path: root/js/lib/geom/brush-stroke.js

/* <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 CanvasController = require("js/controllers/elements/canvas-controller").CanvasController;
var ViewUtils = require("js/helper-classes/3D/view-utils").ViewUtils;

// Todo: This entire class should be converted to a module

///////////////////////////////////////////////////////////////////////
// Class GLBrushStroke
//      representation a sequence points (polyline) created by brush tool.
//      Derived from class GLGeomObj
///////////////////////////////////////////////////////////////////////
var BrushStroke = function GLBrushStroke() {
    ///////////////////////////////////////////////////
    // Instance variables
    ///////////////////////////////////////////////////
    this._Points = [];                      //current state of points in stage-world space (may be different from input)
    this._LocalPoints = [];                 //_Points in local coordinates...do this before rendering the points in the canvas
    this._OrigLocalPoints = [];             //copy of input points without any smoothing
    this._stageWorldCenter  = [0,0,0];      //coordinate for the canvas midPoint: a 3D vector in stage world space
    this._BBoxMin = [0, 0, 0];
    this._BBoxMax = [0, 0, 0];
    this._isDirty = true;
    this._isInit = false;
    
    //the HTML5 canvas that holds this brush stroke
    this._canvas = null;

    //stroke information
    this._strokeWidth = 1.0;
    this._strokeColor = [0.4, 0.4, 0.4, 1.0];
    this._secondStrokeColor = [1, 0.4, 0.4, 1.0];
    this._strokeHardness = 100;
    this._strokeMaterial = null;
    this._strokeStyle = "Solid";
    this._strokeDoSmoothing = false;
    this._strokeUseCalligraphic = false;
    this._strokeAngle = 0;
    this._strokeAmountSmoothing = 0;

    // currently, brush does not support a fill region
    this.canFill = false;

    //threshold that tells us whether two samples are too far apart
    this._MAX_SAMPLE_DISTANCE_THRESHOLD = 5;

    //threshold that tells us whether two samples are too close
    this._MIN_SAMPLE_DISTANCE_THRESHOLD = 2;

    //prevent extremely long paths that can take a long time to render
    this._MAX_ALLOWED_SAMPLES = 5000;

    //drawing context
    this._world = null;

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

    /////////////////////////////////////////////////////////
    // Property Accessors/Setters
    /////////////////////////////////////////////////////////
    this.setCanvas = function(c) {
        this._canvas = c;
    }

    this.setWorld = function (world) {
        this._world = world;
    };

    this.getWorld = function () {
        return this._world;
    };

    this.geomType = function () {
        return this.GEOM_TYPE_BRUSH_STROKE;
    };

    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.setDragPlane = function(p){
        this._dragPlane = p;
    };

    this.getNumPoints = function () {
        if (this._LocalPoints.length)
            return this._LocalPoints.length;
        else
            return this._Points.length;
    };

    this.getPoint = function (index) {
        return this._Points[index].slice(0);
    };

    this.addPoint = function (pt) {
        //add the point only if it is some epsilon away from the previous point
        var numPoints = this._Points.length;
        if (numPoints>0) {
            var threshold = this._MIN_SAMPLE_DISTANCE_THRESHOLD;
            var prevPt = this._Points[numPoints-1];
            var diffPt = [prevPt[0]-pt[0], prevPt[1]-pt[1]];
            var diffPtMag = Math.sqrt(diffPt[0]*diffPt[0] + diffPt[1]*diffPt[1]);
            if (diffPtMag>threshold){
                this._Points.push(pt);
                this._isDirty=true;
                this._isInit = false;
            }
        } else {
            this._Points.push(pt);
            this._isDirty=true;
            this._isInit = false;
        }
    };
    
    this.insertPoint = function(pt, index){
        this._Points.splice(index, 0, pt);
        this._isDirty=true;
        this._isInit = false;
    };

    this.isDirty = function(){
        return this._isDirty;
    };

    this.makeDirty = function(){
        this._isDirty=true;
    };

    this.getStageWorldCenter = function() {
        return this._stageWorldCenter;
    };

    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;
        if (this._strokeWidth<1) {
            this._strokeWidth = 1;
        }
        this._isDirty=true;
    };

    this.getStrokeMaterial = function () {
        return this._strokeMaterial;
    };

    this.setStrokeMaterial = function (m) {
        this._strokeMaterial = m; this._isDirty = true;
    };

    this.getStrokeColor = function () {
        return this._strokeColor;
    };

    this.setStrokeColor = function (c) {
        this._strokeColor = c; this._isDirty = true;
    };

    this.setFillColor = function(c){
        return;
    }; //NO-OP for now as we have no fill region

    this.setSecondStrokeColor = function(c){
        this._secondStrokeColor=c; this._isDirty = true;
    }

    this.setStrokeHardness = function(h){
        if (this._strokeHardness!==h){
            this._strokeHardness=h;
            this._isDirty = true;
        }
    }
    this.getStrokeHardness = function(){
        return this._strokeHardness;
    }

    this.setDoSmoothing = function(s){
        if (this._strokeDoSmoothing!==s) {
            this._strokeDoSmoothing = s;
            this._isDirty = true;
        }
    }

    this.getDoSmoothing = function(){
        return this._strokeDoSmoothing;
    }

    this.setSmoothingAmount = function(a){
        if (this._strokeAmountSmoothing!==a) {
            this._strokeAmountSmoothing = a;
            this._isDirty = true;
        }
    }

    this.getSmoothingAmount = function(){
        return this._strokeAmountSmoothing;
    }

    this.setStrokeUseCalligraphic = function(c){
        if (this._strokeUseCalligraphic!==c){
            this._strokeUseCalligraphic = c;
            this._isDirty = true;
        }
    }

    this.setStrokeAngle = function(a){
        if (this._strokeAngle!==a){
            this._strokeAngle = a;
            this._isDirty = true;
        };
    }

    this.getStrokeUseCalligraphic = function(){
        return this._strokeUseCalligraphic;
    }

    this.getStrokeAngle = function(){
        return this._strokeAngle;
    }

    this.getStrokeStyle = function () {
        return this._strokeStyle;
    };

    this.setStrokeStyle = function (s) {
        this._strokeStyle = s;
    };

    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 local point positions such that the width of the bbox is the newW
        var origX = this._BBoxMin[0];
        var numPoints = this._LocalPoints.length;
        for (var i=0;i<numPoints;i++){
            //compute the distance from the bboxMin
            var oldW = this._LocalPoints[i][0] - origX;
            this._LocalPoints[i] = [(origX + oldW*scaleX),this._LocalPoints[i][1],this._LocalPoints[i][2]];

            oldW = this._OrigLocalPoints[i][0] - origX;
            this._OrigLocalPoints[i] = [(origX + oldW*scaleX),this._OrigLocalPoints[i][1],this._OrigLocalPoints[i][2]];
        }
        this._isDirty = true;
    };

    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 local point positions such that the width of the bbox is the newW
        var origY = this._BBoxMin[1];
        var numPoints = this._LocalPoints.length;
        for (var i=0;i<numPoints;i++){
            //compute the distance from the bboxMin
            var oldH = this._LocalPoints[i][1] - origY;
            this._LocalPoints[i] = [this._LocalPoints[i][0],(origY + oldH*scaleY),this._LocalPoints[i][2]];

            oldH = this._OrigLocalPoints[i][1] - origY;
            this._OrigLocalPoints[i] = [this._OrigLocalPoints[i][0],(origY + oldH*scaleY),this._OrigLocalPoints[i][2]];
        }
        this._isDirty = true;
    };

    this.getWidth = function() {
        if (this._isDirty){
            this.update();
        }
        return this._BBoxMax[0]-this._BBoxMin[0];
    };

    this.getHeight = function() {
        if (this._isDirty){
            this.update();
        }
        return this._BBoxMax[1]-this._BBoxMin[1];
    };

    //remove all the points
    this.clear = function () {
        this._Points = [];
        this._OrigLocalPoints    = [];
        this._isDirty=true;
        this._isInit = false;
    };

    this._addSamples = function() {
        //**** add samples to the long sections of the path --- Catmull-Rom spline interpolation *****
        // instead of the following, may use 4-point subdivision iterations over continuous regions of 'long' segments
        // look at http://www.gvu.gatech.edu/~jarek/Split&Tweak/ for formula

        var numPoints = this._Points.length;
        var numInsertedPoints = 0;
        var newSampledPoints = [];
        var threshold = this._MAX_SAMPLE_DISTANCE_THRESHOLD;//this determines whether a segment between two sample too long
        var prevPt = this._Points[0];
        newSampledPoints.push(this._Points[0]);
        for (var i=1;i<numPoints;i++) {
            var pt = this._Points[i];
            var diff = [pt[0]-prevPt[0], pt[1]-prevPt[1]];
            var distance = Math.sqrt(diff[0]*diff[0]+diff[1]*diff[1]);
            if (distance>threshold){
                //build the control polygon for the Catmull-Rom spline (prev. 2 points and next 2 points)
                var prev = (i===1) ? i-1 : i-2;
                var next = (i===numPoints-1) ? i : i+1;
                var ctrlPts = [this._Points[prev], this._Points[i-1], this._Points[i], this._Points[next]];
                //insert points along the prev. to current point
                var numNewPoints = Math.floor(distance/threshold);
                for (var j=0;j<numNewPoints;j++){
                    var param = (j+1)/(numNewPoints+1);
                    var newpt = this._CatmullRomSplineInterpolate(ctrlPts, param);
                    newSampledPoints.push(newpt);
                    numInsertedPoints++;
                }
            }
            newSampledPoints.push(pt);
            prevPt=pt;

            //end this function if the numPoints has gone above the max. size specified
            if (numPoints> this._MAX_ALLOWED_SAMPLES){
                console.log("leaving the resampling because numPoints is greater than limit:"+this._MAX_ALLOWED_SAMPLES);
                break;
            }
        }
        this._Points = newSampledPoints.slice(0);
        newSampledPoints = [];
    };

    this.init = function(){
        if (!this._isInit){
            // **** add samples to the _Points in stageworld space ****
            this._addSamples();

            // **** compute the 2D (canvas space) coord. of the _Points  ****
            this._buildLocalCoordFromStageWorldCoord();

            // **** turn off the init. flag ****
            this._isInit = true;
            this._isDirty= true;
        }

        // **** update the current brush stroke ****
        // smoothing, re-compute bounding box, etc.
        this.update();
    };

    this._unprojectPt = function(pt, pespectiveDist){
        var retPt = pt.slice(0);
        if (MathUtils.fpCmp(pespectiveDist,-pt[2]) !== 0){
            z = pt[2]*pespectiveDist/(pespectiveDist + pt[2]);
            var x = pt[0]*(pespectiveDist - z)/pespectiveDist,
                y = pt[1]*(pespectiveDist - z)/pespectiveDist;
            retPt[0] = x;  retPt[1] = y;  retPt[2] = z;
        }
        return retPt;
    };

    this._buildLocalCoordFromStageWorldCoord = function() {
        var stage = ViewUtils.getStage();
        var stageOffset = ViewUtils.getElementOffset(stage);
        ViewUtils.setViewportObj(stage);

        var numPoints = this._Points.length;
        var i;

        // ***** compute center of bbox based on stage world coords *****
        var bboxMin = [Infinity, Infinity, Infinity];
        var bboxMax = [-Infinity, -Infinity, -Infinity];
        for (i=0;i<numPoints;i++){
            var pt = this._Points[i];
            for (var d = 0; d < 3; d++) {
                if (bboxMin[d] > pt[d]) {
                    bboxMin[d] = pt[d];
                }
                if (bboxMax[d] < pt[d]) {
                    bboxMax[d] = pt[d];
                }
            }
        }
        //save the center of the bbox for later use (while constructing the canvas)
        this._stageWorldCenter = VecUtils.vecInterpolate(3, bboxMin, bboxMax, 0.5);

        // ***** center the input stageworld data about the center of the bbox *****
        this._LocalPoints = [];
        for (i=0;i<numPoints;i++){
            var localPoint = [this._Points[i][0],this._Points[i][1],this._Points[i][2]];
            localPoint[0]-= this._stageWorldCenter[0];
            localPoint[1]-= this._stageWorldCenter[1];

            // ***** unproject all the centered points and convert them to 2D (plane space)*****
            // (undo the projection step performed by the browser)
            //localPoint = this._unprojectPt(localPoint, 1400); //todo get the perspective distance from the canvas
            localPoint = MathUtils.transformPoint(localPoint, this._planeMatInv);

            //add to the list of local points
            this._LocalPoints.push(localPoint);
        }

        // ***** compute width, height, and midpoint position (in stage world position) of the canvas
        this._updateBoundingBox(); //compute the bbox to obtain the width and height used below
        var halfwidth = 0.5*(this._BBoxMax[0]-this._BBoxMin[0]);
        var halfheight = 0.5*(this._BBoxMax[1]-this._BBoxMin[1]);
        this._OrigLocalPoints    = [];
        for (i=0;i<numPoints;i++) {
            this._LocalPoints[i][0]+= halfwidth;
            this._LocalPoints[i][1]+= halfheight;

            //store the original points
            this._OrigLocalPoints.push([this._LocalPoints[i][0],this._LocalPoints[i][1],this._LocalPoints[i][2]]);
        }
        //update the bbox with the same adjustment as was made for the local points above
        this._BBoxMax[0]+= halfwidth;this._BBoxMin[0]+= halfwidth;
        this._BBoxMax[1]+= halfheight;this._BBoxMin[1]+= halfheight;
    };
    
    this.update = function() {
        if (this._isDirty){
            // **** do smoothing if necessary ****
            this._doSmoothing();

            // **** recompute the bounding box ****
            this._updateBoundingBox();

            // **** offset the local coords to account for the change in bbox ****
            this._offsetLocalCoord(-this._BBoxMin[0], -this._BBoxMin[1]);

            // **** turn off the dirty flag ****
            this._isDirty = false;
        }
    };

    this._offsetLocalCoord = function(deltaW, deltaH){
        var numPoints = this._LocalPoints.length;
        for (var i=0;i<numPoints;i++) {
            this._LocalPoints[i][0]+= deltaW;
            this._LocalPoints[i][1]+= deltaH;
        }
    };

    //I had to write this function to do a deep copy because I think slice(0) creates a copy by reference
    this._copyCoordinates3D = function(srcCoord, destCoord){
        var i=0;
        var numPoints = srcCoord.length;
        for (i=0;i<numPoints;i++){
            destCoord[i] = [srcCoord[i][0],srcCoord[i][1],srcCoord[i][2]];
        }
    };
    this._doSmoothing = function() {
        var numPoints = this._LocalPoints.length;
        if (this._strokeDoSmoothing && numPoints>1) {
            this._copyCoordinates3D(this._OrigLocalPoints   , this._LocalPoints);
            //iterations of Laplacian smoothing (setting the points to the average of their neighbors)
            var numLaplacianIterations = this._strokeAmountSmoothing;
            for (var n=0;n<numLaplacianIterations;n++){
                var newPoints = this._LocalPoints.slice(0); //I think this performs a copy by reference, which would make the following a SOR step
                for (var i=1;i<numPoints-1;i++) {
                    var avgPos = [  0.5*(this._LocalPoints[i-1][0] + this._LocalPoints[i+1][0]),
                                    0.5*(this._LocalPoints[i-1][1] + this._LocalPoints[i+1][1]),
                                    0.5*(this._LocalPoints[i-1][2] + this._LocalPoints[i+1][2])] ;
                    newPoints[i] = avgPos;
                }
                this._LocalPoints = newPoints.slice(0);
            }
        }
    };

    this._updateBoundingBox = function() {
        // *** compute the bounding box *********
        var points = this._LocalPoints;
        var numPoints = points.length;

        this._BBoxMin = [Infinity, Infinity, Infinity];
        this._BBoxMax = [-Infinity, -Infinity, -Infinity];
        if (numPoints === 0) {
            this._BBoxMin = [0, 0, 0];
            this._BBoxMax = [0, 0, 0];
        } else {
            for (var i=0;i<numPoints;i++){
                var pt = points[i];
                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
            }
        }

        //increase the bbox given the stroke width and the angle (in case of calligraphic brush)
        var bboxPadding = this._strokeWidth/2;
        //todo TEMP!
        //bboxPadding = 0; //for now, ignore the effect of stroke width on bounding box
        //end todo TEMP
        //if (this._strokeUseCalligraphic) {
        //todo re-enable this if check once we are able to change the left and top of the brush canvas
        if (false){
            this._BBoxMin[0]-= bboxPadding*Math.cos(this._strokeAngle);
            this._BBoxMin[1]-= bboxPadding*Math.sin(this._strokeAngle);
            this._BBoxMax[0]+= bboxPadding*Math.cos(this._strokeAngle);
            this._BBoxMax[1]+= bboxPadding*Math.sin(this._strokeAngle);
        } else {
            for (var d = 0; d < 3; d++) {
                this._BBoxMin[d]-= bboxPadding;
                this._BBoxMax[d]+= bboxPadding;
            }//for every dimension d from 0 to 2
        }
    };

    this.buildBuffers = function () {
        //return; //no need to do anything for now
    };//buildBuffers()

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

        var numPoints = this.getNumPoints();
        if (numPoints === 0) {
            return; //nothing to do for empty paths
        }

        if (this._isDirty){
            this.update();
        }
        var bboxMin = this.getBBoxMin();
        var bboxMax = this.getBBoxMax();
        var bboxWidth = bboxMax[0] - bboxMin[0];
        var bboxHeight = bboxMax[1] - bboxMin[1];

        if (!this._canvas){
            //set the canvas by querying the world
            this._canvas = this.getWorld().getCanvas();
        }
        if (this._canvas) {
            var newLeft = Math.round(this._stageWorldCenter[0] - 0.5 * bboxWidth);
            var newTop = Math.round(this._stageWorldCenter[1] - 0.5 * bboxHeight);
            //assign the new position, width, and height as the canvas dimensions through the canvas controller
            //CanvasController.setProperty(this._canvas, "left", newLeft+"px");
            //CanvasController.setProperty(this._canvas, "top", newTop+"px");

            CanvasController.setProperty(this._canvas, "width", bboxWidth+"px");
            CanvasController.setProperty(this._canvas, "height", bboxHeight+"px");
            //this._canvas.elementModel.shapeModel.GLWorld.setViewportFromCanvas(this._canvas);
        }


        //get the context
        var ctx = world.get2DContext();
        if (!ctx) {
            throw ("null context in brushstroke render");
        }
        ctx.save();
        ctx.clearRect(0, 0, bboxWidth, bboxHeight);
        this.drawToContext(ctx, false);
        ctx.restore();
    } //this.render()

    this.drawToContext = function(ctx, drawStageWorldPts, stageWorldDeltaX, stageWorldDeltaY, stageWorldToScreenMat){
        var points = this._LocalPoints;
        if (drawStageWorldPts){ //this is usually true when we're drawing the brush stroke on the stage (no canvas yet)
            points = this._Points;
        }
        var numPoints = points.length;
        var tempP, p;
        if (this._strokeUseCalligraphic) {
            //build the stamp for the brush stroke
            var t=0;
            var numTraces = this._strokeWidth;
            var halfNumTraces = numTraces*0.5;
            var opaqueRegionHalfWidth = 0.5*this._strokeHardness*numTraces*0.01; //the 0.01 is to convert the strokeHardness from [0,100] to [0,1]
            var maxTransparentRegionHalfWidth = halfNumTraces-opaqueRegionHalfWidth;

            //todo this brush stamp should be created outside of this function
            //build an angled (calligraphic) brush stamp
            var deltaDisplacement = [Math.cos(this._strokeAngle),Math.sin(this._strokeAngle)];
            deltaDisplacement = VecUtils.vecNormalize(2, deltaDisplacement, 1);
            var startPos = [-halfNumTraces*deltaDisplacement[0],-halfNumTraces*deltaDisplacement[1]];

            var brushStamp = [];
            for (t=0;t<numTraces;t++){
                var brushPt = [startPos[0]+t*deltaDisplacement[0], startPos[1]+t*deltaDisplacement[1]];
                brushStamp.push(brushPt);
            }

            ctx.lineJoin="bevel";
            ctx.lineCap="butt";
            ctx.globalCompositeOperation = 'source-over';
            ctx.globalAlpha = this._strokeColor[3];

            for (t=0;t<numTraces;t++){
                var disp = [brushStamp[t][0], brushStamp[t][1]];
                var alphaVal = 1.0;
                var distFromOpaqueRegion = Math.abs(t-halfNumTraces) - opaqueRegionHalfWidth;
                if (distFromOpaqueRegion>0) {
                    var transparencyFactor = distFromOpaqueRegion/maxTransparentRegionHalfWidth;
                    alphaVal = 1.0 - transparencyFactor;//(transparencyFactor*transparencyFactor);//the square term produces nonlinearly varying alpha values
                    alphaVal *= 0.5; //factor that accounts for lineWidth == 2
                }
                ctx.save();
                if (t === (numTraces-1) || t === 0){
                    ctx.lineWidth = 1;
                } else {
                     //todo figure out the correct formula for the line width
                    ctx.lineWidth=2;
                }
                ctx.strokeStyle="rgba("+parseInt(255*this._strokeColor[0])+","+parseInt(255*this._strokeColor[1])+","+parseInt(255*this._strokeColor[2])+","+alphaVal+")";
                //linearly interpolate between the two stroke colors
                var currStrokeColor = VecUtils.vecInterpolate(4, this._strokeColor, this._secondStrokeColor, t/numTraces);
                //ctx.strokeStyle="rgba("+parseInt(255*currStrokeColor[0])+","+parseInt(255*currStrokeColor[1])+","+parseInt(255*currStrokeColor[2])+","+alphaVal+")";
                ctx.translate(disp[0],disp[1]);
                ctx.beginPath();
                if (drawStageWorldPts) {
                    tempP = points[0].slice(0);
                    tempP[0]+=stageWorldDeltaX; tempP[1]+=stageWorldDeltaY;
                    p = MathUtils.transformAndDivideHomogeneousPoint(tempP, stageWorldToScreenMat);
                } else {
                    p = points[0];
                }
                ctx.moveTo(p[0],p[1]);
                for (var i=0;i<numPoints;i++){
                    if (drawStageWorldPts) {
                        tempP = points[i].slice(0);
                        tempP[0]+=stageWorldDeltaX; tempP[1]+=stageWorldDeltaY;
                        p = MathUtils.transformAndDivideHomogeneousPoint(tempP, stageWorldToScreenMat);
                    } else {
                        p = points[i];
                    }
                    ctx.lineTo(p[0],p[1]);
                }
                ctx.stroke();
                ctx.restore();
            }
        } else {
            ctx.globalCompositeOperation = 'lighter'; //we wish to add up the colors
            ctx.globalAlpha = this._strokeColor[3];
            ctx.lineCap = "round";
            ctx.lineJoin="round";
            var minStrokeWidth = (this._strokeHardness*this._strokeWidth)/100; //the hardness is the percentage of the stroke width that's fully opaque
            var numlayers = 1 + Math.ceil((this._strokeWidth-minStrokeWidth)*0.5);
            var alphaVal = 1.0/(numlayers); //this way the alpha at the first path will be 1
            ctx.strokeStyle="rgba("+parseInt(255*this._strokeColor[0])+","+parseInt(255*this._strokeColor[1])+","+parseInt(255*this._strokeColor[2])+","+alphaVal+")";
            for (var l=0;l<numlayers;l++){
                ctx.beginPath();
                if (drawStageWorldPts) {
                    tempP = points[0].slice(0);
                    tempP[0]+=stageWorldDeltaX; tempP[1]+=stageWorldDeltaY;
                    p = MathUtils.transformAndDivideHomogeneousPoint(tempP, stageWorldToScreenMat);
                } else {
                    p = points[0];
                }
                ctx.moveTo(p[0],p[1]);
                if (numPoints===1){
                    //display a tiny segment as a single point
                   ctx.lineTo(p[0],p[1]+0.01);
                }
                for (var i=1;i<numPoints;i++){
                    if (drawStageWorldPts) {
                        tempP = points[i].slice(0);
                        tempP[0]+=stageWorldDeltaX; tempP[1]+=stageWorldDeltaY;
                        p = MathUtils.transformAndDivideHomogeneousPoint(tempP, stageWorldToScreenMat);
                    } else {
                        p = points[i];
                    }
                    ctx.lineTo(p[0],p[1]);
                }
                ctx.lineWidth=2*l+minStrokeWidth;


                //experiments with shadows
                /*
                ctx.shadowOffsetX = 10;
                ctx.shadowOffsetY = 10;
                ctx.shadowBlur    = 10;
                ctx.shadowColor   = //"rgb("+parseInt(255*this._strokeColor[0])+","+parseInt(255*this._strokeColor[1])+","+parseInt(255*this._strokeColor[2])+")";
                    "#FF6666";  //or use rgb(red, green, blue)
                 */
                ctx.stroke();
            }//for every layer l
        } //if there is no calligraphic stroke
    }; //this.drawToCanvas()


    this.exportJSON = function(){
        var retObject= new Object();
        //the type of this object
        retObject.type = this.geomType();
        retObject.geomType = retObject.type;

        //the geometry for this object
        retObject.localPoints = this._LocalPoints.slice(0);
        this._copyCoordinates3D(this._LocalPoints, retObject.localPoints); //todo is this necessary in addition to the slice(0) above?
        retObject.origLocalPoints = this._OrigLocalPoints.slice(0);
        this._copyCoordinates3D(this._OrigLocalPoints, retObject.origLocalPoints); //todo <ditto>

        retObject.stageWorldCenter = [this._stageWorldCenter[0],this._stageWorldCenter[1],this._stageWorldCenter[2]];
        retObject.planeMat = this._planeMat;
        retObject.planeMatInv = this._planeMatInv;
        retObject.dragPlane = [this._dragPlane[0],this._dragPlane[1],this._dragPlane[2],this._dragPlane[3]];

        //stroke appearance properties
        retObject.strokeWidth = this._strokeWidth;
        retObject.strokeColor = this._strokeColor;
        retObject.strokeHardness = this._strokeHardness;
        retObject.strokeUseCalligraphic = this._strokeUseCalligraphic;
        retObject.strokeAngle = this._strokeAngle;

        //stroke smoothing properties
        retObject.strokeDoSmoothing = this._strokeDoSmoothing;
        retObject.strokeAmountSmoothing = this._strokeAmountSmoothing;

        return retObject;
    };

    this.importJSON = function(jo){
        if (this.geomType()!== jo.geomType){
            return;
        } 
        //the geometry for this object
        this._LocalPoints = jo.localPoints.slice(0);
        this._copyCoordinates3D(jo.localPoints, this._LocalPoints); //todo is this necessary in addition to the slice(0) above?
        this._OrigLocalPoints = jo.origLocalPoints.slice(0);
        this._copyCoordinates3D(jo.origLocalPoints, this._OrigLocalPoints); //todo <ditto>

        this._stageWorldCenter = [jo.stageWorldCenter[0],jo.stageWorldCenter[1],jo.stageWorldCenter[2]];
        this._planeMat = jo.planeMat;
        this._planeMatInv = jo.planeMatInv;
        this._dragPlane = [jo.dragPlane[0],jo.dragPlane[1],jo.dragPlane[2],jo.dragPlane[3]];

        //stroke appearance properties
        this._strokeWidth = jo.strokeWidth;
        this._strokeColor = jo.strokeColor;
        this._strokeHardness = jo.strokeHardness;
        this._strokeUseCalligraphic = jo.strokeUseCalligraphic;
        this._strokeAngle = jo.strokeAngle;

        //stroke smoothing properties
        this._strokeDoSmoothing = jo.strokeDoSmoothing;
        this._strokeAmountSmoothing = jo.strokeAmountSmoothing;

        this._isInit = true; //do not re-initialize this brush stroke
        this._isDirty = true;  //force a re-computation of meta-geometry before rendering
        this.update();      //after this, the stroke is ready to be rendered
    };

    this.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;
    };

    this.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;
    };

}; //function BrushStroke ...class definition

BrushStroke.prototype = Object.create(GeomObj, {});

BrushStroke.prototype._CatmullRomSplineInterpolate = function(ctrlPts, t)
{
    //perform CatmullRom interpolation on the spline...assume t is in [0,1]
    var t2 = t*t;
    var t3 = t2*t;
    var retPoint = [0,0,0];
    for (var i=0;i<3;i++){
        retPoint[i] = 0.5 *(
            (2*ctrlPts[1][i]) +
            (-ctrlPts[0][i] + ctrlPts[2][i]) * t +
            (2*ctrlPts[0][i] - 5*ctrlPts[1][i] + 4*ctrlPts[2][i] - ctrlPts[3][i]) * t2 +
            (-ctrlPts[0][i] + 3*ctrlPts[1][i]- 3*ctrlPts[2][i] + ctrlPts[3][i]) * t3);
    }
    return retPoint;
}
if (typeof exports === "object") {
    exports.BrushStroke = BrushStroke;
}
<