Metric spaces

[brendanzab]

cgmath currently has a MetricSpace trait that is defined for vectors, points, and quaternions:

pub trait MetricSpace: Sized {
    type Metric: BaseFloat;
    fn distance2(self, other: Self) -> Self::Metric;

    fn distance(self, other: Self) -> Self::Metric { ... }
}

Could we consider rejiggering the alga::linear trait hierarchy to add something like this?

[sebcrozet]

Yes, adding metric spaces would be useful. Though I am still not sure what the best definition would be because of the link between dot product (already available on the FiniteDimInnerSpace) and the metric it induces. But any suggestion is welcome!