Have you thought about not using a factory at all, and instead making nice use of the type system? I can think of two different approaches which do this sort of thing:
Option 1:
struct linear {
linear(float x, float y) : x_(x), y_(y){}
float x_;
float y_;
};
struct polar {
polar(float angle, float magnitude) : angle_(angle), magnitude_(magnitude) {}
float angle_;
float magnitude_;
};
struct Vec2 {
explicit Vec2(const linear &l) { /* ... */ }
explicit Vec2(const polar &p) { /* ... */ }
};
Which lets you write things like:
Vec2 v(linear(1.0, 2.0));
Option 2:
you can use "tags" like the STL does with iterators and such. For example:
struct linear_coord_tag linear_coord {}; // declare type and a global
struct polar_coord_tag polar_coord {};
struct Vec2 {
Vec2(float x, float y, const linear_coord_tag &) { /* ... */ }
Vec2(float angle, float magnitude, const polar_coord_tag &) { /* ... */ }
};
This second approach lets you write code which looks like this:
Vec2 v(1.0, 2.0, linear_coord);
which is also nice and expressive while allowing you to have unique prototypes for each constructor.