feature request: split out distance_to_dimension, distance_to_node, and compare

[Shane Stafford]

In some cases where a kd-tree is used to partition space between 
non-orthogonal dimensions (for example, on the surface of a sphere) it 
would be helpful to have two separate distance functors. I thought about 
implementing this myself, but then I also thought that to generalize it 
even more, perhaps the Accessor could be also be dispensed with, 
allowing both the compare and distance functors to take _Val arguments 
(instead of _Acc::result_type arguments).

A tentative proposal:

squared_distance_type distanceToDimension( _Val value1, _Val value2, 
size_t dimension );

squared_distance_type distanceBetweenNodes( _Val value1, _Val value2 );

bool compareInDimension( _Val value1, _Val value2, size_t dimension );

I think the crux of the issue is that functions like 
_S_accumulate_node_distance make the assumption that the kd-tree is 
formed on a cartesian grid, and thus that the one-dimensional distances 
sum in a simple way to give the n-dimensional squared difference.

To give a concrete example, consider a 2D mapping onto half of a unit 
sphere consisting of the zenith angle (-pi<phi<pi) and azimuthal angle 
(-pi/2<theta<pi/2). A kd-tree could be used to partition the space along 
phi and theta. The (great-circle) squared distance from any node to a 
given zenith phi is fairly easy to compute. The squared distance to a 
given azimuth is also straightforward to compute. However, these two 
quantities cannot be summed to give the distance along both dimensions 
(because the distance to an azimuth is dependent on the zenith angle). 
Also, it would be easier to optimize the trig by storing things like 
cos(phi) instead of phi itself, and having a compare functor that takes 
two node values and a dimension would allow optimization of the 
compares, which would use different arithmetic in different dimensions.

Thoughts?

Shane