Binding a templated method of a templated class - how?

[trexxet]

Consider a simple templated class that has several templated constructors and methods:

template <typename T>
struct Rect2D {
	T x, y, width, height;

	Rect2D (T _x, T _y, T _w, T _h) : x (_x), y (_y), width (_w), height (_h) {}
	Rect2D () : x (0), y (0), width (0), height (0) {}

	template <typename U>
	Rect2D (T _x, T _y, const Size2D<U>& size) :
		x (_x), y (_y), width (size.width), height (size.height) {}
	
	template <typename U>
	Rect2D (const Point2D<T>& pos, const Size2D<U>& size) :
		x (pos.x), y (pos.y), width (size.width), height (size.height) {}

	template <typename U>
	void centrify (const Rect2D<U>& outer) {
		if (outer.width < width || outer.height < height)
			return;
		x = (outer.width - width) / 2;
		y = (outer.height - height) / 2;
	}

	Point2D<T> pos () { return Point2D<T> {x, y}; }
	Size2D<T> size () { return Size2D<T> {width, height}; }
};

where Size2D<T> = Point2D<T> = struct { T x, y }.

I'm trying to bind it to Lua. Let's sacrifice ability to have U != T in templates, and consider T = U = C. Then, I can do the following:

	auto bindGeometryR2D = [this] <typename C> (const std::string& name) {
		this->state.new_usertype<Rect2D<C>>(name, sol::constructors<
			Rect2D<C>(),
			Rect2D<C>(C, C, C, C),
			Rect2D<C>(C, C, Size2D<C>),
			Rect2D<C>(Point2D<C>, Size2D<C>)>()
		);
	};
	bindGeometryR2D.operator()<int> ("Rect2D");
        bindGeometryR2D.operator()<double> ("Rect2Dd");

Ok, that works fine:

window = Size2D.new(800, 600)
windowRect = Rect2D.new(0, 0, window)

However, I'm struggling to bind the centrify method. Adding after sol::constructors:

"centrify", &Rect2D<C>::centrify

error: no matching function for call to 'sol::state::new_usertype<Based::Rect2D >(const std::string&, sol::constructors< blah blah blah >, <unresolved overloaded function type>)'

Hm, maybe

"centrify", sol::resolve<Rect2D<C>(const Rect2D<C>&)>(&Rect2D<C>::centrify)

error: no matching function for call to 'resolve<Based::Rect2D(const Based::Rect2D&)>(<unresolved overloaded function type>)

So, how should it be done correctly?

Thank you in advance.

[trexxet]

Some more findings:

"centrify", &Rect2D<C>::centrify<C>

warning: expected 'template' keyword before dependent template name (???)

[trexxet]

Well, the next step solved the issue. Should have listened to the compiler, although at first glance this syntax looks incorrect to me:

"centrify", &Rect2D<C>::template centrify<C>

Quite interesting that if I move the UT outside of the lambda, then the expected syntax from the previous message works fine: &Rect2D<int>::centrify<int>