Can I add an implicit conversion for two classes which I don't directly control?

Question

I'd like to be able to implicitly convert between two classes which are otherwise incompatible.

One of the classes is Microsoft.Xna.Framework.Vector3, and the other is just a Vector class used in an F# project. I'm writing a 3d game in C# with XNA, and -- although it's drawn in 3D, the gameplay takes place in only two dimensions (it's a birds-eye-view). The F# class takes care of the physics, using a 2D vector:

type Vector<'t when 't :> SuperUnit<'t>> =
    | Cartesian of 't * 't
    | Polar of 't * float
    member this.magnitude =
        match this with
        | Cartesian(x, y) -> x.newValue(sqrt (x.units ** 2.0 + y.units ** 2.0))
        | Polar(m, _) -> m.newValue(m.units)
    member this.direction =
        match this with
        | Cartesian(x, y) -> tan(y.units / x.units)
        | Polar(_, d) -> d
    member this.x =
        match this with
        | Cartesian(x, _) -> x
        | Polar(m, d) -> m.newValue(m.units * cos(d))
    member this.y =
        match this with
        | Cartesian(_, y) -> y
        | Polar(m, d) -> m.newValue(m.units * sin(d))

This vector class makes use of the unit system used by the physics project, which takes native F# units of measure and groups them together (units of Distance, Time, Mass, etc).

But XNA uses its own Vector3 class. I want to add an implicit conversion from the F# Vector to the XNA Vector3 which takes care of which two dimensions the gameplay takes place in, which axis is "up", etc. It'd be simple, just Vector v -> new Vector3(v.x, v.y, 0) or something.

I can't figure out how to do it though. I can't add an implicit conversion in F# because the type system (rightly) doesn't allow it. I can't add it to the Vector3 class because that is part of the XNA library. As far as I can tell I can't use an extension method:

class CsToFs
{
    public static implicit operator Vector3(this Vector<Distance> v)
    {
        //...
    }
}

Is an error on the this keyword, and

class CsToFs
{
    public static implicit operator Vector3(Vector<Distance> v)
    {
        return new Vector3((float)v.x.units, (float)v.y.units, 0);
    }

    public static void test()
    {
        var v = Vector<Distance>.NewCartesian(Distance.Meters(0), Distance.Meters(0));
        Vector3 a;
        a = v;
    }
}

is an error on a = v; (cannot implicitly convert...).

Is there a way to do this without being able to put the cast in either of the classes? As a last resort I could open Microsoft.Xna.Framework and do the conversion in F#, but that seems wrong to me -- the physics library shouldn't know or care what framework I'm using to write the game.

Answer 1

No, you can't. The implicit operator has to be defined as a member of one of the classes. However, you can define an extension method (your example didn't work as extension methods have to be in a public static class).

public static class ConverterExtensions
{
    public static Vector ToVector (this Vector3 input)
    {
      //convert
    }
}