// ***************** COPYRIGHT (c) 2009 STEFAN WANER ******************
// *********************** ALL RIGHTS RESERVED ************************
// *** IT ALSO REMAINS TO DO THE TOPMATTER
// Globals
// window.onerror = myErrorTrap;
var windowcropTally = 20;
// will not cut a window in half if more than this number of
// pixels pop out of range as a result
var autoY = true;
var autoGridline = true;
var okToRoll = true;
var theString = "";
var theFunction = ""; // the function
var xGridLines = new Array(); // these are screen coordinates
var yGridLines = new Array();
var xGridLinesActual = new Array(); // these are actual coordinates
var yGridLinesActual = new Array();
// var lineColor = 2; // red
// var lineColorLite = lineColor + 7;
var tminVals = new Array();
var tmaxVals = new Array();
var arraysize = 0; // number of functions
var xArraysize = 0; // number of x-values in evalautor
var maxnum = 5; // max number of functions allowed
var maxnumX = 12; // max number of x-values allowed
var theValues = new makeArray2(maxnumX, maxnum); // copy of evalauator data
var fracMode = false; // fraction mode off default
var numSigDigs = 5; // rounding of y-values default
var maxDenom = 99999;
// ***** Error Messages
if (theLanguage == "en") {
var enterXMinMsg = "You have not entered a number for xMin.";
var enterXMaxMsg = "You have not entered a number for xMax.";
var maxLtMinMsg = "xMax should be greater than xMin";
var maxyLtMinMsg = "yMax should be greater than yMin";
var yMinMsg = "Enter a number for yMin or check 'Auto'.";
var yMaxMsg = "Enter a number for yMax or check 'Auto'.";
var enterSmthgMsg = "You must enter at least one function to graph or one point to plot.";
var enterXMsg = "You must enter at least one value of x.";
var numSigDigMsg = "The Number of Significant Digits must be a number. I am setting it back to 5. Change it to another number if you like.";
}
else {
var enterXMinMsg = "No ha ingresado un numero para xMin.";
var enterXMaxMsg = "No ha ingresado un numero para xMax.";
var maxLtMinMsg = "xMax debe ser mas grande que xMin";
var maxyLtMinMsg = "yMax debe ser mas grande que yMin";
var yMinMsg = "Ingrese numero para yMin o marque 'Auto'.";
var yMaxMsg = "Ingrese numero para yMax o marque 'Auto'.";
var enterSmthgMsg = "Debe ingresar al menos una funcion o un punto para trazar.";
var enterXMsg = "Debe ingresar al menos un valor de x.";
var numSigDigMsg = "El numero de digitos significados debe ser un numero. Estoy cambiando su valor a 5. Puede cambiarlo a un otro numero si quiere.";
}
// ** end error messages
// *** end globals
// *** Error Handler ******
function myErrorTrap(message,url,linenumber) {
alert("It looks like you have entered something wrongly (or perhaps need to use an older version). Press 'Show Examples' to see examples of how to format functions.");
return (true);
} // end of on error
// ********************
// **********Utilities to read in the functions *********
// ********************************************************************
function setUp(){
okToRoll = true;
with(Math){
//Step 1: read the inputs into an array and decide
// how many points there are
var thexCellName = ""; // these are strings to names x1, x2,..
var theInstruction = ""; // a javascript instuction
var doIt = 0; // a dummy variable
//Step 2: Fill the y arrays with the functions
for (var i = 1; i <= maxnum; i++) {
theInstruction = "yVals["+i+"] = stripSpaces(document.theFormA.y"+i+".value);";
doIt = eval(theInstruction);
// now take special steps for derivatives
if ((yVals[i]).substring(0,5) == "deriv") {
var theLength = (yVals[i]).length;
var theDerivArg = (yVals[i]).substring(6,theLength-1);
if (theDerivArg.charAt(0) == "y") {
var theIndex = parseInt(theDerivArg.charAt(1));
if (theIndex < i) yVals[i] = stringDeriv(yVals[theIndex]);
} // is a "yi"
else yVals[i] = stringDeriv((yVals[i]).substring(6,theLength-1));
// alert(yVals[i]);
} // if a derivative
// alert(yVals[i]);
// alert(i);
} // i
// Step 3: Compute how many functions there are
arraysize = maxnum;
// alert(arraysize);
for (i = 1; i <= maxnum; i++) {
if (yVals[i] == "") {
// alert(i);
arraysize = i-1;
i = maxnum}
} // i
} //with math
// Step 4: Read in textarea points
readInTextarea();
if ((arraysize == 0)&&(!plottingPoints)) {alert(enterSmthgMsg); okToRoll = false}
} // setup
// ***********************************************************************
// ************** End of Reading-in Parametric Equations Utility ******
// ***********************************************************************
// ***********************************************************************
// ************** Evaluator Setup Routine ******
// ***********************************************************************
function setUp2() {
okToRoll = true;
var aaa = setUp(); // read in the functions
fracMode = document.theFormC.fracModeButton.checked;
if(!fracMode) {
numSigDigs = document.theFormC.acc.value;
if (isBad(numSigDigs)) {alert(numSigDigMsg); okToRoll = false}
} // if not fraction mode
// Now read in the x-values
with(Math){
//Step 1: read the inputs into an array and decide
// how many points there are
var thexCellName = ""; // these are strings to names x1, x2,..
var theInstruction = ""; // a javascript instuction
var doIt = 0; // a dummy variable
//Step 2: Fill the x array with the x-values
// Note: at this point theywill all be strings
for (var i = 1; i <= maxnumX; i++) {
theInstruction = "xVals["+i+"] = stripSpaces(document.theFormC.x"+i+".value);"
doIt = eval(theInstruction);
} // i
// Step 3: Compute how many functions there are
for (i = 1; i <= maxnumX; i++) {
if (xVals[i] == "") {
xArraysize = i-1;
break
} // encountered blank
} // i
if (xArraysize == 0) {alert(enterXMsg); okToRoll = false}
// alert(xArraysize);
} //with Math
} // end of function setUp2
// ***********************************************************************
// ************** End of Evaluator Setup Routine ******
// ***********************************************************************
// ***********************************************************************
// ************** Evaluate all Routine ******
// ***********************************************************************
function evaluateAll() {
// This evaluates all the functions in nthe table
// we have arraysize many functions and xArraysize many values of x
var theStrg = ""; // a dummy string for parsed functions
var theInstruction = ""; // a javascript instuction
var doIt = 0; // a dummy action
// First clear the current y-values
for (var i = 1; i <= maxnum; i++) {
for (var j = 1; j <= maxnumX; j++) {
theInstruction = "document.theFormC.y"+i+"x"+j+".value = ''";
doIt = eval(theInstruction)
} // j
} // i
// Now Compute the values
for (var j = 1; j <= arraysize; j++) {
theStrg = myParse(yVals[j]);
for (var i = 1; i <= xArraysize; i++) {
x = myEval(xVals[i]); // in case there are inputs like "sin(3)"
y = checkEval(theStrg);
if (y > infinity) y = "infinity";
else if (y < -infinity) y = "-infinity";
if (!fracMode) theInstruction = "document.theFormC.y"+j+"x"+i+".value = roundSigDig(y,numSigDigs)";
else theInstruction = "document.theFormC.y"+j+"x"+i+".value = toFrac(y, maxDenom)";
doIt = eval(theInstruction);
// alert(theInstruction);
} // end i
} // end j
} // end of evaluateAll
// ***********************************************************************
// ************** End of Evaluate all Routine ******
// ***********************************************************************
// **************** Plot All Curves ********************
function readAndPlotCurves(theGraph){
// alert(a + " , " + b + " , " + c + " , " + d);
var theyString = "";
var thexMin = 0;
var thexMax = 0;
var colorNumber = 0;
var theGraphArray = new(Array);
// alert(arraysize);
for (var i = 1; i <= arraysize; i++) {
theyString = yVals[i];
theGraphArray [i-1] = [theyString, theGraph.window[0], theGraph.window[1]];
} // i
theGraph.plottedCurves = theGraphArray;
// alert(theGraphArray);
setUpGraph(theGraph);
// alert(myGraph.yGridStep);
plotAllCurves(theGraph);
// alert("here");
// now the plotted points
var pointsX = new(Array);
var pointsY = new(Array);
pointsX[0] = 0; pointsY[0] = 0;
for (var i = 1; i <= numPoints; i++) {
pointsX[i] = thePlottedPoints[i][1];
pointsY[i] = thePlottedPoints[i][2]
} // i points
theGraph.plottedPointsX = pointsX;
theGraph.plottedPointsY = pointsY;
plotPoints(theGraph, "x", false, "")
} // end of plot
// ******************End of Plot All Curves ***********
// ******** Refreshing Graph During Trace *************
// *** refresh graph
function refreshGraph(theGraph) {
setUpGraph(theGraph);
plotAllCurves(theGraph);
plotPoints(theGraph, "x", false, "");
} // refreshGraph
// *********** Tracing arrows on graphs **************
function addTraceArrows(theGraph) {
var theStr = ' ';
document.writeln(theStr);
}
// *********** Recalling Values **************
function rememberValues() {
if (document.theFormC.y1x1.value != "") {
var theInstruction = ""; // a javascript instuction
var doIt = 0; // a dummy variable
for (var i = 1; i <= maxnumX; i++) {
for (var j = 0; j <= maxnum; j++) {
if (j > 0) theInstruction = " theValues[i][j] = document.theFormC.y"+j+"x"+i+".value";
else theInstruction = " theValues[i][j] = document.theFormC.x"+i+".value";
doIt = eval(theInstruction);
} // j
} // i
} // IF THERE IS SOMETHING IN THE FIRST CELL
} // remember values
function bringBackValues() {
if (document.theFormC.y1x1.value == "") {
var theInstruction = ""; // a javascript instuction
var doIt = 0; // a dummy variable
for (var i = 1; i <= maxnumX; i++) {
for (var j = 0; j <= maxnum; j++) {
if (j > 0) theInstruction = " document.theFormC.y"+j+"x"+i+".value = theValues[i][j]";
else theInstruction = " document.theFormC.x"+i+".value = theValues[i][j]";
doIt = eval(theInstruction);
} // j
} // i
} // if there is nothing in the first cell
} // remember values
// ********* Added Routines and globals for Plotting Points
var plottingPoints = false;
var tab = unescape( "%09" );
var cr = unescape( "%0D" );
var lf = unescape( "%0A" );
var semicolon = unescape( '%3B' );
var comma = ",";
var textareaText = '';
var maxNumPoints = 100;
var numPoints = 0;
var thePlottedPoints = new makeArray2(maxNumPoints,2);
var yMaxPoints = 0;
var yMinPoints = 0;
var xHeight = 5; // height of the plotted Xs
function rememberValuesPoints() {
if (stripSpaces(document.theFormP.thePoints.value) != '')
textareaText = document.theFormP.thePoints.value;
} // remember values
function restoreValuesPoints() {
if (stripSpaces(document.theFormP.thePoints.value) == '')
document.theFormP.thePoints.value = textareaText;
} // restore values
function readInTextarea() {
// reads in points and calculates maximum and minimum y coords
var theString = document.theFormP.thePoints.value;
theString = stripSpaces(theString);
theString = replaceChar(theString,comma,tab);
theString = replaceChar(theString,semicolon,cr);
theString = replaceChar(theString,lf,cr);
// now get rid of strings of more than one tab and one cr's in a row
var doubletab = true; var doublecr = true;
while ( (doubletab) || (doublecr) )
{
if (checkString(theString,tab+tab,false) == -1) doubletab = false;
else theString = replaceSubstring(theString,tab+tab,tab);
if (checkString(theString,cr+cr,false) == -1) doublecr = false;
else theString = replaceSubstring(theString,cr+cr,cr);
} // while
theString = replaceSubstring(theString,tab+cr,cr); // get rid of tab + crs
var xyPoints = parser(theString,cr);
var thePoint = new Array;
numPoints = xyPoints[0];
if (theString.indexOf(tab) == -1) numPoints = 0;
if (numPoints > 0) {
plottingPoints = true;
for (var i = 1; i <= numPoints; i++) {
thePoint = parser(xyPoints[i], tab);
thePlottedPoints[i][1] = parseFloat(thePoint[1]);
thePlottedPoints[i][2] = parseFloat(thePoint[2]);
} // i
// now compute y max and min for these
yMaxPoints = thePlottedPoints[1][2];
yMinPoints = yMaxPoints;
for (var i = 1; i <= numPoints; i++) {
try
{
if (thePlottedPoints[i][2] > yMaxPoints) yMaxPoints = thePlottedPoints[i][2];
else if (thePlottedPoints[i][2] < yMinPoints) yMinPoints = thePlottedPoints[i][2];
}
catch (error)
{
}
} // i
// alert("numPOints = " + numPoints + " ; yMax = " + yMaxPoints + " ; yMin = "+ yMinPoints);
// now scale up a bit so that not on the edge
yMinPoints -= .1*Math.abs(yMinPoints);
yMaxPoints += .1*Math.abs(yMaxPoints);
} // if more than 0 points
else plottingPoints = false;
} // readInTextarea
var basicsRead = false;
function readBasics(theGraph) {
// alert("here");
var theStrg = ""; // dummy string for evaluating functions
autoY = document.theFormB.autoYButton.checked;
autoGridline = document.theFormB.autoGridButton.checked;
// get the graph window information
for (var k = 1; k <= 1; k++)
{
var aa = document.theFormB.a.value;
// alert(aa);
if (aa == "") { alert(enterXMinMsg); okToRoll = false; break;}
//alert(aa);
a = myEval(aa);
if (isNaN(a) ) { alert(enterXMinMsg); okToRoll = false; break;}
var bb = document.theFormB.b.value;
if (bb == "") { alert(enterXMaxMsg); okToRoll = false; break}
b = myEval(bb);
if (isNaN(b) ) { alert(enterXMaxMsg); okToRoll = false; break;}
if ( (okToRoll) && (a >= b)) { alert(maxLtMinMsg); okToRoll = false; break;}
var ppcTest = document.theFormB.ppc.value;
if (isNaN(ppcTest) || (ppcTest == '') ) document.theFormB.ppc.value = 1000;
else myGraph.pointsPerCurve = parseInt(ppcTest);
if(!autoY) {
// alert("Here autoY is off");
var cc = document.theFormB.c.value;
if (cc == "") { alert(yMinMsg); okToRoll = false; break}
c = myEval(cc);
if (isNaN(c) ) { alert(yMinMsg); okToRoll = false; break;}
var dd = document.theFormB.d.value;
if (dd == "") { alert(yMaxMsg); okToRoll = false; break}
d = myEval(dd);
if (isNaN(d) ) { alert(yMaxMsg); okToRoll = false; break;}
if ( (okToRoll) && (c >= d)) { alert(maxyLtMinMsg); okToRoll = false; break;}
// alert(a + " , " + b + " , " + c + " , " + d);
} // end of if autoY
else {
document.theFormB.c.value = ''; // cannnot have it both ways
document.theFormB.d.value = '';
// Must compute ymin and ymax here
var deltax = (b-a)/theGraph.numX;
// alert(deltax);
var maxy = 0;
var miny = 0;
var firstCheck = true;
for (var j = 1; j <= arraysize; j++) {
theStrg = myParse(yVals[j]);
for (var i = 0; i <= theGraph.numX; i++)
{
x = a + i*deltax;
// alert("x = " + x);
y = checkEval(theStrg);
if (!isNaN(y) &&( y < infinity) && (y > -infinity))
{
// alert ("y = " + y);
if (firstCheck)
{
firstCheck = false;
maxy = y;
miny = y
}
if (y > maxy) maxy = y;
else if (y < miny) miny = y;
} // end of if y is a legit number
} // i
// alert(miny);
} // j
// alert("miny = "+miny + "maxy =" + maxy);
// Now cut down the size of the window if necessary
// in the case of graphs shooting off to infinity
// the texhnique is to eliminate "outliers" by cropping
// the window.
// *** Why don't we just compute the st deviation and crop to +- 3s
var cutting_down = true;
var invisible_tally = 0;
var maxSteps = 10, steppes = 0;
while ((cutting_down) && (steppes < maxSteps))
{
steppes ++;
maxy = maxy/2;
miny = miny/2;
invisible_tally = 0;
for (var j = 1; j <= arraysize; j++) {
theStrg = myParse(yVals[j]);
for (var i = 0; i <= theGraph.numX; i++)
{
x = a + i*deltax;
y = checkEval(theStrg);
if (!isNaN(y) &&( y < infinity) && (y > -infinity))
{
if ((y > maxy) || (y < miny))
{
invisible_tally++;
if (invisible_tally > windowcropTally)
{
cutting_down = false;
maxy = 2*maxy;
miny = 2*miny;
i = theGraph.numX;
break;
} // too many invisible;
} // if y > ymax
} // if is a number
} // i
} // j
// by the end of this cutting_down had better be false;
} // while cutting_down
// alert("miny = "+miny + "maxy =" + maxy);
if (miny == maxy) {miny = miny-1; maxy += 1}
// ** following two lines added for plotting points
if (plottingPoints) {
if (yMaxPoints > maxy) maxy = yMaxPoints;
if (yMinPoints < miny) miny = yMinPoints;
}
var scalefactor = 150/(maxy - miny);
// ************
// end of y min and ymax window coords
// ************
c = eval(roundSigDigUpDown (miny,4, false)); // sets the globals
d = eval(roundSigDigUpDown (maxy,4, true));
} // end of else for autoY
// alert("c = " + c + " d = " + d);
// At this point we have the globals a, b, c, d we need
myGraph.window[0] = a;
myGraph.window[1] = b;
myGraph.window[2] = c;
myGraph.window[3] = d;
theGraph.xTicsRange = [];
theGraph.yTicsRange = [];
if(!autoGridline) {
var xk = document.theFormB.xg.value;
if (xk == "") myGraph.xGridStep = 0;
else myGraph.xGridStep = eval(xk);
var yk = document.theFormB.yg.value;
if (yk == "") myGraph.yGridStep = 0;
else myGraph.yGridStep = eval(yk);
} // end of if not autoGridline
else {
document.theFormB.xg.value = '';
document.theFormB.yg.value = ''; // cannnot have it both ways.
var pq = (b-a)/10;
myGraph.xGridStep = pq;
pq = pq = (d-c)/10;
myGraph.yGridStep = pq;
} // end of else for autoGridline
} // end of single loop (k)
if (okToRoll) basicsRead = true;
// now set up tracing parameters
if (okToRoll) {
theGraph.traceStep = roundSigDig((b-a)/theGraph.numX,4);
var theLog = Math.log(abs(theGraph.traceStep))/Math.log(10);
theGraph.decPlacesX = -Math.round(theLog)+1;
var theYInterval = (d-c)/theGraph.numX
theLog = Math.log(abs(theYInterval))/Math.log(10);
theGraph.decPlacesY = -Math.round(theLog)+1;
}
//alert(myGraph.yGridStep);
} // readBasics
function makeArray2 (X,Y)
{
var count;
this.length = X+1;
for (var count = 1; count <= X+1; count++)
// to allow starting at 1
this[count] = new makeArray(Y);
} // makeArray2
function makeArray (Y)
{
var count;
this.length = Y+1;
for (var count = 1; count <= Y+1; count++)
this[count] = 0;
} // makeArray
// ************* miscellaneous fixes
// this cleans up the lower boundary in case of curves tha overshoot
function cleanUp(theGraph) {
with(theGraph) {
if (surroundColor == "white") ctx.fillStyle = "rgb(255, 255, 255)";
else ctx.fillStyle = "rgb(" + surroundColor [0] + "," + surroundColor [1] + "," + surroundColor [2] + ")";
// alert(" " + theGraph.yLabelMargin + ", " + (theGraph.numY-1) + ", " + theGraph.numX+ theGraph.yLabelMargin+ ", " + 10);
ctx.fillRect(theGraph.yLabelMargin, theGraph.numY-1, theGraph.numX+ theGraph.yLabelMargin, 10);
} // with theGraph
} // cleanUp