/* <copyright>
This file contains proprietary software owned by Motorola Mobility, Inc.<br/>
No rights, expressed or implied, whatsoever to this software are provided by Motorola Mobility, Inc. hereunder.<br/>
(c) Copyright 2011 Motorola Mobility, Inc.  All Rights Reserved.
</copyright> */

var VecUtils = require("js/helper-classes/3D/vec-utils").VecUtils;


function SubpathOffsetPoint(pos, mapPos) {
    this.Pos = Vector.create([pos[0],pos[1],pos[2]]);
    this.CurveMapPos = Vector.create([mapPos[0], mapPos[1], mapPos[2]]);
}

function SubpathOffsetTriangle(v0, v1, v2) {
    this.v0 = v0;
    this.v1 = v1;
    this.v2 = v2;
    this.n = Vector.create([0,0,1]); //replace with the actual cross product later
}

function sortNumberAscending(a,b){
    return a-b;
}
function sortNumberDescending(a,b){
    return b-a;
}
function SegmentIntersections(){
    this.paramArray = [];
}

///////////////////////////////////////////////////////////////////////
// Class GLSubpath
//      representation a sequence of cubic bezier curves.
//      Derived from class GLGeomObj
///////////////////////////////////////////////////////////////////////

function GLSubpath() {
    ///////////////////////////////////////////////////
    // Instance variables
    ///////////////////////////////////////////////////
    this._Anchors = [];
    this._BBoxMin = [0, 0, 0];
    this._BBoxMax = [0, 0, 0];
    this._isClosed = false;

    this._samples = [];                 //polyline representation of this curve
    this._sampleParam = [];            //parametric distance of samples, within [0, N], where N is # of Bezier curves (=# of anchor points if closed, =#anchor pts -1 if open)
    this._anchorSampleIndex = [];       //index within _samples corresponding to anchor points
    
    this._UnprojectedAnchors = [];

    //initially set the _dirty bit so we will construct samples
    this._dirty = true;

    //whether or not to use the canvas drawing to stroke/fill
    this._useCanvasDrawing = true;

    //the X and Y location of this subpath's canvas in stage world space of Ninja
    this._canvasX = 0;
    this._canvasY = 0;

    //stroke information
    this._strokeWidth = 0.0;
    this._strokeColor = [0.4, 0.4, 0.4, 1.0];
    this._strokeMaterial;
    this._strokeStyle = "Solid";
    this._materialAmbient = [0.2, 0.2, 0.2, 1.0];
    this._materialDiffuse = [0.4, 0.4, 0.4, 1.0];
    this._materialSpecular = [0.4, 0.4, 0.4, 1.0];
    this._fillColor = [0.4, 0.4, 0.4, 1.0];
    this._fillMaterial;
    this._DISPLAY_ANCHOR_RADIUS = 5;
    //drawing context
    this._world = null;

    //tool that owns this subpath
    this._drawingTool = null;
    this._planeMat = null;
    this._planeMatInv = null;
    this._planeCenter = null;

    this.inheritedFrom = GLGeomObj;
    this.inheritedFrom();

    //used to query what the user selected, OR-able for future extensions
    this.SEL_NONE = 0;          //nothing was selected
    this.SEL_ANCHOR = 1;        //anchor point was selected
    this.SEL_PREV = 2;          //previous handle of anchor point was selected
    this.SEL_NEXT = 4;          //next handle of anchor point was selected
    this.SEL_PATH = 8;          //the path itself was selected
    this._selectMode = this.SEL_NONE;
    this._selectedAnchorIndex = -1;

    this._SAMPLING_EPSILON = 0.5; //epsilon used for sampling the curve
    this._DEFAULT_STROKE_WIDTH = 20; //use only if stroke width not specified
    this._MAX_OFFSET_ANGLE = 10; //max angle (in degrees) between consecutive vectors from curve to offset path

    // (current GLGeomObj complains if buildBuffers/render is added to GLSubpath prototype)
    //buildBuffers
    //  Build the stroke vertices, normals, textures and colors
    //  Add that array data to the GPU using OpenGL data binding
    this.buildBuffers = function () {
        return; //no need to do anything for now
    }//buildBuffers()

    //render
    //  specify how to render the subpath in Canvas2D
    this.render = function () {
        // get the world
        var world = this.getWorld();
        if (!world)  throw( "null world in subpath render" );

         // get the context
        var ctx = world.get2DContext();
        if (!ctx)  throw ("null context in subpath render")

        var numAnchors = this.getNumAnchors();
        if (numAnchors === 0)
            return; //nothing to do for empty paths

        ctx.save();

        this.createSamples(); //dirty bit checked in this function...will generate a polyline representation
        var bboxMin = this.getBBoxMin();
        var bboxMax = this.getBBoxMax();
        var bboxWidth = bboxMax[0] - bboxMin[0];
        var bboxHeight = bboxMax[1] - bboxMin[1];
        var bboxMid = Vector.create([0.5 * (bboxMax[0] + bboxMin[0]), 0.5 * (bboxMax[1] + bboxMin[1]), 0.5 * (bboxMax[2] + bboxMin[2])]);

        ctx.clearRect(0, 0, bboxWidth, bboxHeight);


        ctx.lineWidth = this._strokeWidth;
        ctx.strokeStyle = "black";
        if (this._strokeColor)
            ctx.strokeStyle = MathUtils.colorToHex( this._strokeColor );
        ctx.fillStyle = "white";
        if (this._fillColor)
            ctx.fillStyle = MathUtils.colorToHex( this._fillColor );
        var lineCap = ['butt','round','square'];
        ctx.lineCap = lineCap[1];
        ctx.beginPath();
        var prevAnchor = this.getAnchor(0);
        ctx.moveTo(prevAnchor.getPosX()-bboxMin[0],prevAnchor.getPosY()-bboxMin[1]);
        for (var i = 1; i < numAnchors; i++) {
            var currAnchor = this.getAnchor(i);
            ctx.bezierCurveTo(prevAnchor.getNextX()-bboxMin[0],prevAnchor.getNextY()-bboxMin[1], currAnchor.getPrevX()-bboxMin[0], currAnchor.getPrevY()-bboxMin[1], currAnchor.getPosX()-bboxMin[0], currAnchor.getPosY()-bboxMin[1]);
            prevAnchor = currAnchor;
        }
        if (this._isClosed === true) {
            var currAnchor = this.getAnchor(0);
            ctx.bezierCurveTo(prevAnchor.getNextX()-bboxMin[0],prevAnchor.getNextY()-bboxMin[1], currAnchor.getPrevX()-bboxMin[0], currAnchor.getPrevY()-bboxMin[1], currAnchor.getPosX()-bboxMin[0], currAnchor.getPosY()-bboxMin[1]);
            prevAnchor = currAnchor;
        }
        if (this._isClosed){
            ctx.fill();
        }
        ctx.stroke();

        ctx.restore();
    } //render()

    this.geomType = function () { return this.GEOM_TYPE_CUBIC_BEZIER; }
} //function GLSubpath ...class definition






    /////////////////////////////////////////////////////////
    // Property Accessors/Setters
    /////////////////////////////////////////////////////////
GLSubpath.prototype.setWorld = function (world) { this._world = world; }
GLSubpath.prototype.getWorld = function () { return this._world; }
GLSubpath.prototype.makeDirty = function () {this._dirty = true;}
GLSubpath.prototype.setDrawingTool = function (tool) {this._drawingTool = tool;}
GLSubpath.prototype.getDrawingTool = function () {return this._drawingTool;}
GLSubpath.prototype.setPlaneMatrix = function(planeMat){this._planeMat = planeMat;}
GLSubpath.prototype.setPlaneMatrixInverse = function(planeMatInv){this._planeMatInv = planeMatInv;}
GLSubpath.prototype.setPlaneCenter = function(pc){this._planeCenter = pc;}

GLSubpath.prototype.getCanvasX = function(){return this._canvasX;}
GLSubpath.prototype.getCanvasY = function(){return this._canvasY;}
GLSubpath.prototype.setCanvasX = function(cx){this._canvasX=cx;}
GLSubpath.prototype.setCanvasY = function(cy){this._canvasY=cy;}

GLSubpath.prototype.getIsClosed = function () {return this._isClosed;}
GLSubpath.prototype.setIsClosed = function (isClosed) {
    if (this._isClosed !== isClosed) {
        this._isClosed = isClosed;
        this._dirty = true;
    }
}
GLSubpath.prototype.getNumAnchors = function () { return this._Anchors.length; }
GLSubpath.prototype.getAnchor = function (index) { return this._Anchors[index]; }
GLSubpath.prototype.addAnchor = function (anchorPt) {
    this._Anchors.push(anchorPt);
    this._selectedAnchorIndex = this._Anchors.length-1;
    this._dirty = true;
}

GLSubpath.prototype.insertAnchor = function(anchorPt, index){
    this._Anchors.splice(index, 0, anchorPt);
}

//remove and return anchor at specified index, return null on error
GLSubpath.prototype.removeAnchor = function (index) {
    var retAnchor = null;
    if (index < this._Anchors.length) {
        retAnchor = this._Anchors.splice(index, 1);
        this._dirty = true;
    }
    //deselect the removed anchor if necessary
    if (this._selectedAnchorIndex === index){
        this._selectedAnchorIndex = -1;
    }
    return retAnchor;
}

GLSubpath.prototype.deselectAnchorPoint = function(){
    this._selectedAnchorIndex = -1;
}

GLSubpath.prototype.reversePath = function() {
    var revAnchors = [];
    var numAnchors = this._Anchors.length;
    var lastIndex = numAnchors-1;
    if (lastIndex<0){
        return; //cannot reverse empty path
    }
    for (var i=lastIndex;i>=0;i--) {
        var newAnchor = new GLAnchorPoint();
        var oldAnchor = this._Anchors[i];
        newAnchor.setPos(oldAnchor.getPosX(),oldAnchor.getPosY(),oldAnchor.getPosZ());
        newAnchor.setPrevPos(oldAnchor.getNextX(),oldAnchor.getNextY(),oldAnchor.getNextZ());
        newAnchor.setNextPos(oldAnchor.getPrevX(),oldAnchor.getPrevY(),oldAnchor.getPrevZ());
        revAnchors.push(newAnchor);
    }
    if (this._selectedAnchorIndex >= 0){
        this._selectedAnchorIndex = (numAnchors-1) - this._selectedAnchorIndex;
    }
    this._Anchors = revAnchors;
    this._dirty=true;
}

//remove all the anchor points
GLSubpath.prototype.clearAllAnchors = function () {
    this._Anchors = [];
    this._isClosed = false;
    this._dirty = true;
}

GLSubpath.prototype.insertAnchorAtParameter = function(index, param) {
    if (index+1 >= this._Anchors.length && !this._isClosed) {
        return;
    }
    //insert an anchor after the specified index using the parameter, using De Casteljau subdivision
    var nextIndex = (index+1)%this._Anchors.length;

    //build the De Casteljau points
    var P0P1 = VecUtils.vecInterpolate(3, this._Anchors[index].getPos(), this._Anchors[index].getNext(), param);
    var P1P2 = VecUtils.vecInterpolate(3, this._Anchors[index].getNext(), this._Anchors[nextIndex].getPrev(), param);
    var P2P3 = VecUtils.vecInterpolate(3, this._Anchors[nextIndex].getPrev(), this._Anchors[nextIndex].getPos(), param);

    var P0P1P2 = VecUtils.vecInterpolate(3, P0P1, P1P2, param);
    var P1P2P3 = VecUtils.vecInterpolate(3, P1P2, P2P3, param);
    var anchorPos = VecUtils.vecInterpolate(3, P0P1P2, P1P2P3, param);


    //update the next of the anchor at index and prev of anchor at nextIndex
    var isPrevCoincident = false;
    var isNextCoincident = false;
    if (VecUtils.vecDist( 3, P0P1, this._Anchors[index].getNext()) < this._SAMPLING_EPSILON) {
        //no change to the next point
        isPrevCoincident = true;
    } else {
        this._Anchors[index].setNextPos(P0P1[0], P0P1[1], P0P1[2]);
    }

    if (VecUtils.vecDist( 3, P2P3, this._Anchors[nextIndex].getPrev()) < this._SAMPLING_EPSILON) {
        //no change to the prev point
        isNextCoincident = true;
    } else {
        this._Anchors[nextIndex].setPrevPos(P2P3[0], P2P3[1], P2P3[2]);
    }

    //create a new anchor point
    var newAnchor = new GLAnchorPoint();

    if (isPrevCoincident && isNextCoincident){
        anchorPos[0]=P1P2[0];anchorPos[1]=P1P2[1];anchorPos[2]=P1P2[2];
        newAnchor.setPos(anchorPos[0],anchorPos[1],anchorPos[2]);
        newAnchor.setPrevPos(anchorPos[0],anchorPos[1],anchorPos[2]);
        newAnchor.setNextPos(anchorPos[0],anchorPos[1],anchorPos[2]);
    } else {
        newAnchor.setPrevPos(P0P1P2[0], P0P1P2[1], P0P1P2[2]);
        newAnchor.setNextPos(P1P2P3[0], P1P2P3[1], P1P2P3[2]);
        newAnchor.setPos(anchorPos[0], anchorPos[1], anchorPos[2]);
    }

    //insert the new anchor point at the correct index and set it as the selected anchor
    this._Anchors.splice(nextIndex, 0, newAnchor);
    this._selectedAnchorIndex = nextIndex;
    this._dirty = true;
}

GLSubpath.prototype._checkIntersectionWithSamples = function(startIndex, endIndex, point, radius){
    //check whether the point is within the radius distance from the curve represented as a polyline in _samples
    //return the parametric distance along the curve if there is an intersection, else return null
    //will assume that the BBox test is performed outside this function
    if (endIndex<startIndex){
        //go from startIndex to the end of the samples
        endIndex = this._samples.length/3;
    }
    for (var i=startIndex; i<endIndex; i++){
        var seg0 = Vector.create([this._samples[3*i], this._samples[3*i + 1], this._samples[3*i + 2]]);
        var j=i+1;
        var seg1 = Vector.create([this._samples[3*j], this._samples[3*j + 1], this._samples[3*j + 2]]);
        var distToSegment = MathUtils.distPointToSegment(point, seg0, seg1);
        if (distToSegment<=radius){
            var paramDistance = MathUtils.paramPointProjectionOnSegment(point, seg0, seg1); //TODO Optimize! this function was called in distPointToSegment above
            var retParam = this._sampleParam[i] + (this._sampleParam[j] - this._sampleParam[i])*paramDistance;
            return retParam;
        }
    }
    return null;
}
GLSubpath.prototype._checkIntersection = function(controlPts, beginParam, endParam, point, radius) {
    //check whether the point is within radius distance from the curve
    // if there is an intersection, return the parameter value (between beginParam and endParam) of the intersection point, else return null
    var bboxMin = Vector.create([Infinity, Infinity, Infinity]);
    var bboxMax = Vector.create([-Infinity,-Infinity,-Infinity]);
    for (var i=0;i<controlPts.length;i++) {
        for (var d=0;d<3;d++){
            if (controlPts[i][d] < bboxMin[d]){
                bboxMin[d] = controlPts[i][d];
            }
            if (controlPts[i][d] > bboxMax[d]){
                bboxMax[d] = controlPts[i][d];
            }
        }
    }
    //check whether the bbox of the control points contains the point within the specified radius
    for (var d=0;d<3;d++){
        if (point[d] < (bboxMin[d]-radius)){
            return null;
        }
        if (point[d] > (bboxMax[d]+radius)){
            return null;
        }
    }

    //check if the curve is already flat, and if so, check the distance from the segment C0C3 to the point
    //measure distance of C1 and C2 to segment C0-C3
    var distC1 = MathUtils.distPointToSegment(controlPts[1], controlPts[0], controlPts[3]);
    var distC2 = MathUtils.distPointToSegment(controlPts[2], controlPts[0], controlPts[3]);
    var maxDist = Math.max(distC1, distC2);
    var threshold = this._SAMPLING_EPSILON; //this should be set outside this function //TODO
    if (maxDist < threshold) { //if the curve is flat
        var distP = MathUtils.distPointToSegment(point, controlPts[0], controlPts[3]); //TODO we may need to neglect cases where the non-perpendicular distance is used...
        if (distP>radius)
            return null;
        else {
            var param = MathUtils.paramPointProjectionOnSegment(point, controlPts[0], controlPts[3]); //TODO this function is already called in distPointToSegment...optimize by removing redundant call
            //var param = VecUtils.vecDist(3, point, controlPts[0])/VecUtils.vecDist(3, controlPts[3], controlPts[0]);
            if (param<0)
                param=0;
            if (param>1)
                param=1;

            return beginParam + (endParam-beginParam)*param;
        }
    }

    //subdivide this curve using De Casteljau interpolation
    var C0_ = VecUtils.vecInterpolate(3, controlPts[0], controlPts[1], 0.5);
    var C1_ = VecUtils.vecInterpolate(3, controlPts[1], controlPts[2], 0.5);
    var C2_ = VecUtils.vecInterpolate(3, controlPts[2], controlPts[3], 0.5);

    var C0__ = VecUtils.vecInterpolate(3, C0_, C1_, 0.5);
    var C1__ = VecUtils.vecInterpolate(3, C1_, C2_, 0.5);

    var C0___ = VecUtils.vecInterpolate(3, C0__, C1__, 0.5);

    //recursively sample the first half of the curve
    var midParam = (endParam+beginParam)*0.5;
    var param1 = this._checkIntersection(Vector.create([controlPts[0],C0_,C0__,C0___]), beginParam, midParam, point, radius);
    if (param1!==null){
        return param1;
    }

    //recursively sample the second half of the curve
    var param2 = this._checkIntersection(Vector.create([C0___,C1__,C2_,controlPts[3]]), midParam, endParam, point, radius);
    if (param2!==null){
        return param2;
    }

    //no intersection, so return null
    return null;
}

//whether the point lies within the bbox given by the four control points
GLSubpath.prototype._isWithinBoundingBox = function(point, ctrlPts, radius) {
    var bboxMin = Vector.create([Infinity, Infinity, Infinity]);
    var bboxMax = Vector.create([-Infinity,-Infinity,-Infinity]);
    for (var i=0;i<ctrlPts.length;i++) {
        for (var d=0;d<3;d++){
            if (ctrlPts[i][d] < bboxMin[d]){
                bboxMin[d] = ctrlPts[i][d];
            }
            if (ctrlPts[i][d] > bboxMax[d]){
                bboxMax[d] = ctrlPts[i][d];
            }
        }
    }
    //check whether the bbox of the control points contains the point within the specified radius
    for (var d=0;d<3;d++){
        if (point[d] < (bboxMin[d]-radius)){
            return false;
        }
        if (point[d] > (bboxMax[d]+radius)){
            return false;
        }
    }
    return true;
}

GLSubpath.prototype.pickAnchor = function (pickX, pickY, pickZ, radius) {
    var numAnchors = this._Anchors.length;
    var selAnchorIndex = -1;
    var retCode = this.SEL_NONE;
    var radSq = radius * radius;
    var minDistance = Infinity;
    for (var i = 0; i < numAnchors; i++) {
        var distSq = this._Anchors[i].getDistanceSq(pickX, pickY, pickZ);
        //check the anchor point
        if (distSq < minDistance && distSq < radSq) {
            selAnchorIndex = i;
            minDistance = distSq;
        }
    }//for every anchor i
    return selAnchorIndex;
}

GLSubpath.prototype.getSelectedAnchorIndex = function () { return this._selectedAnchorIndex; }
GLSubpath.prototype.getSelectedMode = function () { return this._selectMode; }

GLSubpath.prototype.getNumPoints = function () { return this._samples.length; }

GLSubpath.prototype.getBBoxMin = function () { return this._BBoxMin; }
GLSubpath.prototype.getBBoxMax = function () { return this._BBoxMax; }

GLSubpath.prototype.getStrokeWidth = function () { return this._strokeWidth; }
GLSubpath.prototype.setStrokeWidth = function (w) { this._strokeWidth = w; }
GLSubpath.prototype.getStrokeMaterial = function () { return this._strokeMaterial; }
GLSubpath.prototype.setStrokeMaterial = function (m) { this._strokeMaterial = m; }
GLSubpath.prototype.getStrokeColor = function () { return this._strokeColor; }
GLSubpath.prototype.setStrokeColor = function (c) { this._strokeColor = c; }
GLSubpath.prototype.getStrokeStyle = function () { return this._strokeStyle; }
GLSubpath.prototype.setStrokeStyle = function (s) { this._strokeStyle = s; }
GLSubpath.prototype.getFillMaterial = function() {return this._fillMaterial;}
GLSubpath.prototype.setFillMaterial = function(m){ this._fillMaterial = m;}
GLSubpath.prototype.getFillColor = function() {return this._fillColor;}
GLSubpath.prototype.setFillColor = function(c){this._fillColor = c;}

GLSubpath.prototype.setWidth = function () {//NO-OP for now
}
GLSubpath.prototype.setHeight = function () {//NO-OP for now
}

GLSubpath.prototype.copyFromSubpath = function (subpath) {
    this.clearAllAnchors();
    for (var i = 0; i < subpath.getNumAnchors(); i++) {
        var oldAnchor = subpath.getAnchor(i);
        var newAnchor = new GLAnchorPoint();
        newAnchor.setPos(oldAnchor.getPosX(), oldAnchor.getPosY(), oldAnchor.getPosZ());
        newAnchor.setPrevPos(oldAnchor.getPrevX(), oldAnchor.getPrevY(), oldAnchor.getPrevZ());
        newAnchor.setNextPos(oldAnchor.getNextX(), oldAnchor.getNextY(), oldAnchor.getNextZ());
        this.addAnchor(newAnchor);
    }
    this.setIsClosed(subpath.getIsClosed());
    this.setStrokeWidth(subpath.getStrokeWidth());
}

GLSubpath.prototype.translate = function (tx, ty, tz) {
    for (var i=0;i<this._Anchors.length;i++){
        this._Anchors[i].translateAll(tx,ty,tz);
    }
    this._dirty = true;
}


GLSubpath.prototype._getCubicBezierPoint = function(C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, param) {
    var t = param;
    var t2 = t * t;
    var t3 = t * t2;
    var s = 1 - t;
    var s2 = s * s;
    var s3 = s * s2;
    var Px = s3 * C0X + 3 * s2 * t * C1X + 3 * s * t2 * C2X + t3 * C3X;
    var Py = s3 * C0Y + 3 * s2 * t * C1Y + 3 * s * t2 * C2Y + t3 * C3Y;
    var Pz = s3 * C0Z + 3 * s2 * t * C1Z + 3 * s * t2 * C2Z + t3 * C3Z;
    return Vector.create([Px,Py, Pz]);
}

GLSubpath.prototype.getCubicBezierPoint = function(startIndex, param){
    var C0X = this._Anchors[startIndex].getPosX();
    var C0Y = this._Anchors[startIndex].getPosY();
    var C0Z = this._Anchors[startIndex].getPosZ();
    var C1X = this._Anchors[startIndex].getNextX();
    var C1Y = this._Anchors[startIndex].getNextY();
    var C1Z = this._Anchors[startIndex].getNextZ();
    var nextIndex = (startIndex +1)% this._Anchors.length;
    var C2X = this._Anchors[nextIndex].getPrevX();
    var C2Y = this._Anchors[nextIndex].getPrevY();
    var C2Z = this._Anchors[nextIndex].getPrevZ();
    var C3X = this._Anchors[nextIndex].getPosX();
    var C3Y = this._Anchors[nextIndex].getPosY();
    var C3Z = this._Anchors[nextIndex].getPosZ();
    return this._getCubicBezierPoint(C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, param);
}

GLSubpath.prototype._sampleCubicBezierUniform = function (C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, beginParam, endParam) {
    //for now, sample using regularly spaced parameter values
    var numSteps = 11; //hard-coded for now
    var stepSize = 0.1; // = 1/(numSteps-1)
    for (var i = 0; i < numSteps; i++) {
        var t = i * stepSize;
        var t2 = t * t;
        var t3 = t * t2;
        var s = 1 - t;
        var s2 = s * s;
        var s3 = s * s2;
        var Px = s3 * C0X + 3 * s2 * t * C1X + 3 * s * t2 * C2X + t3 * C3X;
        var Py = s3 * C0Y + 3 * s2 * t * C1Y + 3 * s * t2 * C2Y + t3 * C3Y;
        var Pz = s3 * C0Z + 3 * s2 * t * C1Z + 3 * s * t2 * C2Z + t3 * C3Z;
        this._samples.push(Px);
        this._samples.push(Py);
        this._samples.push(Pz);

        if (beginParam && endParam) {
            this._sampleParam.push(beginParam + (endParam-beginParam)*t);
        }
    }
}

// _sampleCubicBezier
//  queries the Bezier curve and adaptively samples it, adds samples in this._samples
GLSubpath.prototype._sampleCubicBezier = function (C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, beginParam, endParam) {
    var C0 = Vector.create([C0X, C0Y, C0Z]);
    var C1 = Vector.create([C1X, C1Y, C1Z]);
    var C2 = Vector.create([C2X, C2Y, C2Z]);
    var C3 = Vector.create([C3X, C3Y, C3Z]);

    //measure distance of C1 and C2 to segment C0-C3
    var distC1 = MathUtils.distPointToSegment(C1, C0, C3);
    var distC2 = MathUtils.distPointToSegment(C2, C0, C3);
    var maxDist = Math.max(distC1, distC2);

    //if max. distance is smaller than threshold, early exit
    var threshold = this._SAMPLING_EPSILON; //this should be set outside this function
    if (maxDist < threshold) {
        //push the endpoints and return
        this._samples.push(C0X);
        this._samples.push(C0Y);
        this._samples.push(C0Z);

        this._samples.push(C3X);
        this._samples.push(C3Y);
        this._samples.push(C3Z);

        this._sampleParam.push(beginParam);
        this._sampleParam.push(endParam);
        return;
    }

    //subdivide this curve
    var C0_ = VecUtils.vecAdd(3, C0, C1); C0_ = VecUtils.vecScale(3, C0_, 0.5);
    var C1_ = VecUtils.vecAdd(3, C1, C2); C1_ = VecUtils.vecScale(3, C1_, 0.5);
    var C2_ = VecUtils.vecAdd(3, C2, C3); C2_ = VecUtils.vecScale(3, C2_, 0.5);

    var C0__ = VecUtils.vecAdd(3, C0_, C1_); C0__ = VecUtils.vecScale(3, C0__, 0.5);
    var C1__ = VecUtils.vecAdd(3, C1_, C2_); C1__ = VecUtils.vecScale(3, C1__, 0.5);

    var C0___ = VecUtils.vecAdd(3, C0__, C1__); C0___ = VecUtils.vecScale(3, C0___, 0.5);

    var midParam = beginParam + (endParam-beginParam)*0.5;
    //recursively sample the first half of the curve
    this._sampleCubicBezier(C0X, C0Y, C0Z,
                    C0_[0], C0_[1], C0_[2],
                    C0__[0], C0__[1], C0__[2],
                    C0___[0], C0___[1], C0___[2], beginParam, midParam);

    //recursively sample the second half of the curve
    this._sampleCubicBezier(C0___[0], C0___[1], C0___[2],
                    C1__[0], C1__[1], C1__[2],
                    C2_[0], C2_[1], C2_[2],
                    C3X, C3Y, C3Z, midParam, endParam);
}

///////////////////////////////////////////////////////////
// Methods
///////////////////////////////////////////////////////////
//  createSamples
//  stores samples of the subpath in _samples
GLSubpath.prototype.createSamples = function () {
    if (this._dirty) {
        //clear any previously computed samples
        this._samples = [];
        this._sampleParam = [];
        this._anchorSampleIndex = [];

        var numAnchors = this._Anchors.length;
        if (numAnchors > 1) {
            //start with the first anchor position (since the Bezier curve start point is not added in the sample function below)
            //this._samples.push(this._Anchors[0].getPosX());
            //this._samples.push(this._Anchors[0].getPosY());
            //this._samples.push(this._Anchors[0].getPosZ());

            for (var i = 0; i < numAnchors - 1; i++) {
                //get the control points
                var C0X = this._Anchors[i].getPosX();
                var C0Y = this._Anchors[i].getPosY();
                var C0Z = this._Anchors[i].getPosZ();

                var C1X = this._Anchors[i].getNextX();
                var C1Y = this._Anchors[i].getNextY();
                var C1Z = this._Anchors[i].getNextZ();

                var C2X = this._Anchors[i + 1].getPrevX();
                var C2Y = this._Anchors[i + 1].getPrevY();
                var C2Z = this._Anchors[i + 1].getPrevZ();

                var C3X = this._Anchors[i + 1].getPosX();
                var C3Y = this._Anchors[i + 1].getPosY();
                var C3Z = this._Anchors[i + 1].getPosZ();

                var beginParam = i;
                var endParam = i+1;
                this._anchorSampleIndex.push(this._samples.length/3); //index of sample corresponding to anchor i
                this._sampleCubicBezier(C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, beginParam, endParam);
            } //for every anchor point i, except last

            if (this._isClosed) {
                var i = numAnchors - 1;
                //get the control points
                var C0X = this._Anchors[i].getPosX();
                var C0Y = this._Anchors[i].getPosY();
                var C0Z = this._Anchors[i].getPosZ();

                var C1X = this._Anchors[i].getNextX();
                var C1Y = this._Anchors[i].getNextY();
                var C1Z = this._Anchors[i].getNextZ();

                var C2X = this._Anchors[0].getPrevX();
                var C2Y = this._Anchors[0].getPrevY();
                var C2Z = this._Anchors[0].getPrevZ();

                var C3X = this._Anchors[0].getPosX();
                var C3Y = this._Anchors[0].getPosY();
                var C3Z = this._Anchors[0].getPosZ();

                var beginParam = i;
                var endParam = i+1;
                this._anchorSampleIndex.push(this._samples.length/3); //index of sample corresponding to anchor i
                this._sampleCubicBezier(C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, beginParam, endParam);
            } else {
                this._anchorSampleIndex.push((this._samples.length/3) - 1); //index of sample corresponding to last anchor
            }
        } //if (numAnchors >== 2) {

        //re-compute the bounding box (this also accounts for stroke width, so assume the stroke width is set)
        this.computeBoundingBox(true);

    } //if (this._dirty)
    this._dirty = false;
}

GLSubpath.prototype.computeBoundingBox = function(useSamples){
    this._BBoxMin = [Infinity, Infinity, Infinity];
    this._BBoxMax = [-Infinity, -Infinity, -Infinity];
    if (useSamples) {
        var numPoints = this._samples.length/3;
        if (numPoints === 0) {
            this._BBoxMin = [0, 0, 0];
            this._BBoxMax = [0, 0, 0];
        } else {
            for (var i=0;i<numPoints;i++){
                var pt = Vector.create([this._samples[3*i],this._samples[3*i + 1],this._samples[3*i + 2]]);
                for (var d = 0; d < 3; d++) {
                    if (this._BBoxMin[d] > pt[d]) {
                        this._BBoxMin[d] = pt[d];
                    }
                    if (this._BBoxMax[d] < pt[d]) {
                        this._BBoxMax[d] = pt[d];
                    }
                }//for every dimension d from 0 to 2
            }
        }
    }
    else{
        //build a bbox of the anchor points, not the path itself
        var numAnchors = this._Anchors.length;
        var anchorPts = [Vector.create([0,0,0]), Vector.create([0,0,0]), Vector.create([0,0,0])];
        if (numAnchors === 0) {
            this._BBoxMin = [0, 0, 0];
            this._BBoxMax = [0, 0, 0];
        } else {
            for (var i = 0; i < numAnchors; i++) {
                anchorPts[0] = (Vector.create([this._Anchors[i].getPosX(),this._Anchors[i].getPosY(),this._Anchors[i].getPosZ()]));
                anchorPts[1] = (Vector.create([this._Anchors[i].getPrevX(),this._Anchors[i].getPrevY(),this._Anchors[i].getPrevZ()]));
                anchorPts[2] = (Vector.create([this._Anchors[i].getNextX(),this._Anchors[i].getNextY(),this._Anchors[i].getNextZ()]));

                for (var p=0;p<3;p++){
                    for (var d = 0; d < 3; d++) {
                        if (this._BBoxMin[d] > anchorPts[p][d]) {
                            this._BBoxMin[d] = anchorPts[p][d];
                        }
                        if (this._BBoxMax[d] < anchorPts[p][d]) {
                            this._BBoxMax[d] = anchorPts[p][d];
                        }
                    }//for every dimension d from 0 to 2
                } //for every anchorPts p from 0 to 2
            } //for every anchor point i
        } //else of if (numSamples === 0) {
    }//else of if useSamples

    //increase the bbox given the stroke width
    for (var d = 0; d < 3; d++) {
        this._BBoxMin[d]-= this._strokeWidth/2;
        this._BBoxMax[d]+= this._strokeWidth/2;
    }//for every dimension d from 0 to 2
}

//returns v such that it is in [min,max]
GLSubpath.prototype._clamp = function (v, min, max) {
    if (v < min)
        return min;
    if (v > max)
        return max;
    return v;
},

    //input: point sIn in stage-world space, planeMidPt in stage-world space, matrix planeMat that rotates plane into XY (parallel to view plane), inverse of planeMat
//returns: sIn 'unprojected'
GLSubpath.prototype.unprojectPoint = function ( sIn, planeMidPt, planeMat, planeMatInv)
{
    var s = sIn.slice(0);
    s[0] -= planeMidPt[0];  s[1] -= planeMidPt[1]; //bring s to the center of the plane

    // unproject the point s
    var i;
    var viewZ = 1400;
    if (MathUtils.fpCmp(viewZ,-s[2]) !== 0){
        z = s[2]*viewZ/(viewZ + s[2]);
        var x = s[0]*(viewZ - z)/viewZ,
            y = s[1]*(viewZ - z)/viewZ;
        s[0] = x;  s[1] = y;  s[2] = z;
    }

    // add the translation back in
     s[0] += planeMidPt[0];   s[1] += planeMidPt[1];

    return s;
},

GLSubpath.prototype.computeUnprojectedNDC = function (pos, bboxMid, bboxDim, r, l, t, b, z, zn) {
    //unproject pos from stageworld to unprojected state
    var ppos = this.unprojectPoint(pos, this._planeCenter, this._planeMat, this._planeMatInv);

    //make the coordinates lie in [-1,1]
    var x = (ppos[0] - bboxMid[0]) / bboxDim[0];
    var y = -(ppos[1] - bboxMid[1]) / bboxDim[1];

    //x and y should never be outside the [-1,1] range
    x = this._clamp(x, -1, 1);
    y = this._clamp(y, -1, 1);

    //apply the perspective transform
    x *= -z * (r - l) / (2.0 * zn);
    y *= -z * (t - b) / (2.0 * zn);

    ppos[0] = x;
    ppos[1] = y;
    ppos[2] = 0; //z;
    return ppos;
}


GLSubpath.prototype.makeStrokeMaterial = function()
{
    var strokeMaterial;
    if (this.getStrokeMaterial())
        strokeMaterial = this.getStrokeMaterial().dup();
    else
        strokeMaterial = new FlatMaterial();

    if (strokeMaterial)
    {
        strokeMaterial.init();
        //if(!this.getStrokeMaterial() && this._strokeColor)
        if(this._strokeColor)
         {
            strokeMaterial.setProperty("color", this._strokeColor);
        }
    }

    this._materialArray.push( strokeMaterial );
    this._materialTypeArray.push( "stroke" );

    return strokeMaterial;
}

GLSubpath.prototype.makeFillMaterial = function()
{
    var fillMaterial;
    if (this.getFillMaterial())
        fillMaterial = this.getFillMaterial().dup();
    else
        fillMaterial = new FlatMaterial();

    if (fillMaterial)
    {
        fillMaterial.init();
        //if(!this.getFillMaterial() && this._fillColor)
        if (this._fillColor)
        {
            fillMaterial.setProperty("color", this._fillColor);
        }
    }

    this._materialArray.push( fillMaterial );
    this._materialTypeArray.push( "fill" );

    return fillMaterial;
}

GLSubpath.prototype.getNearVertex = function( eyePt, dir ){
    //get the parameters used for computing perspective transformation
    var bboxDim = [];
    var bboxMid = [];
    bboxDim[0] = 0.5 * (this._BBoxMax[0] - this._BBoxMin[0]);
    bboxMid[0] = 0.5 * (this._BBoxMax[0] + this._BBoxMin[0]);
    bboxDim[1] = 0.5 * (this._BBoxMax[1] - this._BBoxMin[1]);
    bboxMid[1] = 0.5 * (this._BBoxMax[1] + this._BBoxMin[1]);
    bboxDim[2] = 0.5 * (this._BBoxMax[2] - this._BBoxMin[2]);
    bboxMid[3] = 0.5 * (this._BBoxMax[2] + this._BBoxMin[2]);

    // convert the stroke vertices into normalized device coordinates
    var world = this.getWorld();
    if (!world) return null;
    var aspect = world.getAspect();
    var zn = world.getZNear(), zf = world.getZFar();
    var t = zn * Math.tan(world.getFOV() * Math.PI / 360.0),    //top of the frustum
        b = -t,                                                 //bottom
        r = aspect * t,                                         //right
        l = -r;                                                 //left

    // calculate the object coordinates from their NDC coordinates
    var z = -world.getViewDistance();

    // the eyePt and dir are in WebGL space...we need to convert each anchor point into the WebGL space
    var numAnchors = this._Anchors.length;
    var selAnchorPpos = null;
    var minDistance = Infinity;
    for (var i = 0; i < numAnchors; i++) {
        var anchorPos = Vector.create([this._Anchors[i].getPosX(), this._Anchors[i].getPosY(), this._Anchors[i].getPosZ()]);
        var ppos = this.computeUnprojectedNDC(anchorPos, bboxMid, bboxDim, r, l, t, b, z, zn);
        var dist = MathUtils.distPointToRay(ppos, eyePt, dir);
        if (dist < minDistance) {
            selAnchorPpos = ppos;
            minDistance = dist;
        }
    }
    return selAnchorPpos;
}

GLSubpath.prototype.getNearPoint = function( eyePt, dir ){
    return null;
}

//returns true if P is left of line through l0 and l1 or on it
GLSubpath.prototype.isLeft = function(l0, l1, P){
    var signedArea = (l1[0]-l0[0])*(P[1] - l0[1]) - (P[0]-l0[0])*(l1[1]-l0[1]);
    if (signedArea>=0)
        return true;
    else
        return false;
}
//returns true if 2D point p is contained within 2D quad given by r0,r1,r2,r3 (need not be axis-aligned)
GLSubpath.prototype.isPointInQuad2D = function(r0,r1,r2,r3,p){
    //returns true if the point is on the same side of the segments r0r1, r1r2, r2r3, r3r0
    var isLeft0 = this.isLeft(r0,r1,p);
    var isLeft1 = this.isLeft(r1,r2,p);
    var isLeft2 = this.isLeft(r2,r3,p);
    var isLeft3 = this.isLeft(r3,r0,p);
    var andAll = isLeft0 & isLeft1 & isLeft2 & isLeft3;
    if (andAll)
        return true;
    var orAll = isLeft0 | isLeft1 | isLeft2 | isLeft3;
    if (!orAll)
        return true;
    return false;
}


GLSubpath.prototype.export = function()
{
    var rtnStr = "type: " + this.geomType() + "\n";

    rtnStr += "strokeWidth: "	+ this._strokeWidth	+ "\n";
    rtnStr += "strokeStyle: "	+ this._strokeStyle	+ "\n";

    rtnStr += "strokeMat: ";
    if (this._strokeMaterial)
        rtnStr += this._strokeMaterial.getName();
    else
        rtnStr += "flatMaterial";
    rtnStr += "\n";

    rtnStr += "fillMat: ";
    if (this._fillMaterial)
        rtnStr += this._fillMaterial.getName();
    else
        rtnStr += "flatMaterial";
    rtnStr += "\n";

    var isClosedStr = "false";
    if (this._isClosed)
        isClosedStr = "true";
    rtnStr += "isClosed: "      + isClosedStr + "\n";

    //add the anchor points
    var numAnchors = this._Anchors.length;
    rtnStr += "numAnchors: "    + numAnchors        + "\n";
    for (var i=0;i<numAnchors;i++){
        rtnStr += "anchor"+i+"x: " + this._Anchors[i].getPosX() + "\n";
        rtnStr += "anchor"+i+"y: " + this._Anchors[i].getPosY() + "\n";
        rtnStr += "anchor"+i+"z: " + this._Anchors[i].getPosZ() + "\n";

        rtnStr += "anchor"+i+"prevx: " + this._Anchors[i].getPrevX() + "\n";
        rtnStr += "anchor"+i+"prevy: " + this._Anchors[i].getPrevY() + "\n";
        rtnStr += "anchor"+i+"prevz: " + this._Anchors[i].getPrevZ() + "\n";

        rtnStr += "anchor"+i+"nextx: " + this._Anchors[i].getNextX() + "\n";
        rtnStr += "anchor"+i+"nexty: " + this._Anchors[i].getNextY() + "\n";
        rtnStr += "anchor"+i+"nextz: " + this._Anchors[i].getNextZ() + "\n";
    }
    return rtnStr;
}

GLSubpath.prototype.import = function( importStr )
{
    this._strokeWidth		= this.getPropertyFromString( "strokeWidth: ",	importStr );
    this._strokeStyle		= this.getPropertyFromString( "strokeStyle: ",	importStr );
    var strokeMaterialName	= this.getPropertyFromString( "strokeMat: ",	importStr );
    var fillMaterialName	= this.getPropertyFromString( "fillMat: ",		importStr );

    var strokeMat = MaterialsLibrary.getMaterial( strokeMaterialName );
    if (!strokeMat)
    {
        console.log( "object material not found in library: " + strokeMaterialName );
        strokeMat = new FlatMaterial();
    }
    this._strokeMaterial = strokeMat;

    var fillMat = MaterialsLibrary.getMaterial( fillMaterialName );
    if (!fillMat)
    {
        console.log( "object material not found in library: " + fillMaterialName );
        fillMat = new FlatMaterial();
    }
    this._fillMaterial = fillMat;

    var isClosedStr = this.getPropertyFromString( "isClosed: ", importStr);
    this._isClosed = isClosedStr === "true";

    var numAnchors = this.getPropertyFromString("numAnchors: ", importStr);
    for (var i=0;i<numAnchors;i++) {
        var posX = this.getPropertyFromString("anchor"+i+"x", importStr);
        var posY = this.getPropertyFromString("anchor"+i+"y", importStr);
        var posZ = this.getPropertyFromString("anchor"+i+"z", importStr);

        var prevX = this.getPropertyFromString("anchor"+i+"prevx", importStr);
        var prevY = this.getPropertyFromString("anchor"+i+"prevy", importStr);
        var prevZ = this.getPropertyFromString("anchor"+i+"prevz", importStr);

        var nextX = this.getPropertyFromString("anchor"+i+"nextx", importStr);
        var nextY = this.getPropertyFromString("anchor"+i+"nexty", importStr);
        var nextZ = this.getPropertyFromString("anchor"+i+"nextz", importStr);

        var newAnchor = new GLAnchorPoint();
        newAnchor.setPos(posX, posY, posZ);
        newAnchor.setPrevPos(prevX, prevY, prevZ);
        newAnchor.setNextPos(nextX, nextY, nextZ);
        this._selectedSubpath.addAnchor(newAnchor);
    }
}

GLSubpath.prototype.collidesWithPoint = function (x, y, z) {
    if (x < this._BBoxMin[0]) return false;
    if (x > this._BBoxMax[0]) return false;
    if (y < this._BBoxMin[1]) return false;
    if (y > this._BBoxMax[1]) return false;
    if (z < this._BBoxMin[2]) return false;
    if (z > this._BBoxMax[2]) return false;

    return true;
}

GLSubpath.prototype.collidesWithPoint = function (x, y) {
    if (x < this._BBoxMin[0]) return false;
    if (x > this._BBoxMax[0]) return false;
    if (y < this._BBoxMin[1]) return false;
    if (y > this._BBoxMax[1]) return false;

    return true;
}


//pick the path point closest to the specified location, return null if some anchor point (or its handles) is within radius, else return the parameter distance
GLSubpath.prototype.pickPath = function (pickX, pickY, pickZ, radius) {
    var numAnchors = this._Anchors.length;
    var selAnchorIndex = -1;
    var retCode = this.SEL_NONE;
    var radSq = radius * radius;
    var minDistance = Infinity;
    for (var i = 0; i < numAnchors; i++) {
        var distSq = this._Anchors[i].getDistanceSq(pickX, pickY, pickZ);
        //check the anchor point
        if (distSq < minDistance && distSq < radSq) {
            selAnchorIndex = i;
            minDistance = distSq;
            retCode = retCode | this.SEL_ANCHOR;
        }
    }//for every anchor i

    //check the prev and next of the selected anchor if the above did not register a hit
    if (this._selectedAnchorIndex>=0 && selAnchorIndex === -1) {
        var distSq = this._Anchors[this._selectedAnchorIndex].getPrevDistanceSq(pickX, pickY, pickZ);
        if (distSq < minDistance && distSq < radSq){
            selAnchorIndex = this._selectedAnchorIndex;
            minDistance = distSq;
            retCode = retCode | this.SEL_PREV;
        } else {
            //check the next for this anchor point
            distSq = this._Anchors[this._selectedAnchorIndex].getNextDistanceSq(pickX, pickY, pickZ);
            if (distSq<minDistance && distSq<radSq){
                selAnchorIndex = this._selectedAnchorIndex;
                minDistance = distSq;
                retCode = retCode | this.SEL_NEXT;
            }
        }
    }
    var retParam = null;
    if (retCode !== this.SEL_NONE) {
        retCode = retCode | this.SEL_PATH; //ensure that path is also selected if anything else is selected
        this._selectedAnchorIndex = selAnchorIndex;
    } else {
        this._selectedAnchorIndex = -1;
        var numSegments = this._isClosed ? numAnchors : numAnchors-1;
        for (var i = 0; i < numSegments; i++) {
            var nextIndex = (i+1)%numAnchors;
            //check if the point is close to the bezier segment between anchor i and anchor nextIndex
            var controlPoints = Vector.create([Vector.create([this._Anchors[i].getPosX(),this._Anchors[i].getPosY(),this._Anchors[i].getPosZ()]),
                Vector.create([this._Anchors[i].getNextX(),this._Anchors[i].getNextY(),this._Anchors[i].getNextZ()]),
                Vector.create([this._Anchors[nextIndex].getPrevX(),this._Anchors[nextIndex].getPrevY(),this._Anchors[nextIndex].getPrevZ()]),
                Vector.create([this._Anchors[nextIndex].getPosX(),this._Anchors[nextIndex].getPosY(),this._Anchors[nextIndex].getPosZ()])]);
            var point = Vector.create([pickX, pickY, pickZ]);
            if (this._isWithinBoundingBox(point, controlPoints, radius)) {
                //var intersectParam = this._checkIntersection(controlPoints, 0.0, 1.0, point, radius);
                var intersectParam = this._checkIntersectionWithSamples(this._anchorSampleIndex[i], this._anchorSampleIndex[nextIndex], point, radius);
                console.log("intersectParam:"+intersectParam);
                if (intersectParam){
                    retCode = retCode | this.SEL_PATH;
                    retParam = intersectParam-i; //make the retParam go from 0 to 1
                    this._selectedAnchorIndex = i;
                    break;
                }
            }
        }//for every anchor i
    }
    this._selectMode = retCode;
    return retParam;
}     //GLSubpath.pickPath function