lkarch.org/tools/mathisfun/www.mathsisfun.com/calculus/images/function-graph-2deriv.js

var my={};function functiongraph2derivMain(){this.version='0.91';w=470;h=700;my.svgQ=false;my.svg=new SVG();my.examples=[['sin(x)','cos(x)','-sin(x)'],['x^2','2x','2'],['x^3','3x^2','6x'],['x^4','4x^3','12x^2'],['1/x','-x^(-2)','2x^(-3)'],['e^x','e^x','e^x']];my.exampleNo=0;graphLt=0;graphTp=0;graphWd=450;graphHt=190;coords=new Coords(graphLt,graphTp,graphWd,graphHt,-4,-2.4,4,2.4,true);canvasWd=graphWd;canvasHt=graphHt;clrs=["blue","rgb(0,222,0)","red"];var s='';s+='<style>input[type="radio"]:checked+label {font-weight: bold;}</style>';s+='<div style="position:relative; width:'+w+'px; height:'+h+'px; border-radius: 10px;  margin:auto; display:block; background-color: #ddeeff; ">';var radios=[];for(var i=0;i<my.examples.length;i++){var opt=my.examples[i][0];opt=opt.replace(/\^([0-9x])/g,'<sup>$1</sup>');radios[i]=opt;}
s+='<div style="text-align:center; color:black; font: 17px Arial; z-index: 2; margin-bottom:5px;">';s+=getRadioHTML('Example','example',radios,'chgExample');s+='</div>';s+='<div style="text-align:center; color:black; font: 17px Arial; z-index: 2;">';s+='<span style="color:black; font: 16px Arial; z-index: 2;">Zoom:</span>';s+='<input type="range" id="r1" value="0.5" min="0" max="1" step=".01"  style="z-index:2; width:200px; height:17px; border: none; position:relative; top: 5px; " oninput="onZoomChg(0,this.value)" onchange="onZoomChg(1,this.value)" />';s+='<button style="font: 16px Arial;" class="togglebtn"  onclick="zoomReset()" >Reset</button>';s+='</div>';var yPos=77;my.titles=['f(x)',"f'(x)","f''(x)"]
for(var i=0;i<my.titles.length;i++){s+='<canvas id="gfx'+(i*2)+'" width="'+canvasWd+'" height="'+canvasHt+'" style="position:absolute; left:5px; top:'+yPos+'px; z-index:1; margin-left: 5px; background-color: #ffffff; border: 1px solid black;"></canvas>';s+='<canvas id="gfx'+(i*2+1)+'" width="'+canvasWd+'" height="'+canvasHt+'" style="position:absolute; left:5px; top:'+yPos+'px; z-index:1; margin-left: 5px; border: 1px solid black;"></canvas>';s+='<div id="title'+i+'" style="position:absolute; left:12px; top:'+yPos+'px; color:'+clrs[i]+'; font: bold 25px Arial; z-index: 2;">'+my.titles[i]+'</div>';yPos+=canvasHt+10;}
s+='<div id="copyrt" style="font: 11px Arial; color: #6600cc; position:absolute; left:5px; bottom:3px;">&copy; 2017 MathsIsFun.com  v'+this.version+'</div>';s+='</div>';document.write(s);my.els=[];my.gs=[];for(var i=0;i<my.titles.length*2;i++){var elx=document.getElementById('gfx'+i);ratio=3;elx.width=canvasWd*ratio;elx.height=canvasHt*ratio;elx.style.width=canvasWd+"px";elx.style.height=canvasHt+"px";var gx=elx.getContext("2d");gx.setTransform(ratio,0,0,ratio,0,0);gx.translate(0.5,0.5);my.els.push(elx);my.gs.push(gx);if(i%2){elx.addEventListener("mousemove",mouseMoveListener,false);elx.addEventListener('touchstart',ontouchstart,false);elx.addEventListener('touchmove',ontouchmove,false);}}
window.addEventListener("mouseup",mouseUpListener,false);window.addEventListener('touchend',ontouchend,false);el=my.els[0];currZoom=1;polarQ=false;aVal=1;var inStr=getQueryVariable('func1');if(inStr){inStr=decodeURIComponent(inStr);document.getElementById('f0').value=inStr;}
inStr=getQueryVariable('func2');if(inStr){inStr=decodeURIComponent(inStr);document.getElementById('f1').value=inStr;}
if(inStr=getQueryVariable('xmin'))coords.xStt=parseFloat(inStr);if(inStr=getQueryVariable('xmax'))coords.xEnd=parseFloat(inStr);if(inStr=getQueryVariable('ymin'))coords.yStt=parseFloat(inStr);if(inStr=getQueryVariable('ymax'))coords.yEnd=parseFloat(inStr);coords.calcScale();parser=new Parser();dragging=false;downX=0;downY=0;prevX=0;prevY=0;my.ptsQ=false;my.pts=[];var shapeRad=9;my.minX=shapeRad;my.maxX=graphWd-shapeRad;my.minY=shapeRad;my.maxY=graphHt-shapeRad;my.fnLine=[];my.dragPtQ=false;makePts();redraw();}
function chgExample(n){my.exampleNo=n;redraw();}
function redraw(){var ex=my.examples[my.exampleNo];for(var i=0;i<my.titles.length;i++){var g=my.gs[i*2];g.clearRect(0,0,el.width,el.height);var graph=new Graph(g,coords);graph.drawGraph();doPlot(g,ex[i],clrs[i],1.5,'xy');var t=ex[i];t=t.replace(/\^([0-9x\-\(\)]*)/g,'<sup>$1</sup>');t=my.titles[i]+': '+t;document.getElementById('title'+i).innerHTML=t;}}
function makePts(){var i;var tempX;var tempY;var tempColor;var pos=[[140,80,"A"],[420,240,"B"]];my.pts=[];for(i=0;i<pos.length;i++){var tempX=pos[i][0];var tempY=pos[i][1];var tempColor="rgb("+0+","+0+","+255+")";my.pts.push(new Pt(tempX,tempY,9,tempColor));}}
function Pt(x,y,rad,clr){this.setPx(x,y);this.rad=rad;this.clr=clr;}
Pt.prototype.setPx=function(x,y){this.x=x;this.y=y;this.xVal=coords.toXVal(this.x);this.yVal=coords.toYVal(this.y);}
Pt.prototype.getPxX=function(){return coords.toXPix(this.xVal);}
Pt.prototype.getPxY=function(){return coords.toYPix(this.yVal);}
Pt.prototype.snap=function(line){var minD=9999;var minPt=[];for(var i=0;i<line.length;i++){var pt=line[i];if(pt!=0){var d=dist(pt[0]-this.x,pt[1]-this.y);if(d<minD){minD=d;minPt=pt;}}}
if(minD<20){this.setPx(minPt[0],minPt[1]);}}
function showSlopes(xPix){coords.calcScale();var ex=my.examples[my.exampleNo];for(var i=0;i<3;i++){showSlope(xPix,my.gs[i*2+1],ex[i])}}
function showSlope(xPix,g,fn){g.clearRect(0,0,el.width,el.height);parser.newParse(fn);var xVal=coords.toXVal(xPix);parser.setVarVal("x",xVal);yVal=parser.getVal();yPix=coords.toYPix(yVal,false);if(yPix>0&&yPix<graphHt){drawSpot(g,xPix,yPix);var dx=(coords.xEnd-coords.xStt)/1000
var slope=parser.getSlope(dx);if(slope!=undefined){var deltaX=100;var deltaY=deltaX*slope;g.strokeStyle='black';g.beginPath();g.moveTo(xPix-deltaX,yPix+deltaY);g.lineTo(xPix+deltaX,yPix-deltaY);g.stroke();}}}
function drawSpot(g,x,y){g.lineWidth=1;g.fillStyle="rgba(0, 0, 255, 0.2)";g.beginPath();g.arc(x,y,7,0,2*Math.PI,false);g.stroke();g.fill();g.strokeStyle="black";g.beginPath();var r=11;g.moveTo(x-r,y);g.lineTo(x+r,y);g.moveTo(x,y-r);g.lineTo(x,y+r);g.stroke();}
function drawPts(){console.log("drawPts");coords.calcScale();my.fixed=parseInt(-Math.log(coords.xScale))-1;if(my.fixed<3)my.fixed=3;if(my.fixed>11)my.fixed=11;var i;var g=g2;g2.clearRect(0,0,el2.width,el2.height);var dbg="";for(i=0;i<my.pts.length;i++){var pt=my.pts[i];var x=pt.getPxX();var y=pt.getPxY();g.fillStyle="rgba(0, 0, 255, 0.3)";g.beginPath();g.arc(x,y,pt.rad,0,2*Math.PI,false);g.fill();g.fillStyle="rgba(0, 0, 0, 0.8)";g.beginPath();g.arc(x,y,2,0,2*Math.PI,false);g.fill();g.font="14px Arial";g.fillStyle='blue';var s='';if(true){s+=String.fromCharCode(65+i);}else{s+='('+fmt1(pt.xVal);s+=', '+fmt1(pt.yVal)+')';}
g.fillText(s,x+5,y-5);}
if(my.pts.length>=2)doSlope(my.pts[0],my.pts[1]);}
function doSlope(p0,p1){var g=g2;s='';var pxd=dist(coords.toXPix(p0.xVal)-coords.toXPix(p1.xVal),coords.toYPix(p0.yVal)-coords.toYPix(p1.yVal));if(pxd<4){s+='too close';var xMid=(coords.toXPix(p0.xVal)+coords.toXPix(p1.xVal))/2
var yMid=(coords.toYPix(p0.yVal)+coords.toYPix(p1.yVal))/2;g.fillStyle='rgba(255,100,0,0.8)';g.font='bold 26px Arial';g.fillText('?',xMid+20,yMid+10)}else{g.strokeStyle='rgba(255,100,0,0.5)';g.lineWidth=3;g.beginPath();if(p0.xVal>p1.xVal){var temp=p0;p0=p1;p1=temp;}
g.moveTo(p0.getPxX(),p0.getPxY());g.lineTo(p1.getPxX(),p1.getPxY());g.fill();g.stroke();var xstr0=fmt1(p0.xVal);var ystr0=fmt1(p0.yVal);var xstr1=fmt1(p1.xVal);var ystr1=fmt1(p1.yVal);var x0=parseFloat(xstr0);var y0=parseFloat(ystr0);var x1=parseFloat(xstr1);var y1=parseFloat(ystr1);var m=(p0.yVal-p1.yVal)/(p0.xVal-p1.xVal);if(x0-x1==0){s+='vertical slope';}else{s+="Slope = ";if(y1<0)ystr1='('+ystr1+')';s+="("+ystr0+" - "+ystr1+")";s+=" / ";if(x1<0)xstr1='('+xstr1+')';s+="("+xstr0+" - "+xstr1+")";s+="\n"
s+="          = ";s+=fmt1(y0-y1);s+=" / ";s+=fmt1(x0-x1);s+="\n"
s+="          = ";s+=fmt(m,4);}
var xMid=(coords.toXPix(p0.xVal)+coords.toXPix(p1.xVal))/2
var yMid=(coords.toYPix(p0.yVal)+coords.toYPix(p1.yVal))/2;g.fillStyle='rgba(255,100,0,0.8)';g.font='bold 16px Arial';g.fillText(fmt(m,4),xMid+10,yMid+10)}
var div=document.getElementById('info');div.value=s;}
function drawSlopeHuh(e){g.clear();var d0=drags[0];var ln=new Line(d0.getPt(),d0.getPt());slopeAngle+=0.03;ln.setAngle(slopeAngle);ln.setLen(200,true);g.lineStyle(4,'#ff4400',0.6);HiGraphics.drawLine(g,ln.a.x,ln.a.y,ln.b.x,ln.b.y);}
function fmt(num,digits){if(num==Number.POSITIVE_INFINITY)
return "undefined";if(num==Number.NEGATIVE_INFINITY)
return "undefined";num=num.toPrecision(digits);num=num.replace(/0+$/,"");if(num.charAt(num.length-1)==".")num=num.substr(0,num.length-1);if(Math.abs(num)<1e-15)num=0;return num;}
function fmt1(num){if(num==Number.POSITIVE_INFINITY)
return "undefined";if(num==Number.NEGATIVE_INFINITY)
return "undefined";digits=my.fixed;num=num.toFixed(digits);num=num.replace(/0+$/,"");if(num.charAt(num.length-1)==".")num=num.substr(0,num.length-1);if(Math.abs(num)<1e-15)num=0;return num;}
function hitTest(pt,mx,my){var dx;var dy;dx=mx-pt.getPxX();dy=my-pt.getPxY();return(dx*dx+dy*dy<pt.rad*pt.rad);}
function linkPop(){var pop=document.getElementById('linkpop');pop.style.transitionDuration="0.3s";pop.style.opacity=1;pop.style.zIndex=12;pop.style.left='100px';document.getElementById('linkbox').value=makeURL();}
function doSVG(){var graph=new Graph(g,coords);graph.makeSVG();var s=my.svg.getText();console.log(s);}
function makeURL(){var s="../data/function-grapherd41d.html?";var f0=document.getElementById('f0').value;if(f0.length>0){s+="func1="+encodeURIComponent(f0)+"&";}
var f1=document.getElementById('f1').value;if(f1.length>0){s+="func2="+encodeURIComponent(f1)+"&";}
s+="xmin="+coords.xStt.toPrecision(4)+"&";s+="xmax="+coords.xEnd.toPrecision(4)+"&";s+="ymin="+coords.yStt.toPrecision(4)+"&";s+="ymax="+coords.yEnd.toPrecision(4)+"&";s=s.substr(0,s.length-1);return(s);}
function linkPopClose(){var pop=document.getElementById('linkpop');pop.style.opacity=0;pop.style.zIndex=1;pop.style.left='-500px';}
function onaChg(n,v){aVal=v;var div=document.getElementById('aval');div.innerHTML=v;div.style.left=(170+v*100)+'px';redraw();}
function togglePts(){my.ptsQ=!my.ptsQ;toggleBtn('ptsBtn',my.ptsQ);toggleBtn('fitBtn',my.ptsQ);redraw();}
function togglePolar(){polarQ=!polarQ;toggleBtn('polarBtn',polarQ);redraw();}
function toggleBtn(btn,onq){if(onq){document.getElementById(btn).classList.add("hi");document.getElementById(btn).classList.remove("lo");}else{document.getElementById(btn).classList.add("lo");document.getElementById(btn).classList.remove("hi");}}
function zoomReset(){coords=new Coords(graphLt,graphTp,graphWd,graphHt,-5,-3,5,3,true);redraw();}
function zoomFit(){var valPts=[];for(var i=0;i<my.pts.length;i++){var pt=my.pts[i];valPts.push(new Pt(pt.xVal,pt.yVal,1,''));}
coords.fitToPts(valPts,1.1);redraw();}
function doExample(){exampleNo=(++exampleNo)%examples.length;document.getElementById('f0').value=examples[exampleNo];redraw();}
function ontouchstart(evt){var touch=evt.targetTouches[0];evt.clientX=touch.clientX;evt.clientY=touch.clientY;evt.touchQ=true;mouseMoveListener(evt);evt.preventDefault();}
function ontouchmove(evt){var touch=evt.targetTouches[0];evt.clientX=touch.clientX;evt.clientY=touch.clientY;evt.touchQ=true;mouseMoveListener(evt);evt.preventDefault();}
function ontouchend(evt){dragging=false;}
function mouseDownListener(evt){var bRect=el.getBoundingClientRect();var mouseX=(evt.clientX-bRect.left)*(el.width/ratio/bRect.width);var mouseY=(evt.clientY-bRect.top)*(el.height/ratio/bRect.height);downX=mouseX;downY=mouseY;prevX=mouseX;prevY=mouseY;dragging=true;my.dragPtQ=false;if(my.ptsQ){for(i=0;i<my.pts.length;i++){var pt=my.pts[i];if(hitTest(pt,mouseX,mouseY)){dragNo=i;my.dragPtQ=true;dragHoldX=mouseX-pt.getPxX();dragHoldY=mouseY-pt.getPxY();dragIndex=i;}}}
if(dragging){}
if(evt.preventDefault){evt.preventDefault();}
else if(evt.returnValue){evt.returnValue=false;}
return false;}
function mouseUpListener(evt){var bRect=el.getBoundingClientRect();var mouseX=(evt.clientX-bRect.left)*(el.width/ratio/bRect.width);var mouseY=(evt.clientY-bRect.top)*(el.height/ratio/bRect.height);if(my.dragPtQ){posX=mouseX-dragHoldX;posX=(posX<my.minX)?my.minX:((posX>my.maxX)?my.maxX:posX);posY=mouseY-dragHoldY;posY=(posY<my.minY)?my.minY:((posY>my.maxY)?my.maxY:posY);var pt=my.pts[dragIndex];pt.setPx(posX,posY);pt.snap(my.fnLine);drawPts();}else{if(Math.abs(mouseX-downX)<2&&Math.abs(mouseY-downY)<2){coords.newCenter(mouseX,mouseY);redraw();}}
my.dragPtQ=false;dragging=false;}
function mouseMoveListener(evt){var bRect=el.getBoundingClientRect();var mouseX=(evt.clientX-bRect.left)*(el.width/ratio/bRect.width);var mouseY=(evt.clientY-bRect.top)*(el.height/ratio/bRect.height);if(dragging){if(my.dragPtQ){posX=mouseX-dragHoldX;posX=(posX<my.minX)?my.minX:((posX>my.maxX)?my.maxX:posX);posY=mouseY-dragHoldY;posY=(posY<my.minY)?my.minY:((posY>my.maxY)?my.maxY:posY);var pt=my.pts[dragIndex];pt.setPx(posX,posY);pt.snap(my.fnLine);drawPts();}else{var moveX=prevX-mouseX;var moveY=mouseY-prevY;if(Math.abs(moveX)>1||Math.abs(moveY)>1){coords.drag(moveX,moveY);redraw();prevX=mouseX;prevY=mouseY;}}}else{showSlopes(mouseX);}}
function onZoomChg(n,v){var scaleBy=(v*2+0.01)/currZoom;coords.scale(scaleBy);currZoom*=scaleBy;if(n==1){currZoom=1;document.getElementById('r1').value=0.5;}
redraw();}
function drawPlot(g,plotType,gaps){gaps=null;switch(plotType){case "implicit":drawNewton(1);break;case "newton2":drawNewton(2);break;case "signchange":drawImplicitSign(2,plotType);break;case "shaded":drawShaded(2,plotType);break;default:}
var breakQ=true;var prevxPix=-1;var prevyPix=-1;var yState=9;var ptNumMin;var ptNumMax;switch(plotType){case "xy":case "dydx":ptNumMin=0;ptNumMax=coords.width;break;case "polar":var revFrom=0;var revTo=4;var angle0=revFrom*6.2832;var angle1=revTo*6.2832;points=Math.min(Math.max(600,(revTo-revFrom)*250),3000);stepSize=(angle1-angle0)/points;if(stepSize==0)
stepSize=1;ptNumMin=Math.floor(angle0/stepSize);ptNumMax=Math.ceil(angle1/stepSize);break;case "para":var tFrom=0;var tTo=3;var points=Math.min(Math.max(600,(tTo-tFrom)*250),3000);var stepSize=(tTo-tFrom)/points;if(stepSize==0)
stepSize=1;ptNumMin=Math.floor(tFrom/stepSize);ptNumMax=Math.ceil(tTo/stepSize);break;default:}
var line=[];var prevxVal=Number.NEGATIVE_INFINITY;var prevyVal=Number.NEGATIVE_INFINITY;var recipdx=1/coords.xScale;for(var ptNum=0;ptNum<=ptNumMax;ptNum++){var xVal;var yVal;var xPix;var yPix;switch(plotType){case "xy":xPix=ptNum;xVal=coords.xStt+xPix*coords.xScale;parser.setVarVal("x",xVal);yVal=parser.getVal();yPix=coords.toYPix(yVal,false);break;case "dydx":xPix=ptNum;xVal=coords.xStt+xPix*coords.xScale;parser.setVarVal("x",xVal);var thisyVal=parser.getVal();yVal=(thisyVal-prevyVal)*recipdx;prevyVal=thisyVal;break;case "polar":var angle=ptNum*stepSize;parser.setVarVal("x",angle);var radius=parser.getVal();xVal=radius*Math.cos(angle);yVal=radius*Math.sin(angle);break;case "para":xPix=ptNum;var t=coords.xStt+xPix*coords.xScale;var xy=conicVals(t);xVal=xy[0];yVal=xy[1];if(this.vals["b"]>1.1){if(yVal<-0.95&&yVal>-1.05){pt1[0]=xy[0];pt1[1]=xy[1];}}else{if(yVal<-this.vals["b"]*0.7&&yVal>-this.vals["b"]*0.8){pt1[0]=xy[0];pt1[1]=xy[1];}}
break;default:}
var prevbreakQ=breakQ;breakQ=false;var prevyState=yState;yState=0;if(yVal<coords.yStt)
yState=-1;if(yVal>coords.yEnd)
yState=1;if(yVal==Number.NEGATIVE_INFINITY){yState=-1;yVal=coords.yStt-coords.yScale*10;}
if(yVal==Number.POSITIVE_INFINITY){yState=1;yVal=coords.yEnd+coords.yScale*10;}
breakQ=prevyState*yState!=0;if(isNaN(yVal)){yState=9;breakQ=true;}
if(plotType=="polar"||plotType=="para"){xVal=Math.min(Math.max(coords.xStt-coords.xScale*10,xVal),coords.xEnd+coords.xScale*10);xPix=(xVal-coords.xStt)/coords.xScale;}
yVal=Math.min(Math.max(coords.yStt-coords.yScale*10,yVal),coords.yEnd+coords.yScale*10);yPix=(coords.yEnd-yVal)/coords.yScale;if(breakQ){if(prevbreakQ){}else{if(yState<9){line.push([xPix,yPix]);}}}else{if(prevbreakQ){if(prevyState<9){line.push(0);line.push([prevxPix,prevyPix]);line.push([xPix,yPix]);}else{line.push(0);line.push([xPix,yPix]);}}else{line.push([xPix,yPix]);}}
prevxVal=xVal;prevxPix=xPix;prevyPix=yPix;}
if(my.svgQ)my.svg=new SVG();var sttQ=true;g.beginPath();for(var i=0,len=line.length;i<len;i++){var pt=line[i];if(pt==0){g.stroke();sttQ=true;}else{if(sttQ){g.beginPath();g.moveTo(pt[0],pt[1]);sttQ=false;}else{g.lineTo(pt[0],pt[1]);}}}
g.stroke();my.fnLine=my.fnLine.concat(line);if(my.svgQ){sttQ=true;for(i=0,len=line.length;i<len;i++){var pt=line[i];if(pt==0){sttQ=true;}else{if(sttQ){my.svg.moveTo(pt[0],pt[1]);sttQ=false;}else{my.svg.lineTo(pt[0],pt[1]);}}}}}
function doPlot(g,fn,clr,lineWd,typ){var start=new Date().getTime();my.fnLine=[];if(fn.length>0){fn=fn.substr(0,1000);parser.radiansQ=this.radQ;parser.setVarVal('a',aVal);parser.newParse(fn);g.strokeStyle=clr;g.lineWidth=lineWd;if(polarQ){drawPlot(g,'polar');}else{drawPlot(g,typ);}}
var end=new Date().getTime();var time=end-start;}
function fixParentheses(s){var sttParCount=0;var endParCount=0;for(var i=0;i<s.length;i++){if(s.charAt(i)=="(")
sttParCount++;if(s.charAt(i)==")")
endParCount++;}
while(sttParCount<endParCount){s="("+s;sttParCount++;}
while(endParCount<sttParCount){s+=")";endParCount++;}
return(s);}
function getRadioHTML(prompt,id,lbls,func){var s='';s+='<div style="display:inline-block; border: 1px solid white; border-radius:5px; padding:3px; margin:3px; background-color:rgba(255,255,255,0.5);">';s+=prompt+':';for(var i=0;i<lbls.length;i++){var idi=id+i;var lbl=lbls[i];var check='';if(i==0)check='  checked="checked" ';s+='<input id="'+idi+'" type="radio" name="'+id+'" value="'+lbl+'" onclick="'+func+'('+i+');"'+check+'  autocomplete="off">';s+='<label for="'+idi+'">'+lbl+' </label>';}
s+='</div>';return s;}
function Coords(left,top,width,height,xStt,yStt,xEnd,yEnd,uniScaleQ){this.left=left;this.top=top;this.width=width;this.height=height;this.xStt=xStt;this.yStt=yStt;this.xEnd=xEnd;this.yEnd=yEnd;this.uniScaleQ=uniScaleQ;this.xLogQ=false;this.yLogQ=false;this.calcScale();}
Coords.prototype.calcScale=function(){if(this.xLogQ){if(this.xStt<=0)
this.xStt=1;if(this.xEnd<=0)
this.xEnd=1;}
if(this.yLogQ){if(this.yStt<=0)
this.yStt=1;if(this.yEnd<=0)
this.yEnd=1;}
var temp;if(this.xStt>this.xEnd){temp=this.xStt;this.xStt=this.xEnd;this.xEnd=temp;}
if(this.yStt>this.yEnd){temp=this.yStt;this.yStt=this.yEnd;this.yEnd=temp;}
var xSpan=this.xEnd-this.xStt;if(xSpan<=0)xSpan=1e-9;this.xScale=xSpan/this.width;this.xLogScale=(Math.log(this.xEnd)-Math.log(this.xStt))/this.width;var ySpan=this.yEnd-this.yStt;if(ySpan<=0)ySpan=1e-9;this.yScale=ySpan/this.height;this.yLogScale=(Math.log(this.yEnd)-Math.log(this.yStt))/this.height;if(this.uniScaleQ&&!this.xLogQ&&!this.yLogQ){var newScale=Math.max(this.xScale,this.yScale);this.xScale=newScale;xSpan=this.xScale*this.width;var xMid=(this.xStt+this.xEnd)/2;this.xStt=xMid-xSpan/2;this.xEnd=xMid+xSpan/2;this.yScale=newScale;ySpan=this.yScale*this.height;var yMid=(this.yStt+this.yEnd)/2;this.yStt=yMid-ySpan/2;this.yEnd=yMid+ySpan/2;}};Coords.prototype.scale=function(factor,xMid,yMid){if(typeof xMid=='undefined')xMid=(this.xStt+this.xEnd)/2;this.xStt=xMid-(xMid-this.xStt)*factor;this.xEnd=xMid+(this.xEnd-xMid)*factor;if(typeof yMid=='undefined')yMid=(this.yStt+this.yEnd)/2;this.yStt=yMid-(yMid-this.yStt)*factor;this.yEnd=yMid+(this.yEnd-yMid)*factor;this.calcScale();};Coords.prototype.drag=function(xPix,yPix){this.xStt+=xPix*this.xScale;this.xEnd+=xPix*this.xScale;this.yStt+=yPix*this.yScale;this.yEnd+=yPix*this.yScale;this.calcScale();};Coords.prototype.newCenter=function(x,y){var xMid=this.xStt+x*this.xScale;var xhalfspan=(this.xEnd-this.xStt)/2;this.xStt=xMid-xhalfspan;this.xEnd=xMid+xhalfspan;var yMid=this.yEnd-y*this.yScale;var yhalfspan=(this.yEnd-this.yStt)/2;this.yStt=yMid-yhalfspan;this.yEnd=yMid+yhalfspan;this.calcScale();};Coords.prototype.fitToPts=function(pts,borderFactor){for(var i=0;i<pts.length;i++){var pt=pts[i];if(i==0){this.xStt=pt.x;this.xEnd=pt.x;this.yStt=pt.y;this.yEnd=pt.y;}else{this.xStt=Math.min(this.xStt,pt.x);this.xEnd=Math.max(this.xEnd,pt.x);this.yStt=Math.min(this.yStt,pt.y);this.yEnd=Math.max(this.yEnd,pt.y);}}
var xMid=(this.xStt+this.xEnd)/2;var xhalfspan=borderFactor*(this.xEnd-this.xStt)/2;this.xStt=xMid-xhalfspan;this.xEnd=xMid+xhalfspan;var yMid=(this.yStt+this.yEnd)/2;var yhalfspan=borderFactor*(this.yEnd-this.yStt)/2;this.yStt=yMid-yhalfspan;this.yEnd=yMid+yhalfspan;this.calcScale();};Coords.prototype.toXPix=function(val,useCornerQ){if(this.xLogQ){return this.left+(Math.log(val)-Math.log(xStt))/this.xLogScale;}else{return this.left+((val-this.xStt)/this.xScale);}};Coords.prototype.toYPix=function(val){if(this.yLogQ){return this.top+(Math.log(yEnd)-Math.log(val))/this.yLogScale;}else{return this.top+((this.yEnd-val)/this.yScale);}};Coords.prototype.toPtVal=function(pt,useCornerQ){return new Pt(this.toXVal(pt.x,useCornerQ),this.toYVal(pt.y,useCornerQ));};Coords.prototype.toXVal=function(pix,useCornerQ){if(useCornerQ){return this.xStt+(pix-this.left)*this.xScale;}else{return this.xStt+pix*this.xScale;}};Coords.prototype.toYVal=function(pix,useCornerQ){if(useCornerQ){return this.yEnd-(pix-top)*this.yScale;}else{return this.yEnd-pix*this.yScale;}};Coords.prototype.getTicks=function(stt,span,ratio){var ticks=[];var inter=this.tickInterval(span/ratio,false);var tickStt=Math.ceil(stt/inter)*inter;var i=0;do{var tick=tickStt+i*inter;tick=Number(tick.toPrecision(8));ticks.push([tick,1]);i++;}while(tick<stt+span);inter=this.tickInterval(span/ratio,true);for(i=0;i<ticks.length;i++){var t=ticks[i][0];if(Math.abs(Math.round(t/inter)-(t/inter))<0.001){ticks[i][1]=0;}}
return ticks;};Coords.prototype.tickInterval=function(span,majorQ){var pow10=Math.pow(10,Math.floor(Math.log(span)*Math.LOG10E));var mantissa=span/pow10;if(mantissa>=3.6){if(majorQ){return(5*pow10);}else{return(1*pow10);}}
if(mantissa>=2.2){if(majorQ){return(2*pow10);}else{return(0.2*pow10);}}
if(mantissa>=1.3){if(majorQ){return(0.5*pow10);}else{return(0.2*pow10);}}
if(mantissa>=0.6){if(majorQ){return(0.5*pow10);}else{return(0.1*pow10);}}
if(majorQ){return(0.2*pow10);}else{return(0.1*pow10);}};function Graph(g,coords){this.g=g;this.coords=coords;this.xLinesQ=true;this.yLinesQ=true;this.xValsQ=true;this.yValsQ=true;this.skewQ=false;}
Graph.prototype.makeSVG=function(){this.hzAxisY=coords.toYPix(0);if(this.hzAxisY<0)this.hzAxisY=0;if(this.hzAxisY>coords.height)this.hzAxisY=coords.height;this.hzNumsY=this.hzAxisY+14;if(this.hzAxisY>coords.height-10)this.hzNumsY=coords.height-3;this.vtAxisX=coords.toXPix(0);if(this.vtAxisX<0)this.vtAxisX=0;if(this.vtAxisX>coords.width)this.vtAxisX=coords.width;this.vtNumsX=this.vtAxisX-5;if(this.vtAxisX<10)this.vtNumsX=20;my.svg.moveTo(coords.toXPix(coords.xStt,false),this.hzAxisY);my.svg.lineTo(coords.toXPix(coords.xEnd,false),this.hzAxisY);my.svg.moveTo(this.vtAxisX,coords.toYPix(coords.yStt,false));my.svg.lineTo(this.vtAxisX,coords.toYPix(coords.yEnd,false));}
Graph.prototype.drawGraph=function(){this.hzAxisY=coords.toYPix(0);if(this.hzAxisY<0)this.hzAxisY=0;if(this.hzAxisY>coords.height)this.hzAxisY=coords.height;this.hzNumsY=this.hzAxisY+14;if(this.hzAxisY>coords.height-10)this.hzNumsY=coords.height-3;this.vtAxisX=coords.toXPix(0);if(this.vtAxisX<0)this.vtAxisX=0;if(this.vtAxisX>coords.width)this.vtAxisX=coords.width;this.vtNumsX=this.vtAxisX-5;this.vtNumsAlign='right';if(this.vtAxisX<30){this.vtNumsX=this.vtAxisX+4;this.vtNumsAlign='left';if(this.vtAxisX<0){this.vtNumsX=6;}}
if(coords.xLogQ){this.drawLinesLogX();}else{if(this.xLinesQ){this.drawHzLines();}}
if(coords.yLogQ){this.drawLinesLogY();}else{if(this.yLinesQ){this.drawVtLines();}}};Graph.prototype.drawVtLines=function(){var g=this.g;g.lineWidth=1;var ticks=coords.getTicks(coords.xStt,coords.xEnd-coords.xStt,graphWd/100);for(var i=0;i<ticks.length;i++){var tick=ticks[i];var xVal=tick[0];var tickLevel=tick[1];if(tickLevel==0){g.strokeStyle="rgba(0,0,256,0.3)";}else{g.strokeStyle="rgba(0,0,256,0.1)";}
var xPix=coords.toXPix(xVal,false);g.beginPath();g.moveTo(xPix,coords.toYPix(coords.yStt,false));g.lineTo(xPix,coords.toYPix(coords.yEnd,false));g.stroke();if(tickLevel==0&&this.xValsQ){g.fillStyle="#0000ff";g.font="bold 12px Verdana";g.textAlign="center";g.fillText(xVal.toString(),xPix,this.hzNumsY);}}
if(this.skewQ)
return;g.lineWidth=1.5;g.strokeStyle="#ff0000";g.beginPath();g.moveTo(this.vtAxisX,coords.toYPix(coords.yStt,false));g.lineTo(this.vtAxisX,coords.toYPix(coords.yEnd,false));g.stroke();g.beginPath();g.fillStyle=g.strokeStyle;g.drawArrow(this.vtAxisX,coords.toYPix(coords.yEnd),15,2,20,10,Math.PI/2,10,false);g.stroke();g.fill();};Graph.prototype.drawHzLines=function(){var g=this.g;g.lineWidth=1;var ticks=coords.getTicks(coords.yStt,coords.yEnd-coords.yStt,graphHt/100);for(var i=0;i<ticks.length;i++){var tick=ticks[i];var yVal=tick[0];var tickLevel=tick[1];if(tickLevel==0){g.strokeStyle="rgba(0,0,256,0.3)";}else{g.strokeStyle="rgba(0,0,256,0.1)";}
var yPix=coords.toYPix(yVal,false);g.beginPath();g.moveTo(coords.toXPix(coords.xStt,false),yPix);g.lineTo(coords.toXPix(coords.xEnd,false),yPix);g.stroke();if(tickLevel==0&&this.yValsQ){g.fillStyle="#ff0000";g.font="bold 12px Verdana";g.textAlign=this.vtNumsAlign;g.fillText(yVal.toString(),this.vtNumsX,yPix+5);}}
if(this.skewQ)
return;g.lineWidth=2;g.strokeStyle="#0000ff";g.beginPath();g.moveTo(coords.toXPix(coords.xStt,false),this.hzAxisY);g.lineTo(coords.toXPix(coords.xEnd,false),this.hzAxisY);g.stroke();g.beginPath();g.fillStyle=g.strokeStyle;g.drawArrow(coords.toXPix(coords.xEnd,false),this.hzAxisY,15,2,20,10,0,10,false);g.stroke();g.fill();};function Parser(){this.operators="+-*(/),^.";this.rootNode;this.tempNode=[];this.Variable="x";this.errMsg="";this.radiansQ=true;this.vals=[];for(var i=0;i<26;i++){this.vals[i]=0;}
this.reset();}
Parser.prototype.setVarVal=function(varName,newVal){switch(varName){case "x":this.vals[23]=newVal;break;case "y":this.vals[24]=newVal;break;case "z":this.vals[25]=newVal;break;default:if(varName.length==1){this.vals[varName.charCodeAt(0)-'a'.charCodeAt(0)]=newVal;}}};Parser.prototype.getVal=function(){return(this.rootNode.walk(this.vals));};Parser.prototype.getSlope=function(dx){var x=this.vals[23];this.vals[23]=x-dx/2;var yLt=this.rootNode.walk(this.vals);this.vals[23]=x+dx/2;var yRt=this.rootNode.walk(this.vals);return(yRt-yLt)/dx;};Parser.prototype.newParse=function(s){this.reset();s=s.split(" ").join("");s=s.split("<22>").join("../index.html");s=s.split("[").join("(");s=s.split("]").join(")");s=s.replace(/\u2212/g,'-');s=s.replace(/\u00F7/g,'../index.html');s=s.replace(/\u00D7/g,'*');s=s.replace(/\u00B2/g,'^2');s=s.replace(/\u00B3/g,'^3');s=s.replace(/\u221a/g,'sqrt');s=this.fixParentheses(s);s=this.fixUnaryMinus(s);s=this.fixImplicitMultply(s);this.rootNode=this.parse(s);};Parser.prototype.fixParentheses=function(s){var sttParCount=0;var endParCount=0;for(var i=0;i<s.length;i++){if(s.charAt(i)=="(")sttParCount++;if(s.charAt(i)==")")endParCount++;}
while(sttParCount<endParCount){s="("+s;sttParCount++;}
while(endParCount<sttParCount){s+=")";endParCount++;}
return(s);};Parser.prototype.fixUnaryMinus=function(s){var x=s+"\n";var y="";var OpenQ=false;var prevType="(";var thisType="";for(var i=0;i<s.length;i++){var c=s.charAt(i);if(c>="0"&&c<="9"){thisType="N";}else{if(this.operators.indexOf(c)>=0){if(c=="-"){thisType="-";}else{thisType="O";}}else{if(c=="."||c==this.Variable){thisType="N";}else{thisType="C";}}
if(c=="("){thisType="(";}
if(c==")"){thisType=")";}}
x+=thisType;if(prevType=="("&&thisType=="-"){y+="0";}
if(OpenQ){switch(thisType){case "N":break;default:y+=")";OpenQ=false;}}
if(prevType=="O"&&thisType=="-"){y+="(0";OpenQ=true;}
y+=c;prevType=thisType;}
if(OpenQ){y+=")";OpenQ=false;}
return(y);};Parser.prototype.fixImplicitMultply=function(s){var x=s+"\n";var y="";var prevType="?";var prevName="";var thisType="?";var thisName="";for(var i=0;i<s.length;i++){var c=s.charAt(i);if(c>="0"&&c<="9"){thisType="N";}else{if(this.operators.indexOf(c)>=0){thisType="O";thisName="";}else{thisType="C";thisName+=c;}
if(c=="("){thisType="(";}
if(c==")"){thisType=")";}}
x+=thisType;if(prevType=="N"&&thisType=="C"){y+="*";thisName="";}
if(prevType=="N"&&thisType=="("){y+="*";}
if(prevType==")"&&thisType=="("){y+="*";}
if(thisType=="("){switch(prevName){case "i":case "pi":case "e":case "a":case this.Variable:y+="*";break;}}
y+=c;prevType=thisType;prevName=thisName;}
return(y);};Parser.prototype.reset=function(){this.tempNode=[];this.errMsg="";};Parser.prototype.parse=function(s){if(s==""){return new MathNode("real","0",this.radiansQ);}
if(isNumeric(s)){return new MathNode("real",s,this.radiansQ);}
if(s.charAt(0)=="$"){if(isNumeric(s.substr(1))){return this.tempNode[Number(s.substr(1))];}}
var sLo=s.toLowerCase();if(sLo.length==1){if(sLo>="a"&&sLo<="z"){return new MathNode("var",sLo,this.radiansQ);}}
switch(sLo){case "pi":return new MathNode("var",sLo,this.radiansQ);break;}
var bracStt=s.lastIndexOf("(");if(bracStt>-1){var bracEnd=s.indexOf(")",bracStt);if(bracEnd<0){this.errMsg+="Missing ')'\n";return new MathNode("real","0",this.radiansQ);}
var isParam=false;if(bracStt==0){isParam=false;}else{var prefix=s.substr(bracStt-1,1);isParam=this.operators.indexOf(prefix)<=-1;}
if(!isParam){this.tempNode.push(this.parse(s.substr(bracStt+1,bracEnd-bracStt-1)));return this.parse(s.substr(0,bracStt)+"$"+(this.tempNode.length-1).toString()+s.substr(bracEnd+1,s.length-bracEnd-1));}else{var startM=-1;for(var u=bracStt-1;u>-1;u--){var found=this.operators.indexOf(s.substr(u,1));if(found>-1){startM=u;break;}}
nnew=new MathNode("func",s.substr(startM+1,bracStt-1-startM),this.radiansQ);nnew.addchild(this.parse(s.substr(bracStt+1,bracEnd-bracStt-1)));this.tempNode.push(nnew);return this.parse(s.substr(0,startM+1)+"$"+(this.tempNode.length-1).toString()+s.substr(bracEnd+1,s.length-bracEnd-1));}}
var k;var k1=s.lastIndexOf("+");var k2=s.lastIndexOf("-");if(k1>-1||k2>-1){if(k1>k2){k=k1;var nnew=new MathNode("op","add",this.radiansQ);nnew.addchild(this.parse(s.substr(0,k)));nnew.addchild(this.parse(s.substr(k+1,s.length-k-1)));return nnew;}else{k=k2;nnew=new MathNode("op","sub",this.radiansQ);nnew.addchild(this.parse(s.substr(0,k)));nnew.addchild(this.parse(s.substr(k+1,s.length-k-1)));return nnew;}}
k1=s.lastIndexOf("*");k2=s.lastIndexOf("../index.html");if(k1>-1||k2>-1){if(k1>k2){k=k1;nnew=new MathNode("op","mult",this.radiansQ);nnew.addchild(this.parse(s.substr(0,k)));nnew.addchild(this.parse(s.substr(k+1,s.length-k-1)));return nnew;}else{k=k2;nnew=new MathNode("op","div",this.radiansQ);nnew.addchild(this.parse(s.substr(0,k)));nnew.addchild(this.parse(s.substr(k+1,s.length-k-1)));return nnew;}}
k=s.indexOf("^");if(k>-1){nnew=new MathNode("op","pow",this.radiansQ);nnew.addchild(this.parse(s.substr(0,k)));nnew.addchild(this.parse(s.substr(k+1,s.length-k-1)));return nnew;}
if(isNumeric(s)){return new MathNode("real",s,this.radiansQ);}else{if(s.length==0){return new MathNode("real","0",this.radiansQ);}else{this.errMsg+="'"+s+"' is not a number.\n";return new MathNode("real","0",this.radiansQ);}}};function MathNode(typ,val,radQ){this.tREAL=0;this.tVAR=1;this.tOP=2;this.tFUNC=3;this.radiansQ=true;this.setNew(typ,val,radQ);}
MathNode.prototype.setNew=function(typ,val,radQ){this.radiansQ=typeof radQ!=='undefined'?radQ:true;this.clear();switch(typ){case "real":this.typ=this.tREAL;this.r=Number(val);break;case "var":this.typ=this.tVAR;this.v=val;break;case "op":this.typ=this.tOP;this.op=val;break;case "func":this.typ=this.tFUNC;this.op=val;break;}
return(this);};MathNode.prototype.clear=function(){this.r=1;this.v="";this.op="";this.child=[];this.childCount=0;};MathNode.prototype.addchild=function(n){this.child.push(n);this.childCount++;return(this.child[this.child.length-1]);};MathNode.prototype.getLevelsHigh=function(){var lvl=0;for(var i=0;i<this.childCount;i++){lvl=Math.max(lvl,this.child[i].getLevelsHigh());}
return(lvl+1);};MathNode.prototype.isLeaf=function(){return(this.childCount==0);};MathNode.prototype.getLastBranch=function(){if(this.isLeaf()){return(null);}
for(var i=0;i<this.childCount;i++){if(!this.child[i].isLeaf()){return(this.child[i].getLastBranch());}}
return(this);};MathNode.prototype.fmt=function(htmlQ){htmlQ=typeof htmlQ!=='undefined'?htmlQ:true;var s="";if(this.typ==this.tOP){switch(this.op.toLowerCase()){case "add":s="+";break;case "sub":s=htmlQ?"&minus;":"-";break;case "mult":s=htmlQ?"&times;":"x";break;case "div":s=htmlQ?"&divide;":"/";break;case "pow":s="^";break;default:s=this.op;}}
if(this.typ==this.tREAL){s=this.r.toString();}
if(this.typ==this.tVAR){if(this.r==1){s=this.v;}else{if(this.r!=0){s=this.r+this.v;}}}
if(this.typ==this.tFUNC){s=this.op;}
return s;};MathNode.prototype.walkFmt=function(){var s=this.walkFmta(true,"");s=s.replace("Infinity","Undefined");return s;};MathNode.prototype.walkFmta=function(noparq,prevop){var s="";if(this.childCount>0){var parq=false;if(this.op=="add")parq=true;if(this.op=="sub")parq=true;if(prevop=="div")parq=true;if(noparq)parq=false;if(this.typ==this.tFUNC)parq=true;if(this.typ==this.tOP){}else{s+=this.fmt(true);}
if(parq)s+="(";for(var i=0;i<this.childCount;i++){if(this.typ==this.tOP&&i>0)s+=this.fmt();s+=this.child[i].walkFmta(false,this.op);if(this.typ==this.tFUNC||(parq&&i>0)){s+=")";}}}else{s+=this.fmt();if(prevop=="sin"||prevop=="cos"||prevop=="tan"){if(this.radiansQ){s+=" rad";}else{s+="&deg;";}}}
return s;};MathNode.prototype.walkNodesFmt=function(level){var s="";for(var i=0;i<level;i++){s+="|   ";}
s+=this.fmt();s+="\n";for(i=0;i<this.childCount;i++){s+=this.child[i].walkNodesFmt(level+1);}
return s;};MathNode.prototype.walk=function(vals){if(this.typ==this.tREAL)return(this.r);if(this.typ==this.tVAR){switch(this.v){case "x":return(vals[23]);break;case "y":return(vals[24]);break;case "z":return(vals[25]);break;case "pi":return(Math.PI);break;case "e":return(Math.exp(1));break;case "a":return(vals[0]);break;case "n":return(vals[13]);break;default:return(0);}}
if(this.typ==this.tOP){var val=0;for(var i=0;i<this.childCount;i++){var val2=0;if(this.child[i]!=null)
val2=this.child[i].walk(vals);if(i==0){val=val2;}else{switch(this.op){case "add":val+=val2;break;case "sub":val-=val2;break;case "mult":val*=val2;break;case "div":val/=val2;break;case "pow":if(val2==2){val=val*val;}else{val=Math.pow(val,val2);}
break;default:}}}
return val;}
if(this.typ==this.tFUNC){var lhs=this.child[0].walk(vals);var angleFact=1;if(!this.radiansQ)angleFact=180/Math.PI;switch(this.op){case "sin":val=Math.sin(lhs/angleFact);break;case "cos":val=Math.cos(lhs/angleFact);break;case "tan":val=Math.tan(lhs/angleFact);break;case "asin":val=Math.asin(lhs)*angleFact;break;case "acos":val=Math.acos(lhs)*angleFact;break;case "atan":val=Math.atan(lhs)*angleFact;break;case "sinh":val=(Math.exp(lhs)-Math.exp(-lhs))/2;break;case "cosh":val=(Math.exp(lhs)+Math.exp(-lhs))/2;break;case "tanh":val=(Math.exp(lhs)-Math.exp(-lhs))/(Math.exp(lhs)+Math.exp(-lhs));break;case "exp":val=Math.exp(lhs);break;case "log":val=Math.log(lhs)*Math.LOG10E;break;case "ln":val=Math.log(lhs);break;case "abs":val=Math.abs(lhs);break;case "deg":val=lhs*180./Math.PI;break;case "rad":val=lhs*Math.PI/180.;break;case "sign":if(lhs<0){val=-1;}else{val=1;}
break;case "sqrt":val=Math.sqrt(lhs);break;case "round":val=Math.round(lhs);break;case "int":val=Math.floor(lhs);break;case "floor":val=Math.floor(lhs);break;case "ceil":val=Math.ceil(lhs);break;case "fact":val=factorial(lhs);break;default:val=NaN;}
return val;}
return val;};function factorial(n){if(n<0)return NaN;if(n<2)return 1;n=n<<0;var i;i=n;var f=n;while(i-->2){f*=i;}
return f;}
function SVG(){this.lineWidth=1;this.lineClr='#000';this.lineAlpha='1';this.fillClr='#def';this.fillAlpha='0.2';this.inLineQ=false;this.inGroupQ=false;this.line=[];this.txt='';this.ftrStr="</svg>";this.txt=this.getHeader();}
SVG.prototype.getHeader=function(){var s="";s+='<?xml version=\"1.0\" standalone=\"no\"?>\n';s+='<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">\n';s+='<svg width="1000px" height="600px" xmlns="http://www.w3.org/2000/svg">\n';s+="<desc>SVG Output</desc>\n";return s;};SVG.prototype.lineStyle=function(thick,clr,alpha){if(thick==0)thick=0.2;this.lineWidth=thick;this.lineClr=clr;};SVG.prototype.beginFill=function(clr,alpha){fillClr=clr;};SVG.prototype.endFill=function(){};SVG.prototype.moveTo=function(x,y){if(this.line.length>1)this.polyline();this.line.push([x,y]);};SVG.prototype.lineTo=function(x,y){this.line.push([x,y]);};SVG.prototype.drawRect=function(x,y,width,height){txt+='<rect x="'+x+'px" y="'+y+'px" width="'+width+'px" height="'+height+'px" style="'+getStyle()+'"/>';};SVG.prototype.drawText=function(x,y,text,rotate){txt+='<text x="'+x+'px" y="'+y+'px" style="'+getFontStyle()+'" transform="rotate('+rotate+' '+x+' '+y+')" '+'>';txt+=text;txt+="</text>";};SVG.prototype.getStyle=function(){var s="";s+="opacity:1;fill:#"+fillClr.toString(16)+";fill-opacity:1;fill-rule:nonzero;";s+="stroke:#"+lineClr.toString(16)+"; stroke-width:"+lineWidth.toString()+"; stroke-linecap:butt; stroke-linejoin:miter; stroke-opacity:1; visibility:visible;";return(s);};SVG.prototype.getFontStyle=function(){var s="";s+="font-size:30px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;";s+="text-align:start; line-height:100.00000381%;";s+="opacity:1; fill:#0000ff; fill-opacity:1; fill-rule:nonzero; stroke:none;";s+="visibility:visible;display:inline;font-family:Komika Text;";return(s);};SVG.prototype.polyline=function(){var s="";s+="<polyline points='";for(var i=0;i<this.line.length;i++){var pt=this.line[i];s+=pt[0].toPrecision(5);s+=" ";s+=pt[1].toPrecision(5);s+=", ";}
s+="' ";clrText='0000ff';s+="stroke-width='"+this.lineWidth.toString()+"' stroke='"+this.lineClr+"' fill='"+this.fillClr+"' ";s+=" />";s+="\n";this.txt+=s;this.line=[];};SVG.prototype.polygon=function(line){var s="";s+="<polygon points='";for(var i=0;i<line.length;i++){if(i>0)s+=", ";var pt=line[i];s+=pt.x.toPrecision(5);s+=" ";s+=pt.y.toPrecision(5);}
s+="' ";s+=this.getStyle();s+=" />";s+="\n";this.txt+=s;};SVG.prototype.getStyle=function(){s='';s+="stroke-width='"+this.lineWidth+"' ";s+="stroke='"+this.lineClr+"' ";s+="fill='"+this.fillClr+"' ";s+="fill-opacity='"+this.fillAlpha+"' ";return s;};SVG.prototype.group=function(id){if(inGroupQ){txt+="</g>\n";}
txt+="<g id='"+id+"'>";inGroupQ=true;};SVG.prototype.getText=function(){if(this.line.length>1)this.polyline();if(this.inGroupQ){this.txt+="</g>\n";}
return(this.txt+this.ftrStr);};function isNumeric(n){return!isNaN(parseFloat(n))&&isFinite(n);}
CanvasRenderingContext2D.prototype.drawArrow=function(x0,y0,totLen,shaftHt,headLen,headHt,angle,sweep,invertQ){var g=this;var pts=[[0,0],[-headLen,-headHt/2],[-headLen+sweep,-shaftHt/2],[-totLen,-shaftHt/2],[-totLen,shaftHt/2],[-headLen+sweep,shaftHt/2],[-headLen,headHt/2],[0,0]];if(invertQ){pts.push([0,-headHt/2],[-totLen,-headHt/2],[-totLen,headHt/2],[0,headHt/2]);}
for(var i=0;i<pts.length;i++){var cosa=Math.cos(-angle);var sina=Math.sin(-angle);var xPos=pts[i][0]*cosa+pts[i][1]*sina;var yPos=pts[i][0]*sina-pts[i][1]*cosa;if(i==0){g.moveTo(x0+xPos,y0+yPos);}else{g.lineTo(x0+xPos,y0+yPos);}}};function getQueryVariable(variable){var query=window.location.search.substring(1);var vars=query.split("&");for(var i=0;i<vars.length;i++){var pair=vars[i].split("=");if(pair[0]==variable){return pair[1];}}
return false;}
function dist(dx,dy){return(Math.sqrt(dx*dx+dy*dy));}