Trait space::MetricPoint [−][src]
Expand description
This trait is implemented by points inside of a metric space.
It is important that all points that implement this trait satisfy the triangle inequality. This requirement basically means that the sum of distances that start at a point A and end at a point B can never be less than the distance from A to B directly. All implementors must also take care to avoid negative numbers, as valid distances are only positive numbers.
In practice, the u64 distance returned by this trait should only be used
to compare distances between points in a metric space. If the distances are added,
one would need to take care of overflow. Regardless of the underlying representation
(float or integer), one can map the metric distance into the set of 64-bit integers.
This may cause some loss of precision, but the choice to use 64 bits of precision
is one that is done with practicality in mind. Specifically, there may be cases
where only a few bits of precision are needed (hamming distance), but there may also
be cases where a 64-bit floating point number may be different by only one bit of precision.
It is trivial to map a 64-bit float to the unsigned integers for comparison, as
IEEE 754 is designed such that a direct
bit-to-bit translation of a 64-bit float to a 64-bit signed integer will compare
as intended using a standard signed integer comparation operation. Anything with more
than 64 bits of precision will need to be truncated.
If you have a floating distance, use f32_metric or f64_metric.