## Monday, 21 August 2017

### Trigonometric functions and integrals with Js and Canvas

This article will look into displaying trigonometric functions with Javascript and HTML5 Canvas.

A plunk is availble so you can test out different trigonometric functions in Javascript yourself. The following link gives you access to the demo:

Plunk Integral of functions using HTML 5 Canvas and Js
The form input of the demo first asks for an equation to display. Supported here is the format that the Math.Js library supports. You can use for example f(x) = sin(x). I have tested it out with 2D functions supporting one variable x. The drop down lets you choose some prefilled equations for you to test out. The different trigonometric functions supported are the usual ones, also the hyperbolic and arc hyperbolic ones can be tested out, plus some polynomial functions and so on. The Math.Js library will build up a function delegate that can be used in the calculation of the integral and the calculation of the function curve itself.

### Further issues around asymptotic behavior

One thing I have seen is that the calculation of the integral fails to detect asymptotic boundary conditions. For example, the tangens function $$f(x) = tan(x)$$ has got several asymptotes vertically. These asymptotes occur at the following x-values: $$\frac{\pi}{2} * (2n+1)$$ for the natural numbers $$\mathbb{N}$$. Detecting such asymptotes can be very hard, since you have to first decide when a function becomes asymptotic, and you also have to test the function at specific intervals and narrow it down. The Riemann sum as an approximation of the integral will fail for such as asymptotic functions. I use the Midpoint rule in an easy manner here by using the average or middle point of the incrment and look at the function value right there. You could also calculate $$f(x)$$ at the minimum and maximum part of the increment and average the two function values instead of calculating the function value at the middle point. One other way is to set the increment at a very low value.
You can also test this out yourself! Try setting the increment to a very low value, like 0.00001! You will see that the integral keeps growing as you lower the increment value. This is because small increments for the Riemann sum will more and more find the true integral of the tagens function in this case.
If you are a math student and have good tips here, I would be happy to know more about the strategy around integrals and Riemann sums to deal with asymptotes!

## Saturday, 19 August 2017

### Integrals in math with Javascript

This article will describe a demo how to calculate and display definite integrals in a web browser using the HTML 5 <Canvas> element and demonstrate an approximation of integrals using the method of summing up the rectangles between a function curve and the x-axis, that is the equation under consideration to do the calculation of the definite integral on. The integral is defined as the area between the function curve and the x-axis.
Note that we in this demo will consider equations on the form of polynomial curves.
The picture reads integration, it should be integrals! Lets first look some math of how to do the integral of our example, we consider polynomials here, which will be defined as:
$$y = f(x) = ax^3 + bx^2 + cx + d$$ The integral will be the areal between the function f(x) between startx and endx. Consider the following definition of the indefinite integral: $$\int f(x)\ dx$$ The definite area is then between startx s and endx e is then: $$\int_s^e f(x)dx$$ Some math ensues of to check the calculation of the integral (area), consider this following example :
$$a = 0.05, b = 0.05, c = 0.05, d = 1$$. We consider x to be between 1 and 4. Manually calculating the area results in the calculated area of 7.614 (the image shows 7.62, but a check showed it to be 7.614).
Calculation of the integral uses in the hand written calculation the start and end x-values and subtracting the end value of the integral formula with the start value. We consider x here to be between [1..4]. As the screen shot of the demo displays, we approximate this integral to the value 7.60 by calculating the integral as the sum of the midpoint rectangles.

The difference in the specific example between the hand written calculation of 7.62 (exact integral) and approximation of 7.60 is because of the fact that we approximate the integral by summing up the rectangles below the curve. Actually in some cases part of the rectangles are above the curve, there is some discrepancy between the approximate rectangle shape and the true shape of the integral. To get an even more exact value, reducing the increment from 0.5 to 0.25 will get a closer value to the exact one. Reducing the increments will result in smaller rectangles (thinner) following the curve more exact.

Now that we see that our math is sound, we can look at a Plunk with a demo displaying this.
Math integral demo - Plunk
In the sample the graph is displayed with Canvas in HTML 5. The following function in Javascript is used to display the integral and the midpoint rectangles:


Graph.prototype.drawPolynomial = function(polynomialequation, a, b, c, d,
increment, isIntegral, color, thickness, startx, endx){

var totalArea = 0.0;

var context = this.context;
context.save();
context.save();
this.transformContext();

context.beginPath();
context.moveTo(this.minX, polynomialequation(a, b, c, d, this.minX));

for(var x = this.minX + this.iteration; x <= this.maxX; x += this.iteration) {
context.lineTo(x, polynomialequation(a, b, c, d, x));
}

context.restore();
context.lineJoin = 'round';
context.lineWidth = thickness;
context.strokeStyle = color;
context.stroke();
context.restore();

if (isIntegral){
var context = this.context;
context.save();
this.transformContext();

var currentY = 0.0;

context.lineWidth = 0.1;
context.strokeStyle = 'red';

for(var x = startx; x < endx; x += increment) {
context.beginPath();
currentY = polynomialequation(a, b, c, d, (x+increment/2.0));
context.rect(x, 0, increment, currentY);
totalArea += increment * currentY;
context.stroke();
}

}

}



The following code is used to get the values for the coefficients of the polynomial equation and draw the polynomial function and the corresponding approximation rectangles for the integral.



$(document).ready(function(){$("#btnDemo").click(function(){

$("#a").val("0.05");$("#b").val("0.05");
$("#c").val("0.05");$("#d").val("1");
$("#increment").val("0.25");$("#startx").val("1.0");
$("#endx").val("4.0");$("#btnGraph").click();

});

$("#btnGraph").click(function(){ var a,b,c,d,increment,startx,endx = 0; a = parseFloat($("#a").val());
b = parseFloat($("#b").val()); c = parseFloat($("#c").val());
d = parseFloat($("#d").val()); increment = parseFloat($("#increment").val());
startx = parseFloat($("#startx").val()); endx = parseFloat($("#endx").val());

var myGraph = new Graph({
canvasId: 'Graph',
minX: -10,
minY: -10,
maxX: 10,
maxY: 10,
unitsPerTick: 1
});

var totalArea = myGraph.drawPolynomial(function(a,b,c,d,x){
return ((a*x*x*x) + (b * x*x) +  c*x + d * 1.0).toFixed(2);
}, a, b, c, d, increment, true, 'blue', 1.0,  startx, endx);

$("#detailsInfo").append("Total area under graph: " + totalArea); }); });  There is a lot of code to digest here, see through the code in the Plunk the article points to. The key points here is that we pass in a function as a delegate to be our Polynomial equation. We also approximate the integral (area) by summing up the rectangles below it. ### Note that this demo also supports calculating the integral when it dips below the positive y axis! ### Fix of reloading functionality One issue with Canvas and a central one is the fact that the Canvas in HTML 5 is a rasterized grid. It is more like a single layer Photoshop image than a vectorized canvas like Illustrator. With that fact in mind, clearing the Canvas for a new redrawing functionality proved hard. In addition, I also use a transformation here from View-Coordinates to Object-Coordinates. A brute force redrawing is therefore preferred. The following ReloadCanvas method will fix this!  function ReloadCanvas(canvasId){ //debugger; var oldCanvas = document.getElementById(canvasId); console.log("Old canvas: " + oldCanvas); var newCanvas = document.createElement('canvas'); var oldWidth = 500; var oldHeight = 500; if (oldCanvas){ oldWidth = oldCanvas.width; oldHeight = oldCanvas.height; oldCanvas.parentNode.removeChild(oldCanvas); } newCanvas.id = 'Graph'; newCanvas.width = oldHeight; newCanvas.height = oldWidth; document.body.appendChild(newCanvas); }  We detach the old canvas and insert a new one into the DOM (Document Object Model). I use here old api methods, you could also resort to more use of jQuery of course. Note that I try to get the old Canvas width and height and copy this to the new blank Canvas that I insert. You must use parentNode here to to the appendChild and removeChild methods to do the replacement of Canvas. This way, we can paint the Canvas again with a fresh new Canvas and have a simpler demo! I have updated the Plunk with a fixed Fork below: Plunk - Integral math demo app This demo also supports not only a convenient reload method to make the demo easier to test out, but also supports "negative integrals", i.e. sections where the integral dips below the x-axis as shown in the following image: ### Note about accuracy The total area calculated uses some rounding here. I used the .toFixed(2) to stick to a precision of 0.01. You can try out .toFixed(3) to test out a better precision. That will calculate even more precise the calculated area. The increments should of course be small and you will also see that some small values are still imprecise. We calculate the y value to be the midpoint of the polynomial f(x) and the midpoint should follow the curve as good as possible. Actually this integral demo app can support other equations that just polynomials. We could support for example trigonometric functions and so on also. I will look at this in a future demo+article! So there you have it, Canvas and Js can tutor kids and students math concepts in Calculus quite elegant in a web browser. We are seeing that Javascript and HTML 5 are now just as powerful as Java applets in the good old days to describe different concepts and prove that once again Math is fun, especially when computers also come into play! ## Note for students What we have used in this demo is the calculation of definite integrals using the Midpoint Rule and Riemann sum. You can read more about it here. This is standard 1st year Calculus syllabus. Riemann Sums (Wikipedia) ## Monday, 7 August 2017 ### Finding intersection between two lines with HTML5 and Javascript This article will look at detecting intersection of two lines using Javascript and using HTML 5 Canvas to display the two lines. A plunk is available here: Plunk - Intersection of two lines We continue from the last article and add a LineIntersection function and add prototype functions. This "class" will help us find the intersection points. The code is as follows:  function LineIntersection (config){ this.m1 = config.m1; this.b1 = config.b1; this.m2 = config.m2; this.b2 = config.b2; this.error = 0; this.marginOfError = 0.01; this.iterations = 0; this.maxIterations = 200; } LineIntersection.prototype.PrintData = function() { console.clear(); console.log("m1: " + this.m1 + " b1: " + this.b1 + " m2: " + this.m2 + " b2: " + this.b2); } LineIntersection.prototype.GetGuess = function(guess){ var newguess = ((this.b2 - this.b1) / (this.m1 - this.m2) + guess) / 2; return newguess; } LineIntersection.prototype.Y1 = function (guess){ return this.m1 * guess + this.b1; } LineIntersection.prototype.Y2 = function (guess){ return this.m2 * guess + this.b2; } LineIntersection.prototype.DeltaY = function (guess){ return Math.abs(this.Y1(guess) - this.Y2(guess)); } LineIntersection.prototype.FindIntersection = function(){ this.iterations = 0; if (this.m1 == this.m2) { alert("The two lines are parallel!"); return { x: "Infinity", y: "Infinity"}; } guess = Math.floor(Math.random() * 10 + 1); do { guess = this.GetGuess(guess); this.error = this.DeltaY(guess); if (this.iterations > this.maxIterations){ break; this.iterations = this.iterations + 1; } } while (this.error > this.marginOfError); return { x: guess.toFixed(2), y: this.Y1(guess).toFixed(2) } } //function LineIntersection  The intersection point is then calculated using the code in the following jQuery button click event handler: $("#btnIntercept").click(function(){
var m1,b1,m2,b2 = 0;

m1 = parseFloat($("#m1").val()); b1 = parseFloat($("#b1").val());
m2 = parseFloat($("#m2").val()); b2 = parseFloat($("#b2").val());

var myGraph = new Graph({
canvasId: 'Graph',
minX: -10,
minY: -10,
maxX: 10,
maxY: 10,
unitsPerTick: 1
});

myGraph.drawLine(m1, b1, 'blue', 3);

myGraph.drawLine(m2, b2, 'red', 4);

var lineIntersect = new LineIntersection({
m1: m1,
b1: b1,
m2: m2,
b2: b2
});

lineIntersect.PrintData();

var intersect = lineIntersect.FindIntersection();
console.log(intersect);
console.log(intersect.x);

myGraph.drawRect(intersect.x, intersect.y, 0.5, 0.5);

$("#detailsInfo").append("Intersection point: " + " X: " + intersect.x + " Y: " + intersect.y);  To plot a dot where the calculated intersection point the following code is used:  Graph.prototype.drawRect = function (x, y, width, height){ var context = this.context; this.transformContext(); context.strokeStyle = 'green'; context.fillRect(x - (width/2), y - (height/2), width, height); }  To move from object space coordinates to display coordinates we make use of the following helper function:  Graph.prototype.transformContext = function() { var context = this.context; // move context to center of canvas this.context.translate(this.centerX, this.centerY); /* * stretch grid to fit the canvas window, and * invert the y scale so that that increments * as you move upwards */ context.scale(this.scaleX, -this.scaleY); };  ## Sunday, 6 August 2017 ### Drawing intercepting lines with HTML 5 and Js - Part One I am working with a sample demo that will draw two lines and calculate the intersection. The demo will use Js and HTML 5 Canvas. I have made a Plunk available here: Canvas line drawing Plunk The image belows shows a rendering of two lines on the form :  y = f(x) = ax + b, y1 = x + 1, y2 = -x + 3  The HTML and Js code is below. I will in the later articles focus on calculating the interception with an iterative approximation method for the intercept. In a future article I will clean up the code and I will look on the code bits and look at Canvas functionality. Here is the code:  <!DOCTYPE html> <html> <head> <meta charset="UTF-8" /> <script data-require="jquery@*" data-semver="3.1.1" src="https://ajax.googleapis.com/ajax/libs/jquery/3.1.1/jquery.min.js"></script> <link data-require="bootstrap-css@*" data-semver="4.0.0-alpha.4" rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0-alpha.4/css/bootstrap.min.css" /> <link rel="stylesheet" href="style.css" /> <script src="script.js"></script> </head> <body> <h1>Intersection of two lines with Canvas and Js </h1> <fieldset> <label>y = mx + b</label> <br /><br /> <table> <tr> <td> <label for="m1">m1:</label> <input id="m1" type="text" style="width:50px" /></td> <td> <label for="b1">b1:</label> <input id="b1" type="text" style="width:50px" /></td> <td> <label for="slope2">m2:</label> <input id="m2" type="text" style="width:50px" /></td> <td> <label for="b2">b2:</label> <input id="b2" type="text" style="width:50px" /></td> </tr> <tr> <td><input id="btnGraph" type="button" value="Draw line" /></td> </tr> </table> <br /> <h3>Graph</h3> <canvas id="Graph" style="background:aliceblue;border:1px solid #AFAFAF" width="600" height="600"></canvas> </fieldset> <script> function Graph(config) { // user defined properties this.canvas = document.getElementById(config.canvasId); this.minX = config.minX; this.minY = config.minY; this.maxX = config.maxX; this.maxY = config.maxY; this.unitsPerTick = config.unitsPerTick; // constants this.axisColor = '#aaa'; this.font = '8pt Calibri'; this.tickSize = 20; // relationships this.context = this.canvas.getContext('2d'); this.rangeX = this.maxX - this.minX; this.rangeY = this.maxY - this.minY; this.unitX = this.canvas.width / this.rangeX; this.unitY = this.canvas.height / this.rangeY; this.centerY = Math.round(Math.abs(this.minY / this.rangeY) * this.canvas.height); this.centerX = Math.round(Math.abs(this.minX / this.rangeX) * this.canvas.width); this.iteration = (this.maxX - this.minX) / 1000; this.scaleX = this.canvas.width / this.rangeX; this.scaleY = this.canvas.height / this.rangeY; // draw x and y axis this.drawXAxis(); this.drawYAxis(); } Graph.prototype.drawXAxis = function() { var context = this.context; context.save(); context.beginPath(); context.moveTo(0, this.centerY); context.lineTo(this.canvas.width, this.centerY); context.strokeStyle = this.axisColor; context.lineWidth = 2; context.stroke(); // draw tick marks var xPosIncrement = this.unitsPerTick * this.unitX; var xPos, unit; context.font = this.font; context.textAlign = 'center'; context.textBaseline = 'top'; // draw left tick marks xPos = this.centerX - xPosIncrement; unit = -1 * this.unitsPerTick; while(xPos > 0) { context.moveTo(xPos, this.centerY - this.tickSize / 2); context.lineTo(xPos, this.centerY + this.tickSize / 2); context.stroke(); context.fillText(unit, xPos, this.centerY + this.tickSize / 2 + 3); unit -= this.unitsPerTick; xPos = Math.round(xPos - xPosIncrement); } // draw right tick marks xPos = this.centerX + xPosIncrement; unit = this.unitsPerTick; while(xPos < this.canvas.width) { context.moveTo(xPos, this.centerY - this.tickSize / 2); context.lineTo(xPos, this.centerY + this.tickSize / 2); context.stroke(); context.fillText(unit, xPos, this.centerY + this.tickSize / 2 + 3); unit += this.unitsPerTick; xPos = Math.round(xPos + xPosIncrement); } context.restore(); }; Graph.prototype.drawYAxis = function() { var context = this.context; context.save(); context.beginPath(); context.moveTo(this.centerX, 0); context.lineTo(this.centerX, this.canvas.height); context.strokeStyle = this.axisColor; context.lineWidth = 2; context.stroke(); // draw tick marks var yPosIncrement = this.unitsPerTick * this.unitY; var yPos, unit; context.font = this.font; context.textAlign = 'right'; context.textBaseline = 'middle'; // draw top tick marks yPos = this.centerY - yPosIncrement; unit = this.unitsPerTick; while(yPos > 0) { context.moveTo(this.centerX - this.tickSize / 2, yPos); context.lineTo(this.centerX + this.tickSize / 2, yPos); context.stroke(); context.fillText(unit, this.centerX - this.tickSize / 2 - 3, yPos); unit += this.unitsPerTick; yPos = Math.round(yPos - yPosIncrement); } // draw bottom tick marks yPos = this.centerY + yPosIncrement; unit = -1 * this.unitsPerTick; while(yPos < this.canvas.height) { context.moveTo(this.centerX - this.tickSize / 2, yPos); context.lineTo(this.centerX + this.tickSize / 2, yPos); context.stroke(); context.fillText(unit, this.centerX - this.tickSize / 2 - 3, yPos); unit -= this.unitsPerTick; yPos = Math.round(yPos + yPosIncrement); } context.restore(); }; Graph.prototype.drawEquation = function(equation, color, thickness) { var context = this.context; context.save(); context.save(); this.transformContext(); context.beginPath(); context.moveTo(this.minX, equation(this.minX)); for(var x = this.minX + this.iteration; x <= this.maxX; x += this.iteration) { context.lineTo(x, equation(x)); } context.restore(); context.lineJoin = 'round'; context.lineWidth = thickness; context.strokeStyle = color; context.stroke(); context.restore(); }; Graph.prototype.drawLine = function(slope, yintercept, color, thickness) { console.log("Inside drawline"); console.log("this.maxX: " + this.maxX + " this.maxY: " + this.maxY); var context = this.context; // draw x and y axis this.drawXAxis(); this.drawYAxis(); //context.clearRect(0, 0, this.canvas.width, this.canvas.height); context.save(); context.save(); this.transformContext(); console.log("this.minX: " + this.minX); console.log("this.iteration: " + this.iteration); console.log("yintercept: " + yintercept); console.log("slope:" + slope); context.beginPath(); context.moveTo(this.minX, slope * this.minX + yintercept); for(var x = this.minX + this.iteration; x <= this.maxX; x += this.iteration) { if (this.iteration % 200 == 0){ console.log("x: " + x + " y: " + (slope * x + yintercept)); } context.lineTo(x, slope * x + yintercept); } context.restore(); context.lineJoin = 'round'; context.lineWidth = thickness; context.strokeStyle = color; context.stroke(); context.restore(); }; Graph.prototype.transformContext = function() { var context = this.context; // move context to center of canvas this.context.translate(this.centerX, this.centerY); /* * stretch grid to fit the canvas window, and * invert the y scale so that that increments * as you move upwards */ context.scale(this.scaleX, -this.scaleY); }; </script> <script>$(document).ready(function(){

$("#btnGraph").click(function(){ var m1,b1,m2,b2 = 0; m1 = parseFloat($("#m1").val());
b1 = parseFloat($("#b1").val()); m2 = parseFloat($("#m2").val());
b2 = parseFloat($("#b2").val()); var myGraph = new Graph({ canvasId: 'Graph', minX: -10, minY: -10, maxX: 10, maxY: 10, unitsPerTick: 1 }); myGraph.drawLine(m1, b1, 'blue', 3); myGraph.drawLine(m2, b2, 'red', 4); //myGraph.drawEquation(function(x) { //return 1 * x; //}, 'red', 3); }); }); </script> </body> </html>  ## Wednesday, 2 August 2017 ### Calculating the square root in Javascript using the Babylonian method Calculating the square root in Javascript is easily done using Math.sqrt(n). But it can be entertaining to use an approximation method instead and build up an algorithm to calculate the square root. We will use the Babylonian method to approximate the square root using an iterative approximation method. The Babylonian method is described in Wikipedia here: Babylonian method. The following image shows how each step of a revised value for the square root is calculated. We calculate the square root of S by using an inital guess and then revise that step by adding that guess with S divided by the guess and dividing by 2. The revised value is then used again as the new guess value. We stop iterating when the margin of error is below a given treshold. In the calculus, x is the step guess value and e is the error. We start the calculation sample by adding in Bootstrap CSS and jQuery.  <!DOCTYPE html> <html> <head> <meta charset="utf-8" /> <script data-require="jquery@*" data-semver="3.1.1" src="https://ajax.googleapis.com/ajax/libs/jquery/3.1.1/jquery.min.js"></script> <link data-require="bootstrap-css@*" data-semver="4.0.0-alpha.4" rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0-alpha.4/css/bootstrap.min.css" /> </head> <body> <br /> <div class="container"> <h2>Find square root in JS with long division algorithm</h2> <hr /> <!-- html code here --> <h3>Estimate Square Root</h3> Enter Number: <input id="num" value="700" size="2" type="text" /> <br /> <input id="submitButton" value="Calculate" type="submit" /> <br /> <br /> <div id="details"></div> </div> <script type="text/javascript"> "use strict"; var x = 25; var guess = 9; var marginOfError = 0.1; var error = 0; var counter = 0; var htmlout = "";$(document).ready(function() {
// function code goes here
function getGuess(g) {
console.log(g);
var newguess = (g + x / g) / 2;
return newguess;
}
$('#submitButton').click(function() { // JavaScript code here console.clear(); counter = 0; x = parseFloat($('#num').val());
guess = Math.floor(Math.random() * x + 1);
error = Math.abs(guess * guess - x);
while (error >= marginOfError) {
guess = getGuess(guess)
error = Math.abs(guess * guess - x);
//console.log(guess);
counter += 1;
}
console.log('Count is ' + counter)
htmlout = "Square Root is " + guess.toFixed(2) + ". It took " + counter + " guesses";
$('#details').html(htmlout); }); }); </script> </body> </html>  Let us clean up the code using classes in Ecmascript 6 (ES6) and use Traceur to support the ES6 syntax.  <!DOCTYPE html> <html> <head> <meta charset="utf-8" /> <script src="https://google.github.io/traceur-compiler/bin/traceur.js"></script> <script src="https://google.github.io/traceur-compiler/bin/BrowserSystem.js"></script> <script src="https://google.github.io/traceur-compiler/src/bootstrap.js"></script> <script data-require="jquery@*" data-semver="3.1.1" src="https://ajax.googleapis.com/ajax/libs/jquery/3.1.1/jquery.min.js"></script> <link data-require="bootstrap-css@*" data-semver="4.0.0-alpha.4" rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0-alpha.4/css/bootstrap.min.css" /> </head> <body> <br /> <div class="container"> <h2>Find square root in JS with long division algorithm</h2> <hr /> <!-- html code here --> <h3>Estimate Square Root</h3> Enter Number: <input id="num" value="700" size="2" type="text" /> <br /> <input id="submitButton" value="Calculate" type="submit" /> <br /> <br /> <div id="details"></div> </div> <script type="text/javascript"> "use strict"; class BabylonianSquareRootSolver { constructor(x_0, S, marginOfError = 0.1){ this.S = S; this.x_0 = x_0; this.marginOfError = marginOfError; } getRevisedSquareRoot (x_n, S){ var revisedValue = (x_n + (S/x_n)) / 2; return revisedValue; } calculateSqrt(){ var counter = 0; var error = 0; var guess = this.x_0; error = Math.abs(this.x_0 * this.x_0 - S); while (error >= marginOfError) { guess = this.getRevisedSquareRoot(guess, this.S) error = Math.abs(guess * guess - this.S); console.log(guess); counter += 1; if (counter > 10) break; } var result = { S : this.S, error : error, iterations : counter, root : guess }; return result; } } var S = 1; var guess = Math.floor(Math.random()*S); var marginOfError = 0.1; var error = 0; var counter = 0; var htmlout = "";$(document).ready(function() {
// function code goes here

$('#submitButton').click(function() { // JavaScript code here console.clear(); counter = 0; S = parseFloat($('#num').val());
guess = Math.floor(Math.random()*S);
var bab = new BabylonianSquareRootSolver(guess, S);

console.log(bab);
var res = bab.calculateSqrt();
htmlout = "Square Root is approximated to " + res.root.toFixed(2) + ". It took " + res.iterations
+ " iterations. The error for this approximation is: " + res.error.toFixed(4);
$('#details').html(htmlout); console.log(bab.calculateSqrt()); }); }); </script> </body> </html>  You can test out the code yourself with the following Plunk: Babylonian method - Plunk Here is an image of the GUI: ## Monday, 17 July 2017 ### Promises in ES6 for async operations This article will present a new feature in ES6 which is the Promise object. This object will ease the burden of programming async operations in Javascript. In classic JS building up multiple asynchronous operations has been cumbersome and there is a lot of ceremony to catch exception. This article will describe some simple uses of Promise(s) and provide some code examples. I will use Plunkr as an editor and Traceur to support ES6 Javascript code. Traceur is a library to provide the necessary ES6 polyfills and shims to allow using ES6 JS code in browsers, regardless of their lacking support of ES6. Of course, more and more browsers support different functionality in ES6 already. I will also use Jasmine to test out these Promise(s) using Test Driven Development (TDD) library Jasmine. First off, we need to add in Traceur and Jasmine. I also include jQuery here. You might want to include these libraries with a local copy and not through a Content Delivery Network (CDN). Add first this to your HTML code:  <!DOCTYPE html> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link data-require="jasmine@2.4.1" data-semver="2.4.1" rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/jasmine/2.4.1/jasmine.css" /> <script data-require="jasmine@2.4.1" data-semver="2.4.1" src="https://cdnjs.cloudflare.com/ajax/libs/jasmine/2.4.1/jasmine.js"></script> <script data-require="jasmine@2.4.1" data-semver="2.4.1" src="https://cdnjs.cloudflare.com/ajax/libs/jasmine/2.4.1/jasmine-html.js"></script> <script data-require="jasmine@2.4.1" data-semver="2.4.1" src="https://cdnjs.cloudflare.com/ajax/libs/jasmine/2.4.1/boot.js"></script> <script src="https://google.github.io/traceur-compiler/bin/traceur.js"></script> <script src="https://google.github.io/traceur-compiler/bin/BrowserSystem.js"></script> <script src="https://google.github.io/traceur-compiler/src/bootstrap.js"></script> <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script> </head>  After adding in the necessary HTML code we will make use of Jasmine. We also create a simple helper function to return a Promise object to a function that returns a Promise object.  function getPromise(value, delay){ return new Promise(resolve => { setTimeout(() => resolve(value), delay); }); } describe("Promises in Ecmascript 6", function(){ it("should execute Promise.race with expected result", function (done){ let promise1 = getPromise('value: 1', 350); let promise2 = getPromise('value: 2', 450); let promise3 = getPromise('value: 3', 550); let fastestPromise = Promise.race([promise1, promise2, promise3 ]); // console.log(fastestPromise); fastestPromise.then(result => { expect(result).toBe('value: 1'); done(); }); //then }); //it }); //describe  We use the built in functionality of Jasmine to test out and wait for asynchronous code to complete, passing into the SPEC function (the function named it) the parameter of done. By calling done(); we signal to Jasmin that the asynchronous code should have completed. Jasmin will wait for a specified time and signal a timeout if it does receive the result from the asynchronous operation. We also here use ES6 arrow functions in the setTimeout method for compact syntax and we use setTimeout to simulate an easy asynchronous operation. Then we build up three Promises by calling the method getPromise. We then use the static method Promise.race which will on a given array of Promise objects return the quickest result. This is in behavior similar to the .WaitAny method in C# Task Parallel Library (TPL) for the happy .Net coders out there. Moving on, we use the .then method on the Promise.race object (which is a Promise itself) and we use Jasmin's expect method (Similar to Assert in NUnit) and expect that the quickest method "won" the race, since it was the function with the shortest delay passed into the method getPromise and its call to setTimout. The Promise object in ES6 will be further built upon in ES2017. Here, the await keywords will be added and make Javascript functional asynchronous programming more syntax-like and operational/behavior like much of that in .Net. Most important, Promises in ES6 makes asynchronous programming and its necessary passing of callbacks and error catching much easier by allowing the programmer to chain multiple asynchronous operations and build asynchronous APIs. Multiple Promises can be passed in, chaining multiple Promises and "paths" of asynchronous operations and multiple async operations can be catched in a single or multiple common error handler with the .catch for error handling and the .then for the chained success function. You can experiment yourself with the code above using Traceur and Jasmin. I have included a Plunk at the following url: ES 6 Promises Plunk sample code Important - Note that inside an asynchronous operation we must signal that the async operation is completed. We use the resolve method or static Promise.resolve method to do that. We can also reject the success of the async operation by using the reject method or static Promise.rejec. The call to done(); is because we use Jasmin as previously described and to support async operations inside a Jasmin TDD spec. Let us also look at another type of Promises, chaining multiple Promises. We use the Promise.resolve method to build up Promises. ## Wednesday, 12 July 2017 ### Using ES6 Generators to implement Where Skip Take This article will present the use of ES6 Generators to implement in Javascript some handy functions for collections (arrays) that can filter and limit the size of that result. The technique will use the new ES6 generator functions. ES6 Generators are functions of Ecmascript 6 that let's the programmer take control of iterators using the yield keyword and use custom logic. We will use Traceur to support ES6 syntax. Traceur is a Javascript compiler in the form of a library. In production you should instead use a transpiler, that rewrites your ES6 syntax into ES2015, which is more supported by current web browsers. One transpiler is Babel. First off we include Traceur into the Html code:  <!DOCTYPE html> <html lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"/> <script src="https://google.github.io/traceur-compiler/bin/traceur.js"></script> <script src="https://google.github.io/traceur-compiler/bin/BrowserSystem.js"></script> <script src="https://google.github.io/traceur-compiler/src/bootstrap.js"></script> <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script> </head> <body bgcolor="teal" style="font-family:Verdana, Courier,Helvetica, Arial"> <h1 style="color:yellow;font-family:Arial">ES6 module demo</h1>  We now have the compiler loaded into our HTML page and can make use of ES6 Generator functions and other ES6 syntax. First lets look at the WHERE function in Javascript. Think of it as WHERE in Linq, we will also use ES6 Arrow functions here, which is an important functional programming concept and syntax that ES6 introduces.  <script type="text/javascript"> var where = function* (predicate, collection){ for (let item of collection){ if (predicate(item)){ yield item; } } }  We assign where here to the function defined at the right hand side. Note the asterisk (star) here. This is what a generator function looks like in ES6. It must not be mixed with function pointers as in C++, the star here is just to separate generator functions with ordinary functions. On a operational level, generator functions are just like iterators in C# that hey hand off control from the function to the program that calls the functions. Generator functions are usually used in iteration loops, which will be seen later on in this article. The where function passes in a predicate (an arrow function that returns a boolean which is true or false of course) and if that predicate on the current item of the collection is true, yield will return that item. The sample also uses the of operator of the collection passed in. Next off, let us look at the take function. This function will take a desired number of the result set and end iteration early if a result set is found. On a very large collection, this is very efficient. Imagine searching a huge collection for a desired item defined by an arrow function and exit early if for example one item is found. Then take(1, mycoll) will return control to the calling program when that item is found.  var take = function* (size, collection){ if (size < 1) return; let count = 0; for (let item of collection){ yield item; count = count + 1; if (count >= size){ return; } } }  Make note that we end the looping here by doing a return when the amount of items return is the desired size specified. Next off, let us look at the Skip function. We could do a reserve on the passed in collection, and use the take function. Instead the Skip method will use tailored logic to iterate on the passed in collection from start to finish, skipping the specified number of items first.  var skip = function* (size, collection){ let skippedItems = 0; for (let item of collection){ skippedItems = skippedItems + 1; //console.log(item); //console.log(skippedItems); if (skippedItems <= size){ continue; } else { yield item; } } }  The sample HTML code below tests out the JS code above using ES6 arrow functions and ES 6 generator functions on a simple array and looping through with our new powerful functional programming constructs that let us search even huge collections with filtering and skipping or taking the desired result.  var coll = [ "Tammy", "Tom", "Betty", "Marge", "Joey", "Tim", "Jane", "Tommy" ]; //console.log(coll); for (let i of take(2, where(n => n.startsWith("T"),coll))){$("body").append("<li>" + i + "</li>");
}


Next off, we will combing all the uses of WHERE, SKIP and TAKE to both filter and provide paging functionality. Consider this code:


var coll = [ "Tammy", "Tom", "Betty", "Marge", "Joey", "Tim", "Jane", "Tommy" ];

console.log(coll);

let pageSize = 1;
let pageIndex = 1;

for (let i of take(pageSize, skip(pageIndex*pageSize, where(n => n.startsWith("T"),coll)))) {
$("body").append("<li>" + i + "</li>"); }  Here we use the following to get a PAGE of our result by using the formula: PAGE_INDEX = TAKE(PAGE_SIZE) of (SKIP(PAGE_INDEX * PAGESIZE) of COLLECTION WHERE Predicate(x)). It is impressive that we can implement Linq like functionality by using ES6 Generator functions in ES6 sticking to ES6 syntax. This promises that Javascript in the future will be a very versatile language when it comes to functional programming. We use Traceur in the meantime to support ES6 syntax in different web browsers. I have included a Plunk in the link below so that you can test this out yourself. ES6 Generator functional programming sample ## Saturday, 8 July 2017 ### Ecmascript 6 Modules in Javascript Javascript is a programming (or scripting) language known for its wide use. It is mature by the fact that it is used for many years since its creation in the mid 90s. But at the same time Javascript or just JS is immature by the fact that it lacks a lot of features built into the language. This is an observed by the large number of different libraries to add features to JS that programmers using other programming languages take for granted. For example, modules and classes are not something easy to create with JS. The good thing is that JS is finally evolving in large steps now with Ecmascript 6 or ES6 with a common standard that many browsers vendors can agree upon. There are different ways to run JS code with ES6 features. One can use a transpiler such as Babel that will rewrite the JS code with ES6 scripts into to compatible ES2015 syntax which more browsers support. Or one can use a javascript library that contains polyfills and fills to support ES6 code in browsers. The sample code in this article has been tested with Internet Explorer 11 and is available as a Plunk. The following url contains the running demo: Plunk with ES6 modules First in this sample a class called Employee is created. This uses ES6 new class feature.  export class Employee { constructor (name) { //console.log("Constructor of Employee"); this._name = name; } get name() { return this._name; } doWork(){ return ${this.name} is working;
}
}


ES6 classes can export a class and then be imported in other classes and build up modules. The employee class also uses ES6 template string feature. Note that the backtick quote is used and ${..} is used to refer to variables. The next class then imports the Employee class. Note that you must change url here to match your Plunk in the running editor to adjust the session url that Plunkr uses to give unique urls. ES6 can support static urls of course.  import {Employee} from "http://run.plnkr.co/gIljKiTbjZ0IOX8b/Employee.js" export class Company { hire(...names) { this.employees = names.map(n => new Employee(n)); } doWork(){ console.log(this.employees);$("body").append("<ul>");
for (let e of this.employees){
console.log(e);
$("body").append(<li style='list-style-type:circle'>${e.doWork()} + "</li>");
}
\$("body").append(">/ul<");
return 1;
}
}


Again the class keyword is used to define a class and then exported to be used in another class or module with the export keyword. To import the Employee class the import keyword. The Company class above uses the rest operator (...) to allow passing in an arbitrary number of elements. Then the map operator built into Arrays in ES6 is used to return a mapped array. The use of the let operator is used and also the of operator of iterable collections.
Finally the sample HTML code below is used to define the use of an ES6 module. Here the script tag with the tag module is used.


<!DOCTYPE html>
<html lang="en">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>

<body bgcolor="teal" style="font-family:Verdana, Courier,Helvetica, Arial">

<h1 style="color:yellow;font-family:Arial">ES6 module demo</h1>
<script type="module">
import {Company} from "http://localhost/babeldemo/src/Company.js"
var c = new Company();
c.hire("Tim", "Tom", "Betty", "Maggie");
c.doWork();
</script>

</body>
</html>


Note that Traceur is a good option to test out ES6 features. In production, using a transpiler such as Babel to create a ES2015 compatible JS code is probably much better since there is a performance cost with Traceur. The reason Traceur is used in this sample is to show how an old browser such as Internet Explorer 11 can run ES6 code with a Javascript library such as Traceur.

To see a compatibility matrix of which browsers supports which ES6, see the Kangax table at the following url:
https://kangax.github.io/compat-table/es6/
With the help of Traceur more browsers can run more feature of ES6 and you can test out and use ES6 in your development or production environments and structure your code with classes and modules for example. Make note that the current state of Javascript module loaders of browsers will be improved in the future. Until then, additional frameworks such as AMD or Require.Js can be used to support module loading in more complex scenarios.

## Sunday, 14 May 2017

### Redis Image Cache Provider

Caching images in web sites and web applications is possible to achieve using many methods. This article presents an image cache provider to use in MVC applications using Redis as a caching server.

First off, create a new MVC web application and add the Nuget package RedisImageCacher (created by me):
RedisImageCacher

 Install-Package RedisImageCacher 

This Nuget package will also add in the dependencies for libraries ServiceStack.Redis and Microsoft.Web.RedisOutputCacheProvider.

Next off, one will need a Redis server. It is possible to install a local Redis server in Windows using the binaries here:

Redis 2.6 Windows (32/64 bits) on GitHub from MSOpenTech.

ASP.NET and Redis

Download Redis 2.6 and start it up on your local developer box. Start the server from a command-line for example :

 C:\redis26\redis-server 

Start a Redis client also from the commandline e.g. :
 C:\redis26\redis-cli 

  <caching>
<outputCache defaultProvider="MyRedisOutputCache">
<providers>
<!-- Either use 'connectionString' and provide all parameters as string OR use 'host','port','accessKey','ssl','connectionTimeoutInMilliseconds' and 'operationTimeoutInMilliseconds'. -->
<!-- 'databaseId' and 'applicationName' can be used with both options. -->
<!--
host = "127.0.0.1" [String]
port = "" [number]
accessKey = "" [String]
ssl = "false" [true|false]
databaseId = "0" [number]
applicationName = "" [String]
connectionTimeoutInMilliseconds = "5000" [number]
operationTimeoutInMilliseconds = "1000" [number]
connectionString = "<Valid StackExchange.Redis connection string>" [String]
loggingClassName = "<Assembly qualified class name that contains logging method specified below>" [String]
loggingMethodName = "<Logging method should be defined in loggingClass. It should be public, static, does not take any parameters and should have a return type of System.IO.TextWriter.>" [String]
/>
-->
<!-- For more details check https://github.com/Azure/aspnet-redis-providers/wiki -->
<!-- Either use 'connectionString' OR 'settingsClassName' and 'settingsMethodName' OR use 'host','port','accessKey','ssl','connectionTimeoutInMilliseconds' and 'operationTimeoutInMilliseconds'. -->
<!-- 'databaseId' and 'applicationName' can be used with both options. -->
<!--
host = "127.0.0.1" [String]
port = "" [number]
accessKey = "" [String]
ssl = "false" [true|false]
databaseId = "0" [number]
applicationName = "" [String]
connectionTimeoutInMilliseconds = "5000" [number]
operationTimeoutInMilliseconds = "1000" [number]
connectionString = "<Valid StackExchange.Redis connection string>" [String]
settingsClassName = "<Assembly qualified class name that contains settings method specified below. Which basically return 'connectionString' value>" [String]
settingsMethodName = "<Settings method should be defined in settingsClass. It should be public, static, does not take any parameters and should have a return type of 'String', which is basically 'connectionString' value.>" [String]
loggingClassName = "<Assembly qualified class name that contains logging method specified below>" [String]
loggingMethodName = "<Logging method should be defined in loggingClass. It should be public, static, does not take any parameters and should have a return type of System.IO.TextWriter.>" [String]
redisSerializerType = "<Assembly qualified class name that implements Microsoft.Web.Redis.ISerializer>" [String]
/> -->
<add name="MyRedisOutputCache" type="Microsoft.Web.Redis.RedisOutputCacheProvider" host="localhost" accessKey="" applicationName="RedisCache" port="6379" ssl="false" />
</providers>
</outputCache>
</caching>



It is also possible to control how long time Image Data is to be kept in the cache in seconds. In web.config:
  <add key="RedisImageCacheTimeout" value="10" />



This sets a timeout of caching image data to 10 seconds for example. It is possible to change this of course, using 600 will cache image data for 10 minutes for example.

To cache an image, the following razor code show an example of its use:
 <img src="@Url.Action("ShowImage", "Images", new { id = Url.Encode("Croatia6-jpg") })" width="500" />

Using the syntax "filename"-"extension" like "myfile1-jpg" and using the embedded controller ImageController and action method ShowImage will also cache the image to Redis. A parameter of id is provided to the file to cache and load or retrieve from cache directly. This will be taken care of by the embedded images controller in the library. It is possible to use different image file formats, such as JPG, GIF, PNG and BMP.

Inside redis-cli Redis Client we can see that loading the image in the example will add a cache item in Redis:
 redis 127.0.0.1:6379> keys * 1) "RedisCache/IMAGEBANK/Content/Images/Croatia6.jpg" 

 Note that images must be put into the Content/Images folder of your MVC solution! A configuration of changing this can be added later to the library. We can also ask Redis how long the cache item will exist until it expires and is removed by using TTL (Time-To-Live): redis 127.0.0.1:6379> ttl "RedisCache/IMAGEBANK/Content/Images/Croatia6.jpg" (integer) 2 

Note that TTL will show -1 if the cache item is expired. Redis client got many other handful commands to control the Redis memory cache, see Redis documentation here: Redis documentation The way the RedisImageCacher is saving data is actually done very generic and can be extended to support other data and cache this. For implementation details, see: ASP.NET and Redis

RedisImageCacher Bitbucket repo

Or if you have Mercurial (hg) installed, from a command-line issue:
 hg clone https://bitbucket.org/toreaurstad/redisimagecacher 

## Friday, 14 April 2017

### AsyncStateMachine in .NET

This article will present a custom AsyncStateMachine that shows how it is possible to create as async awaitable state machine manually. Let's first consider an easy async-await example and implement it using a custom async state machine instead of the default one in .NET. The purpose is to glance more into the inner workings of async. The following code is what is going to be implemented.

class Program
{
static void Main(string[] args)
{
try
{
CallFooAsync();
}
catch (AggregateException ae)
{
Console.WriteLine(string.Join(",",
ae.InnerExceptions.ToList().Select(e => e.Message).ToArray()));
}

Console.WriteLine("Hit any key to continue..");
}

public static async void CallFooAsync()
{
int foo = await FooAsync();
Console.WriteLine(foo);
}

{
return 42;
}


The Main method of the console application is not allowed to have async modifier, so it was necessary to introduce an extra method here. Next off, here is an example of an AsyncStateMachine at its simplest form. It is implemented as a struct.

struct FooAsyncStateMachine : IAsyncStateMachine
{

private int state;

public void MoveNext()
{
//State machine
try
{
if (state == 0)
{
if (awaiter.IsCompleted)
{
state = 1;
goto state1;
}
else
{
state = 1;
methodBuilder.AwaitUnsafeOnCompleted(ref awaiter, ref this);
}
return;
}

state1:
if (state == 1)
{
methodBuilder.SetResult(42);
return;
}
}
catch (Exception ex)
{
methodBuilder.SetException(ex);
return;
}
}

public void SetStateMachine(IAsyncStateMachine stateMachine)
{
methodBuilder.SetStateMachine(stateMachine);
}

}


The IAsyncStateMachine interface has a method called void MoveNext(). This method is called when the async method starts up. This method can be called multiple times. It contains a state variable to control which step is next. The AsyncMethodBuilder is used to control the result returned from the async method. The method SetResult sets the result returned and the method SetException inside a catch sets an exception, if encountered. Thet method SetStateMachine sets the statemachine struct as the state machine struct itself and is also part of the IAsyncStateMachine. Now that the AsyncStateMachine is defined, it is time to kick it off.