[postgis-devel] distance calculations in dynamic number of dimensions

[Nicklas Avén]

Regina

I think you are right.
I also thought about how to compare different units , but hoped someone
would say , there is ways to do it.

The function will give the vector though, as the difference of the first
and second point in the shortestline.

One situation when the different units maybe doesn't matter is to decide
if there will be a collision or not. I mean then the x, y, z distance
shall be 0 and also the time dimension. But i don't know if it works
that way, and it would be a little to narrow and tragic way of using it.

So, I guess we drop it for now, but keep in mind it probably is quite
easily possible.

/Nicklas


On Sun, 2010-10-17 at 21:13 -0400, Paragon Corporation wrote:
> > So, first question, would it be interesting to implement a
> > multidimensional functionality in the distance-calculations.
> > Is it worth the effort, will it attract new user groups in other fields?
> 
> Nicklas,
> 
> This is an interesting topic and one that I have entertained more than I
> would like to admit.  I probably don't know much more than you on the topic,
> but 
> my sense is that its not of much interest unless the distance functions
> return vectors instead of scalars, or have an additional function that takes
> a formula (scalar product operation)  that defines how the dimensions should
> be collapsed to arrive at the scalar value.
> 
> Relevant reading --
> http://en.wikipedia.org/wiki/Scalar_%28mathematics%29#Scalars_of_vector_spac
> es
> 
> For example -- take the classic example that people try to use the 4
> dimensions of space and time.  Lets say we have X,Y,Z,time recorded in unix
> epoch seconds.
> 
> If I were to ask you what is the distance between Nicklas of now and Nicklas
> of 4 seconds ago.  What would your answer be?
> 
> I think it depends.  Even with our simplistic view of X,Y,Z our
> transformation doesn't know how to deal with Z when its not in the same
> units of X and Y.
> 
> I would say (the distance of X,Y,Z , 4 seconds).  We have an idea of how to
> collapse X,Y,Z but how do you collapse the 4 seconds into a single scalar
> with the other coordinates to give it meaning?
> So the only reasonable answer would be to return a vector (I think its
> called a tensor in physics, but my physics is rusty :) ) - the vector has
> the same dimensions of fewer than our input points and then the user can
> define the transformation function that converts it to a scalar quantity.
> 
> Another example -- one not dealing with earthly space would be for example
> in economics the supply , demand (you can even throw time in there).  You
> can think of supply and demand as different coordinates and there are
> numerous theories on how they relate such that you could give some sort of
> scalar distance given two different supply/demands.  Though not sure how
> interesting that would be.  
> 
> 
> > Could it be interesting? Does any other GIS software have this
> functionality?
> So short answer - could be but too much to tackle for 2.0.  Other GIS
> software -- hmm don't know of any -- my guess is you'd have to start looking
> at matrix like tool kits like
> R, S, SAS, Matlab, Mathematica to start getting into the realm you are
> talking about.  Even then, not quite sure they think about it quite the same
> way.
> 
> > I don't know if that will be more difficult with polygons involved...
> As far as polygons go -- that gets messy.  As Paul pointed out once, its
> hard to define what is a valid polygon even in 3D space and I have no idea
> what a polygon means when adding on other dimensions.
> 
> 
> Thanks,
> Regina
> 
> 
> 
> 
> 
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