IKRS.BezierPath.js

/**
 * @author Ikaros Kappler
 * @date 2013-08-19
 * @version 1.0.0
 **/



IKRS.BezierPath = function( pathPoints ) {

    //window.alert( "bezierCurves=" + bezierCurves );
    //window.alert( "pathPoints=" + pathPoints );

    IKRS.Object.call( this );

    if( !pathPoints )
	pathPoints = [];


    this.totalArcLength = 0.0;
    this.bezierCurves = [];
    for( var i = 1; i < pathPoints.length; i++ ) {

	var bounds = new THREE.Box2( pathPoints[i].x - pathPoints[i-1].x, 
				     pathPoints[i].y - pathPoints[i-1].y
				   );

	// window.alert( "pathSegment=(" + pathPoints[i-1].x + "," + pathPoints[i-1].y + ") to (" + pathPoints[i].x + "," + pathPoints[i].y + "); bounds=(" + bounds.max + ", " + bounds.min + ")" );


	// Create a new Bezier curve inside the box
	var bCurve =  new IKRS.CubicBezierCurve( pathPoints[i-1],
						 pathPoints[i],
						 new THREE.Vector2( pathPoints[i-1].x, // + bounds.max/2,
								    pathPoints[i-1].y - bounds.min/2
								  ),
						 // This control point will be auto-adjusted in the next step
						 new THREE.Vector2( pathPoints[i].x + bounds.max/2,
								    pathPoints[i].y // - bounds.min/2
								  )
					       );
	this.bezierCurves.push( bCurve );
	this.totalArcLength += bCurve.getLength();
	
	// Auto adjust the second control point (should be on a linear sub-space)
	if( this.bezierCurves.length >= 2 ) {
	    this.adjustSuccessorControlPoint( this.bezierCurves.length-2, // curveIndex, 
					      true,                       // obtain handle length?
					      true                        // update arc lengths
					    );
	}

    }

}

IKRS.BezierPath.prototype = new IKRS.Object();
IKRS.BezierPath.prototype.constructor = IKRS.BezierPath;

// These variables equal the values from IKRS.CubicBezierCurve
IKRS.BezierPath.prototype.START_POINT         = 0;
IKRS.BezierPath.prototype.START_CONTROL_POINT = 1;
IKRS.BezierPath.prototype.END_CONTROL_POINT   = 2;
IKRS.BezierPath.prototype.END_POINT           = 3;

IKRS.BezierPath.prototype.getLength = function() {
    return this.totalArcLength;
};

IKRS.BezierPath.prototype.computeVerticalAreaSize = function( deltaSize, useAbsoluteValues ) {

    var bounds    = this.computeBoundingBox();
    var relativeX = bounds.xMax;

    //window.alert( "relativeX=" + relativeX );

    var size = 0.0;
    for( var i = 0; i < this.bezierCurves.length; i++ ) {

	size += this.bezierCurves[i].computeVerticalAreaSize( relativeX,         // An imaginary x-axis at the right bound
							      deltaSize, 
							      useAbsoluteValues 
							    );

    }

    return size;
};

IKRS.BezierPath.prototype.computeVerticalRevolutionVolumeSize = function( useAbsoluteValues ) {
    
    var bounds    = this.computeBoundingBox();
    var relativeX = bounds.xMax;
    
    //window.alert( "relativeX=" + relativeX );

    var volume = 0.0;
    for( var i = 0; i < this.bezierCurves.length; i++ ) {

	volume += this.bezierCurves[i].computeVerticalRevolutionVolumeSize( relativeX,         // An imaginary x-axis at the right bound
									    //deltaSize, 
									    useAbsoluteValues 
									  );
	
    }

    return volume;
};

IKRS.BezierPath.prototype.updateArcLengths = function() {

    this.totalArcLength = 0.0;
    for( var i = 0; i < this.bezierCurves.length; i++ ) {

	this.bezierCurves[ i ].updateArcLengths();
	this.totalArcLength += this.bezierCurves[ i ].getLength();

    }

}

IKRS.BezierPath.prototype.getCurveCount = function() {
    return this.bezierCurves.length;
}

IKRS.BezierPath.prototype.getCurveAt = function( curveIndex ) {
    return this.bezierCurves[ curveIndex ];
}

IKRS.BezierPath.prototype.removeEndPoint = function() {

    if( this.bezierCurves.length <= 1 )
	return false;

    var newArray = [ this.bezierCurves.length-1 ];
    for( var i = 0; i < this.bezierCurves.length-1; i++ ) {

	newArray[i] = this.bezierCurves[i];

    }
    
    // Update arc length
    this.totalArcLength -= this.bezierCurves[ this.bezierCurves.length-1 ].getLength();
    this.bezierCurves = newArray;
    
    return true;
}

IKRS.BezierPath.prototype.removeStartPoint = function() {

    if( this.bezierCurves.length <= 1 )
	return false;

    var newArray = [ this.bezierCurves.length-1 ];
    for( var i = 1; i < this.bezierCurves.length; i++ ) {

	newArray[i-1] = this.bezierCurves[i];

    }
    
    // Update arc length
    this.totalArcLength -= this.bezierCurves[ 0 ].getLength();
    this.bezierCurves = newArray;
    
    return true;
}

/**
 * This function joins the bezier curve at the given index with
 * its predecessor.
 **/
IKRS.BezierPath.prototype.joinAt = function( curveIndex ) {

    //window.alert( "curveIndex=" + curveIndex );
    
    if( curveIndex < 0 || curveIndex >= this.bezierCurves.length )
	return false;

    
    var leftCurve  = this.bezierCurves[ curveIndex-1 ];
    var rightCurve = this.bezierCurves[ curveIndex ];


    // Make the length of the new handle double that long
    var leftControlPoint = leftCurve.getStartControlPoint().clone();
    leftControlPoint.sub( leftCurve.getStartPoint() );
    leftControlPoint.multiplyScalar( 2.0 );
    leftControlPoint.add( leftCurve.getStartPoint() );
    
    var rightControlPoint = rightCurve.getEndControlPoint().clone();
    rightControlPoint.sub( rightCurve.getEndPoint() );
    rightControlPoint.multiplyScalar( 2.0 );
    rightControlPoint.add( rightCurve.getEndPoint() );
    

    var newCurve = new IKRS.CubicBezierCurve( leftCurve.getStartPoint(),
					      rightCurve.getEndPoint(),
					      leftControlPoint,
					      rightControlPoint 
					    );
    
    // Place into array
    var newArray = [ this.bezierCurves.length - 1 ];

    for( var i = 0; i < curveIndex-1; i++ ) {
	newArray[ i ] = this.bezierCurves[i];
    }

    newArray[ curveIndex-1 ] = newCurve;
    
    // Shift trailing curves left
    for( var i = curveIndex; i+1 < this.bezierCurves.length; i++ ) {

	newArray[ i ] = this.bezierCurves[ i+1 ];

    }
    
   
    this.bezierCurves = newArray;
    this.updateArcLengths();

    return true;

}

IKRS.BezierPath.prototype.splitAt = function( curveIndex,
					      segmentIndex 
					    ) {

    // Must be a valid curve index
    if( curveIndex < 0 || curveIndex >= this.bezierCurves.length )
	return false;


    var oldCurve = this.bezierCurves[ curveIndex ];


    // Segment must be an INNER point!
    // (the outer points are already bezier end/start points!)
    if( segmentIndex < 1 || segmentIndex-1 >= oldCurve.segmentCache.length )
	return false;


    // Make room for a new curve
    for( var c = this.bezierCurves.length; c > curveIndex; c-- ) {

	// Move one position to the right
	this.bezierCurves[ c ] = this.bezierCurves[ c-1 ];
	
    }

    // Accumulate segment lengths
    var u = 0;
    for( var i = 0; i < segmentIndex; i++ )
	u += oldCurve.segmentLengths[i];
    var tangent = oldCurve.getTangentAt( u );
    //tangent = tangent.normalize(); 
    //window.alert( JSON.stringify(tangent) );
    tangent = tangent.multiplyScalar( 0.25 ); 

    var leftEndControlPoint = oldCurve.segmentCache[ segmentIndex ].clone();
    leftEndControlPoint.sub( tangent );
    
    //tangent.negate();
    var rightStartControlPoint = oldCurve.segmentCache[ segmentIndex ].clone();
    rightStartControlPoint.add( tangent );
    
    // Make the old existing handles a quarter that long
    var leftStartControlPoint = oldCurve.getStartControlPoint().clone();
    // move to (0,0)
    leftStartControlPoint.sub( oldCurve.getStartPoint() );
    leftStartControlPoint.multiplyScalar( 0.25 );
    leftStartControlPoint.add( oldCurve.getStartPoint() );

    var rightEndControlPoint = oldCurve.getEndControlPoint().clone(); // oldCurve.getStartControlPoint().clone();
    // move to (0,0)
    rightEndControlPoint.sub( oldCurve.getEndPoint() );
    rightEndControlPoint.multiplyScalar( 0.25 );
    rightEndControlPoint.add( oldCurve.getEndPoint() );

    var newLeft  = new IKRS.CubicBezierCurve( oldCurve.getStartPoint(),                      // old start point
					      oldCurve.segmentCache[ segmentIndex ],         // new end point
					      leftStartControlPoint,                         // old start control point 
					      leftEndControlPoint                            // new end control point
					    );
    var newRight = new IKRS.CubicBezierCurve( oldCurve.segmentCache[ segmentIndex ],         // new start point
					      oldCurve.getEndPoint(),                        // old end point
					      rightStartControlPoint,                        // new start control point 
					      rightEndControlPoint                           // old end control point
					    );
				    

    // Insert split curve(s) at free index
    this.bezierCurves[ curveIndex ]     = newLeft;
    this.bezierCurves[ curveIndex + 1 ] = newRight;

    
    // Update total arc length, even if there is only a very little change!
    this.totalArcLength -= oldCurve.getLength();

    this.totalArcLength += newLeft.getLength();
    this.totalArcLength += newRight.getLength();


    return true;
}

IKRS.BezierPath.prototype.scale = function( anchor,  // Vector2
					    scaling  // Vector2
					  ) {
    
    for( var i = 0; i < this.bezierCurves.length; i++ ) {

	var curve = this.bezierCurves[ i ];
	
	IKRS.BezierPath._scalePoint( curve.getStartPoint(),        anchor, scaling );
	IKRS.BezierPath._scalePoint( curve.getStartControlPoint(), anchor, scaling );
	IKRS.BezierPath._scalePoint( curve.getEndControlPoint(),   anchor, scaling );
	// Do NOT scale the end point here!
	// Don't forget that the curves are connected and on curve's end point
	// the the successor's start point (same instance)!

    }
    
    // Finally move the last end point (was not scaled yet)
    if( this.bezierCurves.length > 0 ) {

	IKRS.BezierPath._scalePoint( this.bezierCurves[ this.bezierCurves.length-1 ].getEndPoint(),
				     anchor,
				     scaling
				   );
    }
    
    this.updateArcLengths();
    
}


IKRS.BezierPath._scalePoint = function( point,   // Vector2
					anchor,  // Vector2
					scaling  // Vector2
				      ) {
    // Move point to origin
    point.sub( anchor );
    // Apply scaling
    point.setX( point.x * scaling.x );
    point.setY( point.y * scaling.y );
    // Move back to original position
    point.add( anchor );
    
}

IKRS.BezierPath.prototype.getPointAt = function( u ) {

    if( u < 0 || u > this.totalArcLength ) {
	console.log( "[IKRS.BezierPath.getPointAt(u)] u is out of bounds: " + u + "." );
	return null;
    }

    // Find the spline to extract the value from
    var i = 0;
    var uTemp = 0.0;
    
    while( i < this.bezierCurves.length &&
	   (uTemp + this.bezierCurves[i].getLength()) < u 
	 ) {
	
	uTemp += this.bezierCurves[ i ].getLength();
	i++;

    }
    
    //window.alert( i );
    
    // if u == arcLength
    //   -> i is max
    if( i >= this.bezierCurves.length )
	return this.bezierCurves[ this.bezierCurves.length-1 ].getEndPoint().clone();
    
    var bCurve    = this.bezierCurves[ i ];
    var relativeU = u - uTemp;
    
    //window.alert( "relativeU=" + relativeU );

    return bCurve.getPointAt( relativeU );
}

IKRS.BezierPath.prototype.getPoint = function( t ) {
    //window.alert( "IKRS.BezierPath.totalArcLength=" + this.totalArcLength );
    return this.getPointAt( t * this.totalArcLength );
}

IKRS.BezierPath.prototype.getTangent = function( t ) {

    return this.getTangentAt( t * this.totalArcLength );

}

IKRS.BezierPath.prototype.getTangentAt = function( u ) {


    if( u < 0 || u > this.totalArcLength ) {
	console.log( "[IKRS.BezierPath.getTangentAt(u)] u is out of bounds: " + u + "." );
	return null;
    }

    // Find the spline to extract the value from
    var i = 0;
    var uTemp = 0.0;
    
    while( i < this.bezierCurves.length &&
	   (uTemp + this.bezierCurves[i].getLength()) < u 
	 ) {
	
	uTemp += this.bezierCurves[ i ].getLength();
	i++;

    }
    
    //window.alert( i );
    
    // if u == arcLength
    //   -> i is max
    //if( i >= this.bezierCurves.length )
//	return this.bezierCurves[ this.bezierCurves.length-1 ].getEndPoint().clone();
    
    var bCurve    = this.bezierCurves[ i ];
    var relativeU = u - uTemp;
    
    //window.alert( "relativeU["+i+"]=" + relativeU );

    return bCurve.getTangentAt( relativeU );

    // !!!
    //return new THREE.Vector2( 0, 0 );

}


IKRS.BezierPath.prototype.getPerpendicular = function( t ) {

    return this.getPerpendicularAt( t * this.totalArcLength );

}

IKRS.BezierPath.prototype.getPerpendicularAt = function( u ) {


    if( u < 0 || u > this.totalArcLength ) {
	console.log( "[IKRS.BezierPath.getPerpendicularAt(u)] u is out of bounds: " + u + "." );
	return null;
    }

    // Find the spline to extract the value from
    var i = 0;
    var uTemp = 0.0;
    
    while( i < this.bezierCurves.length &&
	   (uTemp + this.bezierCurves[i].getLength()) < u 
	 ) {
	
	uTemp += this.bezierCurves[ i ].getLength();
	i++;

    }
    
    //window.alert( i );
    
    // if u == arcLength
    //   -> i is max
    //if( i >= this.bezierCurves.length )
//	return this.bezierCurves[ this.bezierCurves.length-1 ].getEndPoint().clone();
    
    var bCurve    = this.bezierCurves[ i ];
    var relativeU = u - uTemp;
    
    //window.alert( "relativeU["+i+"]=" + relativeU );

    return bCurve.getPerpendicularAt( relativeU );

    // !!!
    //return new THREE.Vector2( 0, 0 );

}


IKRS.BezierPath.prototype.computeBoundingBox = function() {

    if( this.bezierCurves.length == 0 ) {
	
	// Empty box
	return new IKRS.BoundingBox( 0, 0, 0, 0 );

    }
	

    var boundingBox = this.bezierCurves[ 0 ].computeBoundingBox();
    for( var i = 1; i < this.bezierCurves.length; i++ ) {

	var tmpBounds = this.bezierCurves[ i ].computeBoundingBox();
	boundingBox.xMin = Math.min( boundingBox.xMin, tmpBounds.xMin );
	boundingBox.xMax = Math.max( boundingBox.xMax, tmpBounds.xMax );
	boundingBox.yMin = Math.min( boundingBox.yMin, tmpBounds.yMin );
	boundingBox.yMax = Math.max( boundingBox.yMax, tmpBounds.yMax );
	
    }
    
    return boundingBox;
}


IKRS.BezierPath.prototype.moveCurvePoint = function( curveIndex,      // int
						     pointID,         // int
						     moveAmount       // THREE.Vector2
						   ) {
    var bCurve = this.getCurveAt( curveIndex );
    bCurve.moveCurvePoint( pointID,
			   moveAmount,
			   true,       // move control point, too
			   true        // updateArcLengths
			 );
    //window.alert( "old.x=" + bCurve.getStartPoint().x + ", new.x=" + (this.getCurveAt( curveIndex ).getStartPoint()).x ); 

    // If inner point and NOT control point
    //  --> move neightbour
    if( pointID == this.START_POINT && curveIndex > 0 ) {

	// Set predecessor's control point!
	var predecessor = this.getCurveAt( curveIndex-1 );
	predecessor.moveCurvePoint( this.END_CONTROL_POINT, 
				    moveAmount,
				    true,                    // move control point, too
				    false                    // updateArcLengths
				  );

    } else if( pointID == this.END_POINT && curveIndex+1 < this.bezierCurves.length ) {

	// Set successcor
	var successor = this.getCurveAt( curveIndex+1 );
	successor.moveCurvePoint( this.START_CONTROL_POINT, 
				  moveAmount, 
				  true,                  // move control point, too
				  false                  // updateArcLengths
			  );
			  

    } else if( pointID == this.START_CONTROL_POINT && curveIndex > 0 ) {
	
	this.adjustPredecessorControlPoint( curveIndex, 
					    true,            // obtain handle length?
					    false            // update arc lengths
					  );
					  
    } else if( pointID == this.END_CONTROL_POINT && curveIndex+1 < this.getCurveCount() ) {
	
	this.adjustSuccessorControlPoint( curveIndex, 
					  true,            // obtain handle length?
					  false            // update arc lengths
					);
					  
    }

    // Don't forget to update the arc lengths!
    // Note: this can be optimized as only two curves have changed their lengths!
    this.updateArcLengths();

}


IKRS.BezierPath.prototype.adjustPredecessorControlPoint = function( curveIndex,          // int
								    obtainHandleLength,  // boolean
								    updateArcLengths     // boolean
								  ) {
    
    if( curveIndex <= 0 )
	return false;

    /*
    return this.adjustNeighbourControlPoint( this.getCurveAt( curveIndex ),   // mainCurve, 
					     this.getCurveAt( curveIndex-1 ), //neighbourCurve
					     obtainHandleLength,
					     updateArcLengths
					   );
*/
    var mainCurve      = this.getCurveAt( curveIndex );
    var neighbourCurve = this.getCurveAt( curveIndex-1 );
    return this.adjustNeighbourControlPoint( mainCurve,
					     neighbourCurve,
					     mainCurve.getStartPoint(),            // the reference point
					     mainCurve.getStartControlPoint(),     // the dragged control point
					     neighbourCurve.getEndPoint(),         // the neighbour's point
					     neighbourCurve.getEndControlPoint(),  // the neighbour's control point to adjust
					     obtainHandleLength,
					     updateArcLengths
					   );
}

IKRS.BezierPath.prototype.adjustSuccessorControlPoint = function( curveIndex,          // int
								  obtainHandleLength,  // boolean
								  updateArcLengths     // boolean
								) {
    
    if( curveIndex+1 > this.getCurveCount() )
	return false;


    var mainCurve      = this.getCurveAt( curveIndex );
    var neighbourCurve = this.getCurveAt( curveIndex+1 );
    return this.adjustNeighbourControlPoint( mainCurve,
					     neighbourCurve,
					     mainCurve.getEndPoint(),                // the reference point
					     mainCurve.getEndControlPoint(),         // the dragged control point
					     neighbourCurve.getStartPoint(),         // the neighbour's point
					     neighbourCurve.getStartControlPoint(),  // the neighbour's control point to adjust
					     obtainHandleLength,
					     updateArcLengths
					   );
}

// private
IKRS.BezierPath.prototype.adjustNeighbourControlPoint = function( mainCurve,
								  neighbourCurve,
								  mainPoint,
								  mainControlPoint,
								  neighbourPoint,
								  neighbourControlPoint,
								  obtainHandleLengths,  // boolean
								  updateArcLengths
								) {

    /*
    var neighbourPoint          = neighbourCurve.getEndPoint();
    var neighbourControlPoint   = neighbourCurve.getEndControlPoint();
    
    var mainPoint               = mainCurve.getStartPoint();
    var mainControlPoint        = mainCurve.getStartControlPoint();
    */

    // Calculate start handle length
    var mainHandleBounds        = new THREE.Vector2( mainControlPoint.x - mainPoint.x,
						     mainControlPoint.y - mainPoint.y
						);
    var neighbourHandleBounds   = new THREE.Vector2( neighbourControlPoint.x - neighbourPoint.x,
						     neighbourControlPoint.y - neighbourPoint.y
						   );
    var mainHandleLength        = Math.sqrt( Math.pow(mainHandleBounds.x,2) + Math.pow(mainHandleBounds.y,2) );
    var neighbourHandleLength   = Math.sqrt( Math.pow(neighbourHandleBounds.x,2) + Math.pow(neighbourHandleBounds.y,2) );

    if( mainHandleLength <= 0.1 ) 
	return; // no secure length available for division
    
    
    // Just invert the main handle
    
    neighbourControlPoint.set( neighbourPoint.x - mainHandleBounds.x * (neighbourHandleLength/mainHandleLength),
			       neighbourPoint.y - mainHandleBounds.y * (neighbourHandleLength/mainHandleLength)
			     );
    neighbourCurve.updateArcLengths();

}


IKRS.BezierPath.prototype.clone = function() {

    var path = new IKRS.BezierPath( null );
    for( var i = 0; i < this.bezierCurves.length; i++ ) {
	
	path.bezierCurves.push( this.bezierCurves[i].clone() );
	
	// Connect splines
	if( i > 0 )
	    path.bezierCurves[i-1].endPoint = path.bezierCurves[i].startPoint;
	
    }

    path.updateArcLengths();

    return path;
}

IKRS.BezierPath.prototype.equals = function( path ) {

    if( !path )
	return false;
    
    // Check if path contains the credentials
    if( !path.bezierCurves )
	return false;

    if( typeof path.bezierCurves.length == "undefined" )
	return false;

    if( path.bezierCurves.length != this.bezierCurves.length )
	return false;

    for( var i = 0; i < this.bezierCurves.length; i++ ) {

	if( !this.bezierCurves[i].equals(path.bezierCurves[i]) )
	    return false;

    }

    return true;
}

IKRS.BezierPath.prototype.toJSON = function( prettyFormat ) {

    //window.alert( "[IKRS.BezierPath.toJSON()] this.bezierCurves.length=" + this.bezierCurves.length );

    var buffer = [];
    buffer.push( "[" ); // array begin
    for( var i = 0; i < this.bezierCurves.length; i++ ) {

	if( i > 0 ) 
	    buffer.push( "," );

	if( prettyFormat)
	    buffer.push( "\n\t" );
	else
	    buffer.push( " " );
	
	buffer.push( this.bezierCurves[i].toJSON( prettyFormat ) );

    }
    if( this.bezierCurves.length != 0 )
	buffer.push( " " );
    buffer.push( "]" ); // array end
      
    return buffer.join( "" ); // Convert to string, with empty separator.
}

IKRS.BezierPath.fromJSON = function( jsonString ) {

    var obj = JSON.parse( jsonString );

    return IKRS.BezierPath.fromArray( obj );
}

IKRS.BezierPath.fromArray = function( arr ) {

    //window.alert( (typeof arr) + ", " + JSON.stringify( arr ) );
    
    if( !Array.isArray(arr) )
	throw "[IKRS.BezierPath.fromArray] Passed object must be an array.";
    
    if( arr.length < 2 )
	throw "[IKRS.BezierPath.fromArray] Passed array must contain at least two bezier curves (has " + arr.length + ").";
    
    // Create an empty bezier path
    var bPath = new IKRS.BezierPath( null );
    var lastCurve = null;
    for( var i = 0; i < arr.length; i++ ) {
	
	// Convert object to bezier curve
	var bCurve = IKRS.CubicBezierCurve.fromObject( arr[i] );
	// Set curve start point?
	// (avoid duplicate point instances!)
	if( lastCurve )
	    bCurve.startPoint = lastCurve.endPoint;
	
	// Add to path's internal list
	bPath.bezierCurves.push( bCurve );
	bPath.totalArcLength += bCurve.getLength();
	
	
	lastCurve = bCurve;
    }   
    // Bezier segments added.
    // Recalculate length?
    //bPath.updateArcLengths();
    
    // Done
    

    return bPath;
}

/*
// Try JSON conversion
var tmpPoints = [];
tmpPoints.push( new THREE.Vector2( -200, 200 ) );
tmpPoints.push( new THREE.Vector2( 0,    40 ) );
tmpPoints.push( new THREE.Vector2( 200,  -130 ) );
var tmpBPath = new IKRS.BezierPath( tmpPoints );
window.alert( "tmpBPath=" + tmpBPath );
var tmpJSON  = tmpBPath.toJSON();
window.alert( "tmpJSON=" + tmpJSON );
// Re-construct path from JSON string
var tmpBPath2 = IKRS.BezierPath.fromJSON( tmpJSON );
window.alert( "tmpBPath2=" + tmpBPath2.toJSON() );
*/

//window.alert( "IKRS.BezierPath.prototype=" + IKRS.BezierPath.prototype );