//input: an object with x and y properties
//output: a normalized vector
var normal = function(vector) {
    var length = Math.pow(Math.pow(vector.x, 2) + Math.pow(vector.y, 2), 0.5);
    if (length === 0) {
        return {x:0, y:0};
    } else {
        return {x:(vector.x / length), y:(vector.y / length)};
    }
};

//input: x and y
//output: the angle in radians
var angle = function(x, y) {
    var theta = Math.atan(y / x);
    if (x < 0) {
        theta += Math.PI;
    } else if (y < 0) {
        theta += 2*Math.PI;
    }
    return theta;
};

//remove all instances of input value from array
Array.prototype.cleanse = function (value) {
    for (var i = 0; i < this.length - 1;) {
        if (this[i] === value) {
            this.splice(i, 1);
        } else {
            ++i;
        }
    }
};

//creates the Array.isArray(obj) if it's not supported
if (!Array.isArray) {
    Array.isArray = function (vArg) {
        return Object.prototype.toString.call(vArg) === "[object Array]";
    };
}

Array.prototype.removegiven = function (key, values) {
    if (Array.isArray(values)) {
        for (var j = 0; j <= values.length - 1; j++) {
            for (var k = 0; k <= this.length - 1; k++) {
                if (this[k][key] === values[j]) {
                    this.splice(k, 1);
                }
            }
        }
    }
    else {
        for (var l = 0; l <= this.length - 1;) {
            if (this[l][key] === values) {
                this.splice(l, 1);
            }
            else l++;
        }
    }
}