Add vector subtraction for all points

[Osspial]

PointN implements Add<VectorN>, so it seems natural that Sub<VectorN> should be implemented as well.

[brendanzab]

Not sure if this actually makes sense. You can think of vectors defining the 'difference' between points in space. So:

let start = Point3::new(1, 2);
let end = Point3::new(4, 5);
let translation: Vector3<_> = end - start;

assert_eq!(translation, Vector3::new(3, 3));

Adding a vector to a point corresponds with the reverse - ie. transforming a point by the supplied vector:

let start = Point3::new(1, 2);
let translation = Vector3::new(3, 3));
let end: Point3<_> = start + translation;

assert_eq!(translation, Point3::new(4, 5));

[Osspial]

I can get that, but I think point-vector subtraction makes sense when you think of subtraction as the addition of the negation of the vector. For most types you can currently do this:

let start = Point2::new(5, 5);
let translation = Vector2::new(1, 2);
let end: Point2<_> = start + -translation;

assert_eq!(end, Point2::new(4, 3));

However, this adds an extra step to an operation that's supported by the native numeric types with the Sub operator. The bigger issue is that this doesn't actually work when you're dealing with points and vectors of unsigned integers, because negation doesn't make sense for a type which can have no negative values. For those, you have to do subtraction manually on each field which adds unnecessary code clutter.

[brendanzab]

Hmm good points (hah!). Thoughts @sebcrozet? What would your thoughts be about adding vector space subtraction to the EuclideanSpace trait in alga? 😕

[sebcrozet]

Well I think this would be useful. Subtraction makes sense (as an abuse of notations) as long as the vector appears on the right-hand side. I did not add it to EuclideanSpace yet because this caused some weird conflicts with Sub<Point> in generic code (probably a bug in the compiler).

Regarding a the unsigned integer issue, vectors valued with unsigned integers are not part of vector space so they won't be usable with an euclidean space anyway.

[cristicbz]

For what it's worth, I've recently migrated rust-doom to cgmath and this has been a pain point for physics-y things:

1. I want to 'undo' a timestep, by subtracting, say, velocity * timestep.
2. Representing a box as center: Point3 and half_size: Vector3, the minimal coordinates are then min: center - half_size to max: center + half_size.

[brendanzab]

Based on the feedback here, I've decided to merge this. Thanks a bunch everyone!