EN
JavaScript - how to use Monte Carlo method to calculate pi constant number?
6
points
Using JavaScript it is possible to calculate surface area (definite integral) in the following way.
1. Circle surface area calculation example
Main idea of this method is to:
- random big amount of points
- check all time if every next one point is inside a circle or not,
- compute coefficient by dividing number of points inside of circle by outside one point
- multiply the coefficient by square surface area - this way from proportion it is possible to get approximated circle surface area,
- use transformed circle surface area formula to calculate
PInumber.
Note: the longer the simulation is performed, the results are more precised.
// ONLINE-RUNNER:browser;
<!doctype html>
<html>
<head>
<style>
#my-canvas { border: 1px solid gray; }
</style>
<script>
function randomizePoint(range) {
return range * (Math.random() - 0.5);
}
// This method checks the point is inside circle
// with center at (0, 0) point.
//
function checkCondition(circleRadius, pointX, pointY) {
var pointRadius = Math.sqrt(pointX * pointX + pointY * pointY);
if (pointRadius <= circleRadius) {
return true;
}
return false;
}
window.Drawer = function(canvas) {
var context = canvas.getContext('2d');
var xCenter = canvas.width / 2;
var yCenter = canvas.height / 2;
this.clearCanvas = function() {
context.clearRect(0, 0, canvas.width, canvas.height);
};
this.drawPoint = function(x, y, color) {
var tmpX = Math.round(xCenter + x - 1);
var tmpY = Math.round(yCenter + y - 1);
context.strokeStyle = '#fff';
context.fillStyle = color || '#000';
context.fillRect(tmpX, tmpY, 2, 2);
};
this.drawCircle = function(x, y, radius) {
var tmpX = Math.round(xCenter + x - 1);
var tmpY = Math.round(yCenter + y - 1);
context.lineWidth = 0.5;
context.strokeStyle = '#ff0000';
context.fillStyle = '#fff';
context.beginPath();
context.arc(tmpX, tmpY, radius, 0, 2 * Math.PI);
context.stroke();
};
};
</script>
</head>
<body>
<canvas id="my-canvas" width="300" height="300"></canvas>
<script>
var canvas = document.querySelector('#my-canvas');
var drawer = new Drawer(canvas);
var squareArea = canvas.width * canvas.height;
var circleRadius = 150;
var squarePointsCount = 0;
var circlePointsCount = 0;
drawer.clearCanvas();
drawer.drawCircle(0, 0, circleRadius);
function makeIteration() {
for(var i = 0; i < 100; ++i) {
// random coordinates from range -150 to +150
var pointX = randomizePoint(canvas.width);
var pointY = randomizePoint(canvas.height);
if (checkCondition(circleRadius, pointX, pointY)) {
drawer.drawPoint(pointX, pointY, 'red');
circlePointsCount += 1;
} else {
drawer.drawPoint(pointX, pointY, 'silver');
}
squarePointsCount += 1;
}
// next iterations gives computation better precision
// according to number of randomized points
var randomPointsProportion = circlePointsCount / squarePointsCount;
var computatedCircleArea = randomPointsProportion * squareArea;
var computatedPI = computatedCircleArea / (circleRadius * circleRadius);
var computationError = Math.abs(Math.PI - computatedPI);
console.clear();
console.log('PI number:');
console.log(' Expected: ' + Math.PI);
console.log(' Computed: ' + computatedPI);
console.log(' Error: ' + computationError);
}
setInterval(makeIteration, 100);
</script>
</body>
</html>