In Shape, have default impls for everything except path_elements

[richard-uk1]

IIUC it should be possible to implement all other methods in terms of a Bézier path approximation.

[raphlinus]

Generally I think this is a good idea, but there are challenges. My memory on this is not crisp, but I think one reason we didn't do this in the past is that the path_elements method had a tendency to allocate. This was fixed as of 0.8, gated by GATs landing in Rust.

One challenge is that some of the methods (area, winding, bounding_box) do not take an accuracy parameter, as they assume that analytical solutions are possible. That is true for some curve types (cubic Béziers) but not others (Euler spirals). I'm honestly not sure what's the best approach here, and think it deserves some consideration.

Adding an accuracy parameter degrades ergonomics and provides no value when the shape is a Bézier path. Yet, the trait is subtly wrong for curve types that do not admit analytical solutions. Is there a way to fix this without degrading the existing Bézier experience?

[george-steel]

I would say this would make Shape much more useful if all of the methods took accuracy parameters which could be ignored if an analytic solution exists.

I would also suggest exposing the internal versions of these methods on PathSeg (possibly adding their meanings for composable non-closed paths to the documentation) instead of the 0-returning placeholders. Having pub and non-pub methods on a type with the same name and different semantics is quite confusing.