How to constrain movement within the area of a circle

Question

This might be more a geometry related question, but I'm trying to constrain a controller within an area of a circle. I know I have to touch the Math.sin() and Math.cos() methods, but my attemps so far have been fruitless so far.

Here is the jsfiddle: So far I've been able to constrain it to an invisible square. http://jsfiddle.net/maGVK/

Answer 1

So I finally was able to complete this with a bit of everyone's help.

var pointerEl = document.getElementById("pointer");
var canvasEl = document.getElementById("canvas");
var canvas = {
    width: canvasEl.offsetWidth,
    height: canvasEl.offsetHeight,
    top: canvasEl.offsetTop,
    left: canvasEl.offsetLeft
};
canvas.center = [canvas.left + canvas.width / 2, canvas.top + canvas.height / 2];
canvas.radius = canvas.width / 2;


window.onmousemove = function(e) {
    var result = limit(e.x, e.y);
        pointer.style.left = result.x + "px";
        pointer.style.top = result.y + "px";
}

function limit(x, y) {
    var dist = distance([x, y], canvas.center);
    if (dist <= canvas.radius) {
        return {x: x, y: y};
    } 
    else {
        x = x - canvas.center[0];
        y = y - canvas.center[1];
        var radians = Math.atan2(y, x)
           return {
               x: Math.cos(radians) * canvas.radius + canvas.center[0],
               y: Math.sin(radians) * canvas.radius + canvas.center[1]
           }
        } 
    }

function distance(dot1, dot2) {
    var x1 = dot1[0],
        y1 = dot1[1],
        x2 = dot2[0],
        y2 = dot2[1];
    return Math.sqrt(Math.pow(x1 - x2, 2) + Math.pow(y1 - y2, 2));
}

You can see the result here:

http://jsfiddle.net/7Asn6/

Answer 2

var pointerEl = document.getElementById("pointer");
var canvasEl = document.getElementById("canvas");
var canvas = {
    width: canvasEl.offsetWidth,
    height: canvasEl.offsetHeight,
    top: canvasEl.offsetTop,
    left: canvasEl.offsetLeft
};
canvas.center = [canvas.left + canvas.width / 2, canvas.top + canvas.height / 2];
canvas.radius = canvas.width / 2;


window.onmousemove = function(e) {
    var result = limit(e.x, e.y);
    if (!result.limit) {
        pointer.style.left = result.x + "px";
        pointer.style.top = result.y + "px";
    }
}

function limit(x, y) {
    var dist = distance([x, y], canvas.center);
    if (dist <= canvas.radius) {
        return {x: x, y: y};
    } else {
        return {limit: true};
    }
}

function distance(dot1, dot2) {
    var x1 = dot1[0],
        y1 = dot1[1],
        x2 = dot2[0],
        y2 = dot2[1];
    return Math.sqrt(Math.pow(x1 - x2, 2) + Math.pow(y1 - y2, 2));
}  

this could do the work, though the movement is not smooth....that will need more geometry knowledge...
fiddle: http://jsfiddle.net/cRxMa/