From 84332ab81c1b445195f1d9be8bbeae0725c8e758 Mon Sep 17 00:00:00 2001
From: Valerio Virgillito
Date: Tue, 6 Mar 2012 10:58:25 -0800
Subject: Squashed commit of preload-fix into Master

- Requiring all the previously pre-loaded files
- RDGE, Codemirror and gl-matrix are not included via a script tag.

Signed-off-by: Valerio Virgillito <valerio@motorola.com>
---
 js/lib/geom/sub-path.js | 1288 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 1288 insertions(+)
 create mode 100755 js/lib/geom/sub-path.js

(limited to 'js/lib/geom/sub-path.js')

diff --git a/js/lib/geom/sub-path.js b/js/lib/geom/sub-path.js
new file mode 100755
index 00000000..ab54d1e9
--- /dev/null
+++ b/js/lib/geom/sub-path.js
@@ -0,0 +1,1288 @@
+/* <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;
+
+var GeomObj =       require("js/lib/geom/geom-obj").GeomObj;
+var AnchorPoint =   require("js/lib/geom/anchor-point").AnchorPoint;
+var MaterialsModel = require("js/models/materials-model").MaterialsModel;
+
+// TODO Those function do not seems to be used. We should remove them
+function SubpathOffsetPoint(pos, mapPos) {
+    this.Pos = [pos[0],pos[1],pos[2]];
+    this.CurveMapPos = [mapPos[0], mapPos[1], mapPos[2]];
+}
+
+function SubpathOffsetTriangle(v0, v1, v2) {
+    this.v0 = v0;
+    this.v1 = v1;
+    this.v2 = v2;
+    this.n = [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 GeomObj
+///////////////////////////////////////////////////////////////////////
+
+var GLSubpath = 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 = null
+    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 = null;
+    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;
+
+    //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 GeomObj 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
+    };
+
+    //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 = [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 fillColorStr = "rgba("+parseInt(255*this._fillColor[0])+","+parseInt(255*this._fillColor[1])+","+parseInt(255*this._fillColor[2])+","+this._fillColor[3]+")";
+            ctx.fillStyle = fillColorStr;
+        }
+        var lineCap = ['butt','round','square'];
+        ctx.lineCap = lineCap[1];
+        ctx.beginPath();
+
+        /*
+        commenting this out for now because of Chrome bug where coincident endpoints of bezier curve cause the curve to not be rendered
+        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;
+            ctx.fill();
+        }
+        */
+
+
+        var numPoints = this._samples.length/3;
+        ctx.moveTo(this._samples[0]-bboxMin[0],this._samples[1]-bboxMin[1]);
+        for (var i=0;i<numPoints;i++){
+            ctx.lineTo(this._samples[3*i]-bboxMin[0],this._samples[3*i + 1]-bboxMin[1]);
+        }
+        if (this._isClosed === true) {
+            ctx.lineTo(this._samples[0]-bboxMin[0],this._samples[1]-bboxMin[1]);
+        }
+        ctx.fill();
+        ctx.stroke();
+        ctx.restore();
+    }; //render()
+
+    this.geomType = function () {
+        return this.GEOM_TYPE_CUBIC_BEZIER;
+    };
+
+    this.setWidth = function (newW) {
+        if (newW<1) {
+            newW=1; //clamp minimum width to 1
+        }
+
+        //scale the contents of this subpath to lie within this width
+        //determine the scale factor by comparing with the old width
+        var oldWidth = this._BBoxMax[0]-this._BBoxMin[0];
+        if (oldWidth<1) {
+            oldWidth=1;
+        }
+
+        var scaleX = newW/oldWidth;
+        if (scaleX===1) {
+            return; //no need to do anything
+        }
+
+        //scale the anchor point positions such that the width of the bbox is the newW
+        var origX = this._BBoxMin[0];
+        var numAnchors = this._Anchors.length;
+        for (var i=0;i<numAnchors;i++){
+            //compute the distance from the bboxMin
+            var oldW = this._Anchors[i].getPosX() - origX;
+            var prevW = this._Anchors[i].getPrevX() - origX;
+            var nextW = this._Anchors[i].getNextX() - origX;
+
+            this._Anchors[i].setPos(origX + oldW*scaleX,this._Anchors[i].getPosY(),this._Anchors[i].getPosZ());
+            this._Anchors[i].setPrevPos(origX + prevW*scaleX,this._Anchors[i].getPrevY(),this._Anchors[i].getPrevZ());
+            this._Anchors[i].setNextPos(origX + nextW*scaleX,this._Anchors[i].getNextY(),this._Anchors[i].getNextZ());
+        }
+        this.makeDirty();
+    };
+
+    this.setHeight = function (newH) {
+        if (newH<1) {
+            newH=1; //clamp minimum width to 1
+        }
+        //scale the contents of this subpath to lie within this height
+        //determine the scale factor by comparing with the old height
+        var oldHeight = this._BBoxMax[1]-this._BBoxMin[1];
+        if (oldHeight<1){
+            oldHeight=1;
+        }
+
+        var scaleY = newH/oldHeight;
+        if (scaleY===1){
+            return; //no need to do anything
+        }
+
+        //scale the anchor point positions such that the height of the bbox is the newH
+        var origY = this._BBoxMin[1];
+        var numAnchors = this._Anchors.length;
+        for (var i=0;i<numAnchors;i++){
+            //compute the distance from the bboxMin
+            var oldW = this._Anchors[i].getPosY() - origY;
+            var prevW = this._Anchors[i].getPrevY() - origY;
+            var nextW = this._Anchors[i].getNextY() - origY;
+
+            this._Anchors[i].setPos(this._Anchors[i].getPosX(), origY + oldW*scaleY,this._Anchors[i].getPosZ());
+            this._Anchors[i].setPrevPos(this._Anchors[i].getPrevX(), origY + prevW*scaleY,this._Anchors[i].getPrevZ());
+            this._Anchors[i].setNextPos(this._Anchors[i].getNextX(), origY + nextW*scaleY,this._Anchors[i].getNextZ());
+        }
+        this.makeDirty();
+    }
+
+}; //function GLSubpath ...class definition
+
+GLSubpath.prototype = new GeomObj();
+
+/////////////////////////////////////////////////////////
+// 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
+    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 AnchorPoint();
+        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 AnchorPoint();
+
+    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 = [this._samples[3*i], this._samples[3*i + 1], this._samples[3*i + 2]];
+        var j=i+1;
+        var seg1 = [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
+
+            return this._sampleParam[i] + (this._sampleParam[j] - this._sampleParam[i])*paramDistance;
+        }
+    }
+    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 = [Infinity, Infinity, Infinity];
+    var bboxMax = [-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([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([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 = [Infinity, Infinity, Infinity];
+    var bboxMax = [-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;
+    //check if the clicked location is close to the currently selected anchor position
+    if (this._selectedAnchorIndex>=0 && this._selectedAnchorIndex<this._Anchors.length){
+        var distSq = this._Anchors[this._selectedAnchorIndex].getDistanceSq(pickX, pickY, pickZ);
+        //check the anchor point
+        if (distSq < minDistance && distSq < radSq) {
+            selAnchorIndex = this._selectedAnchorIndex;
+            minDistance = distSq;
+            retCode = retCode | this.SEL_ANCHOR;
+        }
+    }
+    //now check if the click location is close to any anchor position
+    if (selAnchorIndex===-1) {
+        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;
+};
+
+//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;
+    //check if the clicked location is close to the currently selected anchor position
+    if (this._selectedAnchorIndex>=0 && this._selectedAnchorIndex<this._Anchors.length){
+        var distSq = this._Anchors[this._selectedAnchorIndex].getDistanceSq(pickX, pickY, pickZ);
+        //check the anchor point
+        if (distSq < minDistance && distSq < radSq) {
+            selAnchorIndex = this._selectedAnchorIndex;
+            minDistance = distSq;
+            retCode = retCode | this.SEL_ANCHOR;
+        }
+    }
+    //now check if the click location is close to any anchor position
+    if (selAnchorIndex===-1) {
+        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 = [[this._Anchors[i].getPosX(),this._Anchors[i].getPosY(),this._Anchors[i].getPosZ()],
+                [this._Anchors[i].getNextX(),this._Anchors[i].getNextY(),this._Anchors[i].getNextZ()],
+                [this._Anchors[nextIndex].getPrevX(),this._Anchors[nextIndex].getPrevY(),this._Anchors[nextIndex].getPrevZ()],
+                [this._Anchors[nextIndex].getPosX(),this._Anchors[nextIndex].getPosY(),this._Anchors[nextIndex].getPosZ()]];
+            var point = [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
+
+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.copyFromSubpath = function (subpath) {
+    this.clearAllAnchors();
+    for (var i = 0; i < subpath.getNumAnchors(); i++) {
+        var oldAnchor = subpath.getAnchor(i);
+        var newAnchor = new AnchorPoint();
+        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.translateAnchors = 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 [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 = [C0X, C0Y, C0Z];
+    var C1 = [C1X, C1Y, C1Z];
+    var C2 = [C2X, C2Y, C2Z];
+    var C3 = [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 = [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 = [[0,0,0], [0,0,0], [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] = ([this._Anchors[i].getPosX(),this._Anchors[i].getPosY(),this._Anchors[i].getPosZ()]);
+                anchorPts[1] = ([this._Anchors[i].getPrevX(),this._Anchors[i].getPrevY(),this._Anchors[i].getPrevZ()]);
+                anchorPts[2] = ([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 = [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 = MaterialsModel.getMaterial( strokeMaterialName );
+    if (!strokeMat) {
+        console.log( "object material not found in library: " + strokeMaterialName );
+        strokeMat = new FlatMaterial();
+    }
+
+    this._strokeMaterial = strokeMat;
+
+    var fillMat = MaterialsModel.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 AnchorPoint();
+        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;
+};
+
+//GLSubpath.prototype = new GeomObj();
+
+if (typeof exports === "object") {
+    exports.SubPath = GLSubpath;
+}
+
-- 
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