Javascript implementation of the Douglas Peucker path simplification algorithm

douglasPeucker.js

var simplifyPath = function( points, tolerance ) {

	// helper classes 
	var Vector = function( x, y ) {
		this.x = x;
		this.y = y;
		
	};
	var Line = function( p1, p2 ) {
		this.p1 = p1;
		this.p2 = p2;
		
		this.distanceToPoint = function( point ) {
			// slope
			var m = ( this.p2.y - this.p1.y ) / ( this.p2.x - this.p1.x ),
				// y offset
				b = this.p1.y - ( m * this.p1.x ),
				d = [];
			// distance to the linear equation
			if (!isNaN(m)) d.push( Math.abs( point.y - ( m * point.x ) - b ) / Math.sqrt( Math.pow( m, 2 ) + 1 ) );
			// distance to p1
			d.push( Math.sqrt( Math.pow( ( point.x - this.p1.x ), 2 ) + Math.pow( ( point.y - this.p1.y ), 2 ) ) );
			// distance to p2
			d.push( Math.sqrt( Math.pow( ( point.x - this.p2.x ), 2 ) + Math.pow( ( point.y - this.p2.y ), 2 ) ) );
			// return the smallest distance
			return d.sort( function( a, b ) {
				return ( a - b ); //causes an array to be sorted numerically and ascending
			} )[0];
		};
	};
	
	var douglasPeucker = function( points, tolerance ) {
		if ( points.length <= 2 ) {
			return [points[0]];
		}
		var returnPoints = [],
			// make line from start to end 
			line = new Line( points[0], points[points.length - 1] ),
			// find the largest distance from intermediate poitns to this line
			maxDistance = 0,
			maxDistanceIndex = 0,
			p;
		for( var i = 1; i <= points.length - 2; i++ ) {
			var distance = line.distanceToPoint( points[ i ] );
			if( distance > maxDistance ) {
				maxDistance = distance;
				maxDistanceIndex = i;
			}
		}
		// check if the max distance is greater than our tollerance allows 
		if ( maxDistance >= tolerance ) {
			p = points[maxDistanceIndex];
			line.distanceToPoint( p, true );
			// include this point in the output 
			returnPoints = returnPoints.concat( douglasPeucker( points.slice( 0, maxDistanceIndex + 1 ), tolerance ) );
			// returnPoints.push( points[maxDistanceIndex] );
			returnPoints = returnPoints.concat( douglasPeucker( points.slice( maxDistanceIndex, points.length ), tolerance ) );
		} else {
			// ditching this point
			p = points[maxDistanceIndex];
			line.distanceToPoint( p, true );
			returnPoints = [points[0]];
		}
		return returnPoints;
	};
	var arr = douglasPeucker( points, tolerance );
	// always have to push the very last point on so it doesn't get left off
	arr.push( points[points.length - 1 ] );
	return arr;
};

I had some problem with the original implementation while working with node.js and found that the slope can be NaN which also causes the y intercept to be NaN and this causes a 'null' to be added to the distance array, and it will always be selected and returned as NaN. This causes all of the points in certain shapes to be deleted except for the start and end points. Checking for NaN fixes the issue for me.

I used this to simplify the polyline representing a transit bus route on a map, using a tolerance of 0.00005 which was semi-empirically derived.