VectorADT.js

function Vector(rep) {
    switch (rep) {
        case Vector.representations.Polar:
            this.vector = { rep: rep, r: arguments[1], a: arguments[2] }
            break;
        case Vector.representations.Rectangular:
            this.vector = { rep: rep, x: arguments[1], y: arguments[2] }
            break;
        default:
            throw Error("Unknown representation " + rep)
    }

    var assertVector = function (vector) {
        if (!(vector instanceof Vector)) {
            throw Error("addend not a Vector")
        }
    }

    var assertPolar = function (vector) {
        if (!(vector.vector.rep === Vector.representations.Polar)) {
            throw Error("vector not in polar representation")
        }
    }

    var polar2Rect = function (vector) {
        assertPolar(vector)
        return Vector.rectangular(Math.cos(vector.vector.a) * vector.vector.r, Math.sin(vector.vector.a) * vector.vector.r);
    }
    
    this.IsRectangular = function() { return this.vector.rep == Vector.representations.Rectangular; }
    this.IsPolar = function() { return this.vector.rep == Vector.representations.Polar; }

    this.Add = function (v2) {
        assertVector(v2);

        if (this.IsRectangular()) {
            if (v2.IsPolar()) {
                return this.Add(polar2Rect(v2));
            }
            return Vector.rectangular(this.vector.x + v2.vector.x, this.vector.y + v2.vector.y)
        }

        if (this.IsPolar()) {
            return polar2Rect(this).Add(v2);
        }
    }
}

Vector.representations = { Rectangular: 0, Polar: 1 }
Vector.polar = function (r, a) {
    return new Vector(Vector.representations.Polar, r, a)
}
Vector.rectangular = function (x,y) {
    return new Vector(Vector.representations.Rectangular, x, y)
}