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

[Paul Ramsey]

Nik,
THanks for keeping your brain whirring. :) I agree, that the
abstraction cost in supporting n-dimensions is not balanced by higher
utility, since the maximum amount of dimensions we measure with the
same units is 3.
P.

On Mon, Oct 18, 2010 at 2:48 PM, Nicklas Avén
<nicklas.aven at jordogskog.no> wrote:
> 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
>>
>>
>>
>>
>>
>> _______________________________________________
>> postgis-devel mailing list
>> postgis-devel at postgis.refractions.net
>> http://postgis.refractions.net/mailman/listinfo/postgis-devel
>>
>
>
> _______________________________________________
> postgis-devel mailing list
> postgis-devel at postgis.refractions.net
> http://postgis.refractions.net/mailman/listinfo/postgis-devel
>