figures.js

function Point(x, y) {
    this.x = x;
    this.y = y;
}

function Figure(position) {
    this.position = position;
}

function Line(position, endPosition) {
    Figure.call(this, position);
    this.endPosition = endPosition;
    this.name = "Line";
    
    this.square = function() {
        return 0;
    }
}
Line.prototype = new Figure;

function Rectangle(position, endPosition) {
    Line.call(this, position, endPosition);
    this.name = "Rectangle"
    
    this.square = function() {
        return (this.endPosition.x - this.position.x) *
               (this.endPosition.y - this.position.y);
    }
}
Rectangle.prototype = new Line;

function Circle(position, radius) {
    Figure.call(this, position);
    this.radius = radius;
    this.name = "Circle";
    
    this.square = function() {
        return Math.PI * this.radius * this.radius;
    }    
}
Circle.prototype = new Figure;


var Intersection = (function() {

    function LineAndLine(a, b) {
        var x1 = a.position.x, y1 = a.position.y,
            x2 = a.endPosition.x, y2 = a.endPosition.y,
            x3 = b.position.x, y3 = b.position.y,
            x4 = b.endPosition.x, y4 = b.endPosition.y;
        
        var result = new Point;
        result.x = ((x1*y2 - y1*x2)*(x3 - x4) - (x1 - x2)*(x3*y4 - y3*x4)) / 
                   ((x1 - x2)*(y3 - y4) - (y1 - y2)*(x3 - x4));
        result.y = ((x1*y2 - y1*x2)*(y3 - y4) - (y1 - y2)*(x3*y4 - y3*x4)) /
                   ((x1 - x2)*(y3 - y4) - (y1 - y2)*(x3 - x4));
        
        return isNaN(result.x) ||
               Math.abs(result.x) != Infinity && 
               Math.abs(result.y) != Infinity &&
               result.x >= Math.min(x1, x2) &&
               result.x >= Math.min(x3, x4) &&
               result.y >= Math.min(y1, y2) &&
               result.y >= Math.min(y3, y4) &&
               result.x <= Math.max(x1, x2) &&
               result.x <= Math.max(x3, x4) &&
               result.y <= Math.max(y1, y2) &&
               result.y <= Math.max(y3, y4);
    }
    
    function convertRectangleToLines(rect) {
        var topLeft = new Point(rect.position.x, rect.endPosition.y),
            bottomRight = new Point(rect.endPosition.x, rect.position.y);
        
        return [new Line(rect.position, topLeft),
                new Line(topLeft, rect.endPosition),
                new Line(rect.endPosition, bottomRight),
                new Line(bottomRight, rect.position)];
    }
        
    function LineAndRectangle(a, b) {    
        var lines = convertRectangleToLines(b);
        for (var i in lines) if (LineAndLine(a, lines[i])) return true;
        return false;
    }
    
    function RectangleAndRectangle(a, b) {
        var linesA = convertRectangleToLines(a),
            linesB = convertRectangleToLines(b);
        for (var i in linesA) for (var j in linesB) if (LineAndLine(linesA[i], linesB[j])) return true;
        return false;
    }
        
    function LineAndCircle(a, b) {
        var x1 = a.position.x + b.position.x,
            y1 = a.position.y + b.position.y;
            x2 = a.endPosition.x + b.position.x;
            y2 = a.endPosition.y + b.position.y;
        
        var dr = Math.sqrt(Math.abs((x2 - x1)*(x2 - x1)) + Math.abs((y2 - y1)*(y2 - y1))),
            D = x1*y2 - x2*y1;
        
        return b.radius*b.radius*dr*dr - D*D >= 0;
    }
    
    function CircleAndRectangle(a, b) {
        var lines = convertRectangleToLines(b);
        for (var i in lines) if (LineAndCircle(lines[i], a)) return true;
        return false;
    }
    
    function CircleAndCircle(a, b) {
        var d = Math.sqrt(Math.pow(a.position.x - b.position.x, 2) + 
                Math.pow(a.position.y - b.position.y, 2));
        return d <= a.radius + b.radius && d >= Math.abs(a.radius - b.radius);
    }
    
    return {
        doIntersect: function(a, b) {
            if (!(a instanceof Figure && b instanceof Figure)) {
                return false;
            }
        
            return a.name.length < b.name.length ? 
                   eval(composeFunction(a, b, "(a, b)")) : 
                   eval(composeFunction(b, a, "(b, a)"));
        }
    }
    
    function composeFunction(a, b, args) {
        return a.name + "And" + b.name + args;
    }
    
})();

index.html

<!DOCTYPE HTML>
<html>

<head>
    <meta charset="UTF-8">
    
    <title>Figures</title>
    <script type="text/javascript" src="figures.js"></script>
    
    <script type="text/javascript">
            
        var line = new Line(new Point(0, 0), new Point(2, 2));
        var line1 = new Line(new Point(2, 0), new Point(1, 10));
        
        var rectangle = new Rectangle(new Point(1, 1), new Point(4, 3));
        var rectangle1 = new Rectangle(new Point(10, 10), new Point(20, 20));
        var circle = new Circle(new Point(2, 2), 3);
        var circle1 = new Circle(new Point(0, 0), 1);
        
        document.write(Intersection.doIntersect(line, line1));

    </script>
    
</head>

<body>   
</body>

</html>