Even more typing

[TheBB]

This PR changes some of the type aliases.

• Let's stop using Numpy's ArrayLike. It's both too general and not general enough: it includes some things that aren't relevant to us, and it excludes (or at least, Mypy seems to be unable to figure out) a few things that we need.
• Same for Scalar: it's too general
• Add some variation to our types: Point, Points, ControlPoints, Knots. Many of these overlap and are similar, but we can use them to signal intent to the user, which is especially useful for all the functions with parameters named x, t, u, etc.

I'll go through the already-typed files to make some changes.

[VikingScientist]

The term "Knots" here is a bit misleading. It refers to a very specific term in the knot vector which the NURBS book denotes as breakpoints. It is defined on the parameter space, but the parametric space is far more general and includes a lot more points than just the knots from the knot vector.

As I understand your proposed change then it is to make the distinction between parametric values and geometric values. i.e. for a spline surface
$$x(u) = \sum_i N_i(u) x_i$$
then x can have multiple components and is defined in the physical space (typehint Point) and u can have multiple components and is defined in the parametric space (typehint Knots). I would object to this notation as a more accurate typehints would be ParametricPoint and GeometricPoint. I don't really like this solution either as it is too verbose. But simply calling it Knot is not good enough either as Knot is to ParametricPoint what ControlPoint is to GeometricPoint.

I do think it is a good idea to have ControlPoints specified as their own typehints since they both have a particular interpretation from at mathematical point of view, and have a special structure (up to 4D tensors) from an implementation point of view.

[VikingScientist]

This is one of the places where I object to referring to parametric evaluation points t as knots. They simply are not knots and it is more misleading to call them as such.

[TheBB]

26 errors left!

[TheBB]

[TheBB]

I don't really like this solution either as it is too verbose. But simply calling it Knot is not good enough either as Knot is to ParametricPoint what ControlPoint is to GeometricPoint.

Well, what would you prefer then? Vector? FloatVector?

We have the following kinds of (long) one-dimensional vectors floating around:

• Knot vectors
• Evaluation parameters

We also have Point, which is a short one-dimensional vector (generally three elements or fewer), which I prefer to have a different name, even if they are conceptually basically the same as the above.

And we have these two- or multi-dimensional array types:

• Points
• Control points

I understand that you want a better name for the first group?