Convert to relative values:
			current.setHandleOut(_handle1.subtract(current._point));
			// And add the new segment, with handleIn set to c2
			this._add([ new Segment(_to, _handle2.subtract(to)) ]);
		},

		quadraticCurveTo: function(handle, to) {
			var _handle = Point.read(arguments),
				to = Point.read(arguments);
			// This is exact:
			// If we have the three quad points: A E D,
			// and the cubic is A B C D,
			// B = E + 1/3 (A - E)
			// C = E + 1/3 (D - E)
			var current = getCurrentSegment(this)._point;
			this.cubicCurveTo(
				_handle.add(current.subtract(_handle).multiply(1 / 3)),
				_handle.add(to.subtract(_handle).multiply(1 / 3)),
				to
			);
		},

		curveTo: function(through, to, parameter) {
			var _through = Point.read(arguments),
				_to = Point.read(arguments),
				t = Base.pick(Base.readValue(arguments), 0.5),
				t1 = 1 - t,
				current = getCurrentSegment(this)._point,
				// handle = (through - (1 - t)^2 * current - t^2 * to) /
				// (2 * (1 - t) * t)
				handle = _through.subtract(current.multiply(t1 * t1))
					.subtract(_to.multiply(t * t)).divide(2 * t * t1);
			if (handle.isNaN())
				throw new Error(
					'Cannot put a curve through points with parameter = ' + t);
			this.quadraticCurveTo(handle, _to);
		},

		// PORT: New implementation back to Scriptographer
		arcTo: function(to, clockwise /* | through, to */) {
			// Get the start point:
			var current = getCurrentSegment(this),
				from = current._point,
				through,
				point = Point.read(arguments),
				// Peek at next value to see if it's clockwise,
				// with true as default value.
				next = Base.pick(Base.peekValue(arguments), true);
			if (typeof next === 'boolean') {
				// arcTo(to, clockwise)
				to = point;
				clockwise = next;
				var middle = from.add(to).divide(2),
				through = middle.add(middle.subtract(from).rotate(
						clockwise ? -90 : 90));
			} else {
				// arcTo(through, to)
				through = point;
				to = Point.read(arguments);
			}
			// Construct the two perpendicular middle lines to (from, through)
			// and (through, to), and intersect them to get the center
			var l1 = new Line(from.add(through).divide(2),
					through.subtract(from).rotate(90)),
			 	l2 = new Line(through.add(to).divide(2),
					to.subtract(through).rotate(90)),
				center = l1.intersect(l2),
				line = new Line(from, to, true),
				throughSide = line.getSide(through);
			if (!center) {
				// If the two lines are colinear, there cannot be an arc as the
				// circle is infinitely big and has no center point. If side is
				// 0, the connecting arc line of this huge circle is a line
				// between the two points, so we can use #lineTo instead.
				// Otherwise we bail out:
				if (!throughSide)
					return this.lineTo(to);
				throw new Error("Cannot put an arc through the given points: "
					+ [from, through, to]);
			}
			var vector = from.subtract(center),
				radius = vector.getLength(),
				extent = vector.getDirectedAngle(to.subtract(center)),
				centerSide = line.getSide(center);
			if (centerSide == 0) {
				// If the center is lying on the line, we might have gotten the
				// wrong sign for extent above. Use the sign of the side of the
				// through point.
				extent = throughSide * Math.abs(extent);
			} else if (throughSide == centerSide) {
				// If the center is on the same side of the line (from, to) as
				// the through point, we're extending bellow 180 degrees and
				// need to adapt extent.
				extent -= 360 * (extent < 0 ? -1 : 1);
			}
			var ext = Math.abs(extent),
				count =  ext >= 360 ? 4 : Math.ceil(ext / 90),
				inc = extent / count,
				half = inc * Math.PI / 360,
				z = 4 / 3 * Math.sin(half) / (1 + Math.cos(half)),
				segments = [];
			for (var i = 0; i <= count; i++) {
				// Explicitely use to point for last segment, since depending
				// on values the calculation adds imprecision:
				var pt = i < count ? center.add(vector) : to;
				var out = i < count ? vector.rotate(90).multiply(z) : null;
				if (i == 0) {
					// Modify startSegment
					current.setHandleOut(out);
				} else {
					// Add new Segment
					segments.push(
						new Segment(pt, vector.rotate(-90).multiply(z), out));
				}
				vector = vector.rotate(inc);
			}
			// Add all segments at once at the end for higher performance
			this._add(segments);
		},

		lineBy: function(vector) {
			vector = Point.read(arguments);
			var current = getCurrentSegment(this);
			this.lineTo(current._point.add(vector));
		},

		curveBy: function(throughVector, toVector, parameter) {
			throughVector = Point.read(throughVector);
			toVector = Point.read(toVector);
			var current = getCurrentSegment(this)._point;
			this.curveTo(current.add(throughVector), current.add(toVector),
					parameter);
		},

		arcBy: function(throughVector, toVector) {
			throughVector = Point.read(throughVector);
			toVector = Point.read(toVector);
			var current = getCurrentSegment(this)._point;
			this.arcBy(current.add(throughVector), current.add(toVector));
		},

		closePath: function() {
			this.setClosed(true);
		}
	};
}, new function() { // A dedicated scope for the tricky bounds calculations
	/**
	 * Returns the bounding rectangle of the item excluding stroke width.
	 */
	function getBounds(matrix, strokePadding) {
		// Code ported and further optimised from:
		// http://blog.hackers-cafe.net/2009/06/how-to-calculate-bezier-curves-bounding.html
		var segments = this._segments,
			first = segments[0];
		if (!first)
			return null;
		var coords = new Array(6),
			prevCoords = new Array(6);
		// Make coordinates for first segment available in prevCoords.
		first._transformCoordinates(matrix, prevCoords, false);
		var min = prevCoords.slice(0, 2),
			max = min.slice(0), // clone
			// Add some tolerance for good roots, as t = 0 / 1 are added
			// seperately anyhow, and we don't want joins to be added with
			// radiuses in getStrokeBounds()
			tMin = Numerical.TOLERANCE,
			tMax = 1 - tMin;
		function processSegment(segment) {
			segment._transformCoordinates(matrix, coords, false);

			for (var i = 0; i < 2; i++) {
				var v0 = prevCoords[i], // prev.point
					v1 = prevCoords[i + 4], // prev.handleOut
					v2 = coords[i + 2], // segment.handleIn
					v3 = coords[i]; // segment.point

				function add(value, t) {
					var padding = 0;
					if (value == null) {
						// Calculate bezier polynomial at t
						var u = 1 - t;
						value = u * u * u * v0
								+ 3 * u * u * t * v1
								+ 3 * u * t * t * v2
								+ t * t * t * v3;
						// Only add strokeWidth to bounds for points which lie
						// within 0 < t < 1. The corner cases for cap and join
						// are handled in getStrokeBounds()
						padding = strokePadding ? strokePadding[i] : 0;
					}
					var left = value - padding,
						right = value + padding;
					if (left < min[i])
						min[i] = left;
					if (right > max[i])
						max[i] = right;

				}
				add(v3, null);

				// Calculate derivative of our bezier polynomial, divided by 3.
				// Dividing by 3 allows for simpler calculations of a, b, c and
				// leads to the same quadratic roots below.
				var a = 3 * (v1 - v2) - v0 + v3,
					b = 2 * (v0 + v2) - 4 * v1,
					c = v1 - v0;

				// Solve for derivative for quadratic roots. Each good root
				// (meaning a solution 0 < t < 1) is an extrema in the cubic
				// polynomial and thus a potential point defining the bounds
				// TODO: Use tolerance here, just like Numerical.solveQuadratic
				if (a == 0) {
					if (b == 0)
					    continue;
					var t = -c / b;
					// Test for good root and add to bounds if good (same below)
					if (tMin < t && t < tMax)
						add(null, t);
					continue;
				}

				var q = b * b - 4 * a * c;
				if (q < 0)
					continue;
				// TODO: Match this with Numerical.solveQuadratic
				var sqrt = Math.sqrt(q),
					f = -0.5 / a,
				 	t1 = (b - sqrt) * f,
					t2 = (b + sqrt) * f;
				if (tMin < t1 && t1 < tMax)
					add(null, t1);
				if (tMin < t2 && t2 < tMax)
					add(null, t2);
			}
			// Swap coordinate buffers
			var tmp = prevCoords;
			prevCoords = coords;
			coords = tmp;
		}
		for (var i = 1, l = segments.length; i < l; i++)
			processSegment(segments[i]);
		if (this._closed)
			processSegment(first);
		return Rectangle.create(min[0], min[1],
					max[0] - min[0], max[1] - min[1]);
	}

	/**
	 * Returns the horizontal and vertical padding that a transformed round
	 * stroke adds to the bounding box, by calculating the dimensions of a
	 * rotated ellipse.
	 */
	function getPenPadding(radius, matrix) {
		if (!matrix)
			return [radius, radius];
		// If a matrix is provided, we need to rotate the stroke circle
		// and calculate the bounding box of the resulting rotated elipse:
		// Get rotated hor and ver vectors, and determine rotation angle
		// and elipse values from them:
		var mx = matrix.createShiftless(),
			hor = mx.transform(Point.create(radius, 0)),
			ver = mx.transform(Point.create(0, radius)),
			phi = hor.getAngleInRadians(),
			a = hor.getLength(),
			b = ver.getLength();
		// Formula for rotated ellipses:
		// x = cx + a*cos(t)*cos(phi) - b*sin(t)*sin(phi)
		// y = cy + b*sin(t)*cos(phi) + a*cos(t)*sin(phi)
		// Derivates (by Wolfram Alpha):
		// derivative of x = cx + a*cos(t)*cos(phi) - b*sin(t)*sin(phi)
		// dx/dt = a sin(t) cos(phi) + b cos(t) sin(phi) = 0
		// derivative of y = cy + b*sin(t)*cos(phi) + a*cos(t)*sin(phi)
		// dy/dt = b cos(t) cos(phi) - a sin(t) sin(phi) = 0
		// This can be simplified to:
		// tan(t) = -b * tan(phi) / a // x
		// tan(t) =  b * cot(phi) / a // y
		// Solving for t gives:
		// t = pi * n - arctan(b * tan(phi) / a) // x
		// t = pi * n + arctan(b * cot(phi) / a)
		//   = pi * n + arctan(b / tan(phi) / a) // y
		var sin = Math.sin(phi),
			cos = Math.cos(phi),
			tan = Math.tan(phi),
			tx = -Math.atan(b * tan / a),
			ty = Math.atan(b / (tan * a));
		// Due to symetry, we don't need to cycle through pi * n solutions:
		return [Math.abs(a * Math.cos(tx) * cos - b * Math.sin(tx) * sin),
				Math.abs(b * Math.sin(ty) * cos + a * Math.cos(ty) * sin)];
	}

	/**
	 * Returns the bounding rectangle of the item including stroke width.
	 */
	function getStrokeBounds(matrix) {
		// See #draw() for an explanation of why we can access _style
		// properties directly here:
		var style = this._style;
		// TODO: Find a way to reuse 'bounds' cache instead?
		if (!style._strokeColor || !style._strokeWidth)
			return getBounds.call(this, matrix);
		var width = style._strokeWidth,
			radius = width / 2,
			padding = getPenPadding(radius, matrix),
			join = style._strokeJoin,
			cap = style._strokeCap,
			// miter is relative to width. Divide it by 2 since we're
			// measuring half the distance below
			miter = style._miterLimit * width / 2,
			segments = this._segments,
			length = segments.length,
			bounds = getBounds.call(this, matrix, padding);
		// Create a rectangle of padding size, used for union with bounds
		// further down
		var joinBounds = new Rectangle(new Size(padding).multiply(2));

		function add(point) {
			bounds = bounds.include(matrix
				? matrix._transformPoint(point, point) : point);
		}

		function addBevelJoin(curve, t) {
			var point = curve.getPoint(t),
				normal = curve.getNormal(t).normalize(radius);
			add(point.add(normal));
			add(point.subtract(normal));
		}

		function addJoin(segment, join) {
			// When both handles are set in a segment, the join setting is
			// ignored and round is always used.
			if (join === 'round' || !segment._handleIn.isZero()
					&& !segment._handleOut.isZero()) {
				bounds = bounds.unite(joinBounds.setCenter(matrix
					? matrix._transformPoint(segment._point) : segment._point));
			} else if (join == 'bevel') {
				var curve = segment.getCurve();
				addBevelJoin(curve, 0);
				addBevelJoin(curve.getPrevious(), 1);
			} else if (join == 'miter') {
				var curve2 = segment.getCurve(),
					curve1 = curve2.getPrevious(),
					point = curve2.getPoint(0),
					normal1 = curve1.getNormal(1).normalize(radius),
					normal2 = curve2.getNormal(0).normalize(radius),
					// Intersect the two lines
					line1 = new Line(point.subtract(normal1),
							Point.create(-normal1.y, normal1.x)),
					line2 = new Line(point.subtract(normal2),
							Point.create(-normal2.y, normal2.x)),
					corner = line1.intersect(line2);
				// Now measure the distance from the segment to the
				// intersection, which his half of the miter distance
				if (!corner || point.getDistance(corner) > miter) {
					addJoin(segment, 'bevel');
				} else {
					add(corner);
				}
			}
		}

		function addCap(segment, cap, t) {
			switch (cap) {
			case 'round':
				return addJoin(segment, cap);
			case 'butt':
			case 'square':
				// Calculate the corner points of butt and square caps
				var curve = segment.getCurve(),
					point = curve.getPoint(t),
					normal = curve.getNormal(t).normalize(radius);
				// For square caps, we need to step away from point in the
				// direction of the tangent, which is the rotated normal
				if (cap === 'square')
					point = point.add(normal.rotate(t == 0 ? -90 : 90));
				add(point.add(normal));
				add(point.subtract(normal));
				break;
			}
		}

		for (var i = 1, l = length - (this._closed ? 0 : 1); i < l; i++) {
			addJoin(segments[i], join);
		}
		if (this._closed) {
			addJoin(segments[0], join);
		} else {
			addCap(segments[0], cap, 0);
			addCap(segments[length - 1], cap, 1);
		}
		return bounds;
	}

	/**
	 * Returns the bounding rectangle of the item including handles.
	 */
	function getHandleBounds(matrix, stroke, join) {
		var coords = new Array(6),
			x1 = Infinity,
			x2 = -x1,
			y1 = x1,
			y2 = x2;
		stroke = stroke / 2 || 0; // Stroke padding
		join = join / 2 || 0; // Join padding, for miterLimit
		for (var i = 0, l = this._segments.length; i < l; i++) {
			var segment = this._segments[i];
			segment._transformCoordinates(matrix, coords, false);
			for (var j = 0; j < 6; j += 2) {
				// Use different padding for points or handles
				var padding = j == 0 ? join : stroke,
					x = coords[j],
					y = coords[j + 1],
					xn = x - padding,
					xx = x + padding,
					yn = y - padding,
					yx = y + padding;
				if (xn < x1) x1 = xn;
				if (xx > x2) x2 = xx;
				if (yn < y1) y1 = yn;
				if (yx > y2) y2 = yx;
			}
		}
		return Rectangle.create(x1, y1, x2 - x1, y2 - y1);
	}

	/**
	 * Returns the rough bounding rectangle of the item that is shure to include
	 * all of the drawing, including stroke width.
	 */
	function getRoughBounds(matrix) {
		// Delegate to handleBounds, but pass on radius values for stroke and
		// joins. Hanlde miter joins specially, by passing the largets radius
		// possible.
		var style = this._style,
			width = style._strokeColor ? style._strokeWidth : 0;
		return getHandleBounds.call(this, matrix, width,
				style._strokeJoin == 'miter'
					? width * style._miterLimit
					: width);
	}

	var get = {
		bounds: getBounds,
		strokeBounds: getStrokeBounds,
		handleBounds: getHandleBounds,
		roughBounds: getRoughBounds
	};

	return {
		_getBounds: function(type, matrix) {
			return get[type].call(this, matrix);
		}
	};
});