From 107f79288ed87a282dd52075640297cc02bdf318 Mon Sep 17 00:00:00 2001
From: Pushkar Joshi
Date: Wed, 1 Feb 2012 12:00:44 -0800
Subject: performance improvement: add most of the GLSubpath functions to its
 prototype

---
 js/helper-classes/RDGE/GLSubpath.js | 2331 +++++++++++++----------------------
 1 file changed, 848 insertions(+), 1483 deletions(-)

(limited to 'js/helper-classes/RDGE/GLSubpath.js')

diff --git a/js/helper-classes/RDGE/GLSubpath.js b/js/helper-classes/RDGE/GLSubpath.js
index 2e4c1631..c4ca1b20 100644
--- a/js/helper-classes/RDGE/GLSubpath.js
+++ b/js/helper-classes/RDGE/GLSubpath.js
@@ -34,6 +34,7 @@ function SegmentIntersections(){
 //      representation a sequence of cubic bezier curves.
 //      Derived from class GLGeomObj
 ///////////////////////////////////////////////////////////////////////
+
 function GLSubpath() {
     ///////////////////////////////////////////////////
     // Instance variables
@@ -49,14 +50,6 @@ function GLSubpath() {
     
     this._UnprojectedAnchors = [];
 
-    //offset path samples and the points on the input path they map to
-    this._offsetPointsLeft = [];
-    this._offsetPointsRight = [];
-
-    //triangles determined by the offset points
-    this._offsetTrianglesLeft = [];
-    this._offsetTrianglesRight = [];
-
     //initially set the _dirty bit so we will construct samples
     this._dirty = true;
 
@@ -87,7 +80,6 @@ function GLSubpath() {
     this._planeMatInv = null;
     this._planeCenter = null;
 
-    // initialize the inherited members
     this.inheritedFrom = GLGeomObj;
     this.inheritedFrom();
 
@@ -104,728 +96,438 @@ function GLSubpath() {
     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
 
-    /////////////////////////////////////////////////////////
-    // Property Accessors/Setters
-    /////////////////////////////////////////////////////////
-    this.setWorld = function (world) { this._world = world; }
-    this.getWorld = function () { return this._world; }
-    this.makeDirty = function () {this._dirty = true;}
-    this.geomType = function () { return this.GEOM_TYPE_CUBIC_BEZIER; }
-    this.setDrawingTool = function (tool) {this._drawingTool = tool;}
-    this.getDrawingTool = function () {return this._drawingTool;}
-    this.setPlaneMatrix = function(planeMat){this._planeMat = planeMat;}
-    this.setPlaneMatrixInverse = function(planeMatInv){this._planeMatInv = planeMatInv;}
-    this.setPlaneCenter = function(pc){this._planeCenter = pc;}
-
-    this.getCanvasX = function(){return this._canvasX;}
-    this.getCanvasY = function(){return this._canvasY;}
-    this.setCanvasX = function(cx){this._canvasX=cx;}
-    this.setCanvasY = function(cy){this._canvasY=cy;}
-        
-    this.getIsClosed = function () {return this._isClosed;}
-    this.setIsClosed = function (isClosed) { 
-        if (this._isClosed !== isClosed) {
-            this._isClosed = isClosed;  
-            this._dirty = true;
-        }
-    }
-    this.getNumAnchors = function () { return this._Anchors.length; }
-    this.getAnchor = function (index) { return this._Anchors[index]; } 
-    this.addAnchor = function (anchorPt) { 
-        this._Anchors.push(anchorPt);
-        this._selectedAnchorIndex = this._Anchors.length-1;
-        this._dirty = true;
-    }
+    // (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()
 
-    this.insertAnchor = function(anchorPt, index){
-        this._Anchors.splice(index, 0, anchorPt);
-    }
+    //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" );
 
-    //remove and return anchor at specified index, return null on error
-    this.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;
-    }
+         // get the context
+        var ctx = world.get2DContext();
+        if (!ctx)  throw ("null context in subpath render")
 
-    this.deselectAnchorPoint = function(){
-        this._selectedAnchorIndex = -1;
-    }
-    
-    this.reversePath = function() {
-        var revAnchors = [];
-        var numAnchors = this._Anchors.length;
-        var lastIndex = numAnchors-1;
-        if (lastIndex<0){
-            return; //cannot reverse empty path
+        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;
         }
-        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._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._selectedAnchorIndex >= 0){
-            this._selectedAnchorIndex = (numAnchors-1) - this._selectedAnchorIndex;
+        if (this._isClosed){
+            ctx.fill();
         }
-        this._Anchors = revAnchors;
-        this._dirty=true;
-    }
+        ctx.stroke();
 
-    //remove all the anchor points
-    this.clearAllAnchors = function () {
-        this._Anchors = [];
-        this._isClosed = false; 
-        this._dirty = true;
-    }
+        ctx.restore();
+    } //render()
 
-    this.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;
+    this.geomType = function () { return this.GEOM_TYPE_CUBIC_BEZIER; }
+} //function GLSubpath ...class definition
 
-        //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();
+    /////////////////////////////////////////////////////////
+    // 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;
+}
 
-        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]);
-        }
+GLSubpath.prototype.insertAnchor = function(anchorPt, index){
+    this._Anchors.splice(index, 0, anchorPt);
+}
 
-        //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;
+//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;
     }
-
-    this._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;
+    //deselect the removed anchor if necessary
+    if (this._selectedAnchorIndex === index){
+        this._selectedAnchorIndex = -1;
     }
-    this._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;
-            }
-        }
+    return retAnchor;
+}
 
-        //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);
+GLSubpath.prototype.deselectAnchorPoint = function(){
+    this._selectedAnchorIndex = -1;
+}
 
-        var C0__ = VecUtils.vecInterpolate(3, C0_, C1_, 0.5);
-        var C1__ = VecUtils.vecInterpolate(3, C1_, C2_, 0.5);
+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;
+}
 
-        var C0___ = VecUtils.vecInterpolate(3, C0__, C1__, 0.5);
+//remove all the anchor points
+GLSubpath.prototype.clearAllAnchors = function () {
+    this._Anchors = [];
+    this._isClosed = false;
+    this._dirty = true;
+}
 
-        //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;
-        }
+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]);
+    }
 
-        //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;
-        }
+    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]);
+    }
 
-        //no intersection, so return null
-        return null;
+    //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]);
     }
 
-    //whether the point lies within the bbox given by the four control points
-    this._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];
-                }
-            }
+    //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;
         }
-        //check whether the bbox of the control points contains the point within the specified radius
+    }
+    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 (point[d] < (bboxMin[d]-radius)){
-                return false;
+            if (controlPts[i][d] < bboxMin[d]){
+                bboxMin[d] = controlPts[i][d];
             }
-            if (point[d] > (bboxMax[d]+radius)){
-                return false;
+            if (controlPts[i][d] > bboxMax[d]){
+                bboxMax[d] = controlPts[i][d];
             }
         }
-        return true;
-    }
-
-    this.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;
     }
-
-    //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
-    this.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;
-                }
-            }
+    //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;
         }
-        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;
-    }     //this.pickPath function
-
-    this.getSelectedAnchorIndex = function () { return this._selectedAnchorIndex; }
-    this.getSelectedMode = function () { return this._selectMode; }
-
-    this.getNumPoints = function () { return this._samples.length; }
-    this.getPoints = function () { this.createSamples(); return this._samples; }
-
-    this.getLeftOffsetPoints = function () { this.createSamples(); return this._offsetPointsLeft; }
-    this.getRightOffsetPoints = function () { this.createSamples(); return this._offsetPointsRight; }
-
-    this.getLeftOffsetTriangles = function () { return this._offsetTrianglesLeft; }
-    this.getRightOffsetTriangles = function () { return this._offsetTrianglesRight; }
-
-    this.getBBoxMin = function () { return this._BBoxMin; }
-    this.getBBoxMax = function () { return this._BBoxMax; }
-
-    this.getStrokeWidth = function () { return this._strokeWidth; }
-    this.setStrokeWidth = function (w) { this._strokeWidth = w; }
-    this.getStrokeMaterial = function () { return this._strokeMaterial; }
-    this.setStrokeMaterial = function (m) { this._strokeMaterial = m; }
-    this.getStrokeColor = function () { return this._strokeColor; }
-    this.setStrokeColor = function (c) { this._strokeColor = c; }
-    this.getStrokeStyle = function () { return this._strokeStyle; }
-    this.setStrokeStyle = function (s) { this._strokeStyle = s; }
-    this.getFillMaterial = function() {return this._fillMaterial;}
-    this.setFillMaterial = function(m){ this._fillMaterial = m;}
-    this.getFillColor = function() {return this._fillColor;}
-    this.setFillColor = function(c){this._fillColor = c;}
-
-    this.setWidth = function () {//NO-OP for now
-    }
-    this.setHeight = function () {//NO-OP for now
-    }
-
-    this.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);
+        if (point[d] > (bboxMax[d]+radius)){
+            return null;
         }
-        this.setIsClosed(subpath.getIsClosed());
-        this.setStrokeWidth(subpath.getStrokeWidth());
     }
 
-    this.translate = function (tx, ty, tz) {
-        for (var i=0;i<this._Anchors.length;i++){
-            this._Anchors[i].translateAll(tx,ty,tz);
+    //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;
         }
-        this._dirty = true;
     }
 
-    //  _cleanupOffsetSamples (offSamples)
-    //  removes retrograde segments of the offset path samples
-    //  returns the cleaned up offset samples
-    this._cleanupOffsetSamples = function (offSamples, width) {
-        var retOffSamples = [];
-        var numSamples = offSamples.length;
-        var keepOffSample = [];
-        for (var i = 0; i < numSamples; i++) {
-            keepOffSample.push(true);
-        }
+    //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);
 
-        //NOTE: this is very slow O(n^2) for now...testing only
-        //remove any sample that's less than 'width' far from any other boundary segment
-        for (var i = 0; i < numSamples; i++) {
-            //build the current offset point
-            var O = Vector.create([offSamples[i].Pos[0], offSamples[i].Pos[1], offSamples[i].Pos[2]]);
-
-            //iterate over all the path segments
-            var numPoints = this._samples.length / 3;
-            for (var j = 0; j < numPoints - 1; j++) {
-                var C0 = Vector.create([this._samples[3 * j], this._samples[3 * j + 1], this._samples[3 * j + 2]]);                 //segment startpoint
-                var C1 = Vector.create([this._samples[3 * (j + 1)], this._samples[3 * (j + 1) + 1], this._samples[3 * (j + 1) + 2]]); //segment endpoint
-                var distToSeg = MathUtils.distPointToSegment(O, C0, C1);
-                if (width - distToSeg > 1) { //if the distance is smaller than the width
-                    keepOffSample[i] = false;
-                    break;
-                } //if (width - distToC > 1 ) { //if the distance is substantially smaller than the width
-            } //for (var j=0;j<numPoints;j++) {
+    var C0___ = VecUtils.vecInterpolate(3, C0__, C1__, 0.5);
 
-        } //for (var i = 0; i < numSamples; i++) {
-
-
-        for (var i = 0; i < numSamples; i++) {
-            if (keepOffSample[i]) {
-                retOffSamples.push(offSamples[i]);
-                continue;
-            }
-
-            //do nothing if we have not yet seen any valid offset samples
-            if (retOffSamples.length === 0)
-                continue;
-
-            //assume this is the first invalid sample
-            var startIndex = i - 1;
-            //find the end index of this range of invalid samples
-            while (keepOffSample[i] === false && (i < numSamples - 1)) {
-                i++;
-            }
-            var endIndex = i;
-
-            //check whether the segment from startIndex->startIndex+1 intersects the segment from endIndex-1->endIndex
-            var seg0Start = Vector.create([offSamples[startIndex].Pos[0],offSamples[startIndex].Pos[1],offSamples[startIndex].Pos[2]]);
-            var seg0End = Vector.create([offSamples[startIndex + 1].Pos[0],offSamples[startIndex + 1].Pos[1],offSamples[startIndex + 1].Pos[2]]);
-            var seg1Start = Vector.create([offSamples[endIndex - 1].Pos[0],offSamples[endIndex - 1].Pos[1],offSamples[endIndex - 1].Pos[2]]);
-            var seg1End = Vector.create([offSamples[endIndex].Pos[0],offSamples[endIndex].Pos[1],offSamples[endIndex].Pos[2]]);
-
-
-            if (seg0Start.length===0 || seg0End.length ===0 || seg1Start.length===0 ||seg1End.length ===0){
-                alert("empty offset point");
-            }
-
-            var intersection = MathUtils.segSegIntersection2D(seg0Start, seg0End, seg1Start, seg1End, 0);
-
-
-            if (intersection) {
-                intersection = MathUtils.makeDimension3(intersection);
-                //add two points for the intersection (one after to the startIndex, another before the endIndex)
-                var newOffsetPoint1 = new SubpathOffsetPoint(intersection, Vector.create([offSamples[startIndex + 1].CurveMapPos[0],offSamples[startIndex + 1].CurveMapPos[1],offSamples[startIndex + 1].CurveMapPos[2]]));
-                retOffSamples.push(newOffsetPoint1);
-                var newOffsetPoint2 = new SubpathOffsetPoint(intersection, Vector.create([offSamples[endIndex - 1].CurveMapPos[0], offSamples[endIndex - 1].CurveMapPos[1], offSamples[endIndex - 1].CurveMapPos[2]]));
-                retOffSamples.push(newOffsetPoint2);
-                 //also add the end point
-                retOffSamples.push(offSamples[endIndex]);
-            }
-
-        } //for (var i = 0; i < numSamples; i++) {
-
-
-
-        return retOffSamples;
+    //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;
     }
 
-    // _triangulateOffset
-    // generate triangles from offset points and add them to the offsetTriangles array
-    this._triangulateOffset = function (offsetPoints, offsetTriangles) {
-        if (offsetPoints.length === 0)
-            return;
-
-        //  triangulate using the fan method (trivial) for every consecutive pair of offset points
-        for (var i = 1; i < offsetPoints.length; i++) {
-            var tri1 = new SubpathOffsetTriangle(offsetPoints[i - 1].CurveMapPos, offsetPoints[i - 1].Pos, offsetPoints[i].CurveMapPos);
-            var tri2 = new SubpathOffsetTriangle(offsetPoints[i].CurveMapPos, offsetPoints[i - 1].Pos, offsetPoints[i].Pos);
-            offsetTriangles.push(tri1);
-            offsetTriangles.push(tri2);
-        }
+    //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;
     }
 
-    //  _addOffsetSamples
-    //  Adds samples to the offset path in places it is not sampled densely enough
-    //TODO: as an optimization, don't add any samples at a concave corners, since those extra points will be removed anyway
-    this._addOffsetSamples = function (offsetPoints) {
-        if (offsetPoints.length === 0)
-            return;
-
-        var retOffsetPoints = [];
-        retOffsetPoints.push(offsetPoints[0]);
-        //compute angle between consecutive vectors from curve to offset
-        for (var i = 1; i < offsetPoints.length; i++) {
-            var prev = offsetPoints[i - 1];
-            var curr = offsetPoints[i];
-            var vec1 = VecUtils.vecSubtract(3, prev.Pos, prev.CurveMapPos);
-            var vec2 = VecUtils.vecSubtract(3, curr.Pos, curr.CurveMapPos);
-            var width = VecUtils.vecMag(3, vec1);
-            //NOTE: the following angle computation works only in 2D
-            var angle = Math.atan2(vec2[1], vec2[0]) - Math.atan2(vec1[1], vec1[0]);
-            //if (angle < 0) angle = angle + Math.PI + Math.PI;
-            angle = angle * 180 / Math.PI;
-            if (angle > 180) {
-                angle = angle - 360;
-            }
-            if (angle < -180) {
-                angle = 360 + angle;
-            }
-            var numNewSamples = Math.floor(Math.abs(angle) / this._MAX_OFFSET_ANGLE);
-            if (numNewSamples > 0) {
-                numNewSamples -= 1; //decrementing gives the correct number of new samples
-            }
-            if (numNewSamples > 10) {
-                numNewSamples = 10; //limit the number of inserted offset samples to 10
-            }
+    //no intersection, so return null
+    return null;
+}
 
-            //build the rotation matrix 
-            var rotAngle = angle / (numNewSamples + 1) * Math.PI / 180; //angle to rotate (in radians)
-            var rotMat = Matrix.RotationZ(rotAngle);
-
-            //build the vector to be transformed
-            var rotVec = VecUtils.vecNormalize(3, vec1, 1);
-
-            for (var s = 0; s < numNewSamples; s++) {
-                //build curve position as a linear combination of prev. and curr
-                var weight = (s + 1) / (numNewSamples + 1);
-                var scaledPos1 = Vector.create([prev.CurveMapPos[0], prev.CurveMapPos[1], prev.CurveMapPos[2]]);
-                VecUtils.vecScale(3, scaledPos1, 1 - weight);
-                var scaledPos2 = Vector.create([curr.CurveMapPos[0], curr.CurveMapPos[1], curr.CurveMapPos[2]]);
-                VecUtils.vecScale(3, scaledPos2, weight);
-                var curvePos = VecUtils.vecAdd(3, scaledPos1, scaledPos2);
-
-                rotVec = MathUtils.transformVector(rotVec, rotMat);
-                var offsetPos = VecUtils.vecAdd(3, curvePos, VecUtils.vecNormalize(3, rotVec, width));
-                var newOffsetPoint = new SubpathOffsetPoint(offsetPos, curvePos);
-                retOffsetPoints.push(newOffsetPoint);
+//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];
             }
-            retOffsetPoints.push(offsetPoints[i]);
-        } //for (var i = 1; i < offsetPoints.length; i++) {
-
-        return retOffsetPoints;
+            if (ctrlPts[i][d] > bboxMax[d]){
+                bboxMax[d] = ctrlPts[i][d];
+            }
+        }
     }
-
-
-    this._addOffsetIntersectionPoints = function (offSamples, isClosed)
-    {
-        if (offSamples.length === 0)
-            return;
-
-        //TODO: implement the O(nlogn) algorithm from the Dutch book instead of the O(n^2) algorithm below
-        var numOrigPoints = offSamples.length;
-        var numOrigSegments = numOrigPoints;
-        if (!isClosed)
-            numOrigSegments--;
-
-         //make an empty list of intersection points for every segment (assuming the segment id is the index of its start point)
-        var segmentIntersectionArray = [];
-        for (var i=0;i<numOrigSegments;i++){
-            var si = new SegmentIntersections();
-            segmentIntersectionArray.push(si);
+    //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;
         }
-
-        for (var i=0;i<numOrigSegments;i++) {
-            //check whether the segment from startIndex->startIndex+1 intersects the segment from endIndex-1->endIndex
-            var seg0Start = Vector.create([offSamples[i].Pos[0],offSamples[i].Pos[1],offSamples[i].Pos[2]]);
-            var nextI = (i+1)%numOrigPoints;
-            var seg0End = Vector.create([offSamples[nextI].Pos[0],offSamples[nextI].Pos[1],offSamples[nextI].Pos[2]]);
-
-            for (var j=0;j<numOrigSegments;j++) {
-                if (i===j)
-                    continue;
-                var seg1Start = Vector.create([offSamples[j].Pos[0],offSamples[j].Pos[1],offSamples[j].Pos[2]]);
-                var nextJ = (j+1)%numOrigPoints;
-                var seg1End = Vector.create([offSamples[nextJ].Pos[0],offSamples[nextJ].Pos[1],offSamples[nextJ].Pos[2]]);
-
-                var intersection = MathUtils.segSegIntersection2D(seg0Start, seg0End, seg1Start, seg1End, 0);
-
-                if (intersection) {
-                    //insert a point between i and i+1, mapped to the curve point in between the curve points
-                    var param = 0;
-                    var delta = seg0End[0]-seg0Start[0];
-                    if (delta===0) {
-                        delta = seg0End[1]-seg0Start[1];
-                        if (delta===0){
-                            param=0; //cannot say anything about parameter...should not happen!
-                        } else {
-                            param = (intersection[1]-seg0Start[1])/delta;
-                        }
-                    } else {
-                        param = (intersection[0]-seg0Start[0])/delta;
-                    }
-                    if (Math.abs(param-1) > 0.01 && Math.abs(param) > 0.01) //if the intersection is not at the endpoint
-                        segmentIntersectionArray[i].paramArray.push(param);
-                }
-            }//for every point j
-        }//for every point i
-
-        var retOffSamples = [] ;//what is built and returned
-        //sort all the intersection points based on the parameter value
-        //AND add the intersection points to the new offset samples
-
-        for (var i=0;i<numOrigSegments;i++){
-            //two existing points 
-            var cmp0 = offSamples[i].CurveMapPos;
-            var cmp1 = offSamples[(i+1)%numOrigPoints].CurveMapPos;
-            var pos0 = offSamples[i].Pos;
-            var pos1 = offSamples[(i+1)%numOrigPoints].Pos;
-            retOffSamples.push(offSamples[i]);
-            segmentIntersectionArray[i].paramArray.sort(sortNumberAscending);
-            for (var j=0;j<segmentIntersectionArray[i].paramArray.length;j++){
-                var param = segmentIntersectionArray[i].paramArray[j];
-                var newIntersection = Vector.create([pos0[0] + param*(pos1[0]-pos0[0]), pos0[1] + param*(pos1[1]-pos0[1]), 0]);
-                var newOffsetPointCurveMapPos = Vector.create([cmp0[0] + param*(cmp1[0]-cmp0[0]), cmp0[1] + param*(cmp1[1]-cmp0[1]), 0]);
-                var newOffsetPoint = new SubpathOffsetPoint(newIntersection, newOffsetPointCurveMapPos);
-                retOffSamples.push(newOffsetPoint);
-            }
-            retOffSamples.push(offSamples[(i+1)%numOrigPoints]);
+        if (point[d] > (bboxMax[d]+radius)){
+            return false;
         }
-        return retOffSamples;
     }
+    return true;
+}
 
-
-    //  _offsetFromSamples
-    //  generates the offset curves (left and right) of width w from the samples (polyline) currently in this._samples
-    this._offsetFromSamples = function (width) {
-        this._offsetPointsLeft = [];
-        this._offsetPointsRight = [];
-        this._offsetTrianglesLeft = [];
-        this._offsetTrianglesRight = [];
-
-        var numPoints = this._samples.length / 3;
-        if (numPoints < 2) {
-            return; //do nothing for 
+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;
+}
 
-        for (var i = 0; i < numPoints; i++) {
-            var C = Vector.create([this._samples[3 * i], this._samples[3 * i + 1], this._samples[3 * i + 2]]); //current point
-            var N = null; //next point
-            if (i < (numPoints - 1)) {
-                N = Vector.create([this._samples[3 * (i + 1)], this._samples[3 * (i + 1) + 1], this._samples[3 * (i + 1) + 2]]);
-            }
-            var P = null; //previous point
-            if (i > 0) {
-                P = Vector.create([this._samples[3 * (i - 1)], this._samples[3 * (i - 1) + 1], this._samples[3 * (i - 1) + 2]]);
-            }
+GLSubpath.prototype.getSelectedAnchorIndex = function () { return this._selectedAnchorIndex; }
+GLSubpath.prototype.getSelectedMode = function () { return this._selectMode; }
 
-            //compute the direction at C (based on averaging across prev. and next if available)
-            var D = null;
-            if (N) {
-                D = VecUtils.vecSubtract(3, N, C);
-                if (P) {
-                    var Dprev = VecUtils.vecSubtract(3, C, P);
-                    D = VecUtils.vecAdd(3, D, Dprev);
-                    D = VecUtils.vecScale(3, D, 0.5);
-                }
-            }
-            else {
-                D = VecUtils.vecSubtract(3, C, P);
-            }
+GLSubpath.prototype.getNumPoints = function () { return this._samples.length; }
 
-            if (!D) {
-                throw ("null direction in _offsetFromSamples");
-                return;
-            }
-            //ignore this point if the D is not significant 
-            var dirLen = VecUtils.vecMag(3, D);
-            if (dirLen < this._SAMPLING_EPSILON) {
-                continue;
-            }
+GLSubpath.prototype.getBBoxMin = function () { return this._BBoxMin; }
+GLSubpath.prototype.getBBoxMax = function () { return this._BBoxMax; }
 
-            D = VecUtils.vecNormalize(3, D, 1.0);
-
-            //compute the perpendicular to D to the left
-            //TODO: for now assume we're only considering D in XY plane
-            var OL = Vector.create([D[1], -1*D[0], D[2]]);
-            OL = VecUtils.vecNormalize(3, OL, width);
-            var OR = Vector.create([-1 * OL[0], -1 * OL[1], -1 * OL[2]]);
-            OR = VecUtils.vecNormalize(3, OR, width);
-            var leftC = VecUtils.vecAdd(3, C, OL);
-            var rightC = VecUtils.vecAdd(3, C, OR);
-
-            var sopl = new SubpathOffsetPoint(leftC, C);
-            this._offsetPointsLeft.push(sopl);
-            if (sopl.Pos.length===0 || sopl.CurveMapPos.length ===0){
-                alert("empty offset point");
-            }
-            var sopr = new SubpathOffsetPoint(rightC, C);
-            this._offsetPointsRight.push(sopr);
-        } //for (var i = 0; i < numPoints; i++) {
+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
+}
 
-        //add offset samples near cusps or corners
-        this._offsetPointsLeft = this._addOffsetSamples(this._offsetPointsLeft);
-        this._offsetPointsRight = this._addOffsetSamples(this._offsetPointsRight);
+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;
+}
 
-        //break up the offset samples at intersections
-        //this._offsetPointsLeft = this._addOffsetIntersectionPoints(this._offsetPointsLeft, this._isClosed);
-        //this._offsetPointsRight = this._addOffsetIntersectionPoints(this._offsetPointsRight , this._isClosed);
 
-        //cleanup of the offset path
-        //this._offsetPointsLeft = this._cleanupOffsetSamples(this._offsetPointsLeft, width);
-        //this._offsetPointsRight = this._cleanupOffsetSamples(this._offsetPointsRight, width);
+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]);
+}
 
-        //triangulate the offset path
-        //this._triangulateOffset(this._offsetPointsLeft, this._offsetTrianglesLeft);
-        //this._triangulateOffset(this._offsetPointsRight, this._offsetTrianglesRight);
-    }
+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);
+}
 
-    this._getCubicBezierPoint = function(C0X, C0Y, C0Z, C1X, C1Y, C1Z, C2X, C2Y, C2Z, C3X, C3Y, C3Z, param) {
-        var t = 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;
@@ -834,889 +536,552 @@ function GLSubpath() {
         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]);
-    }
-
-    this.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);
-    }
+        this._samples.push(Px);
+        this._samples.push(Py);
+        this._samples.push(Pz);
 
-    this._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);
-            }
+        if (beginParam && endParam) {
+            this._sampleParam.push(beginParam + (endParam-beginParam)*t);
         }
     }
+}
 
-    // _sampleCubicBezier 
-    //  queries the Bezier curve and adaptively samples it, adds samples in this._samples
-    this._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);
+// _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;
+    }
 
-        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);
+    //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 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 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);
+    var C0___ = VecUtils.vecAdd(3, C0__, C1__); C0___ = VecUtils.vecScale(3, C0___, 0.5);
 
-        //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);
-    }
+    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);
 
-    ///////////////////////////////////////////////////////////
-    // Methods
-    ///////////////////////////////////////////////////////////
-    //  createSamples
-    //  stores samples of the subpath in _samples
-    this.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 poi