[postgis-devel] Distance operator in presence of M

[Chip Lynch]

On the one hand, storing velocity seems useful if you want to store a lot
of unconnected records; those not in a path.  Physics experiments like to
do this, gravity simulations, video games; anything where you're more
interested in the instantaneous state rather than the historical path, so
doing away with storing velocity could be problematic (also, you could make
use of velocity for kNN independent of time in that situation, per the
other thread).  On the other hand it would be painful if you had a
time-series where one point was NOT as far away from the previous point as
v*t (in whatever direction)... how would you interpolate the position at a
point in time between two records?

But yes, projecting time and space into the same distance equation is
tricky.  If you and I are a mile apart at the same time, or if we were both
in the same place an hour apart, which one is "closer"?  I'd rather stick
with answerable questions... "At what times were we within x distance of
one another" or "how far apart were we at our farthest each day"?

Interesting, tho, keep up the good work.

---Chip

On Fri, Jun 5, 2015 at 8:32 PM, Håvard Tveite <havard.tveite at nmbu.no> wrote:

> On 05. juni 2015 15:51, Sandro Santilli wrote:
>
>> On Fri, Jun 05, 2015 at 09:17:12AM +0200, Havard Tveite wrote:
>>
>>  For operations involving distance calculations, you need to have
>>> a way to compare space+time "distances".  Which is closest of two
>>> points where the spatial distances are 200m and 250m while the
>>> temporal distances are 80 seconds and 60 seconds?
>>> As Greg says, for that you need to have a velocity.
>>> If velocity is supplied as a parameter, it could be possible to
>>> support such operations.
>>>
>>
>> Indeed my work on space+time is currently based on "trajectories"
>> which encode not only velocity but also direction (needed as well).
>>
>
> Velocity can be derived from the trajectory (represented as
> a sequence of space-time positions), but when the sampling
> frequency for the trajectory is too low to capture the
> real world trajectory accurately, I would guess that the
> user would want to be able to specify a velocity (could be
> the users guess on the typical velocity or the maximum
> velocity for that type of object) that is to be used in
> distance calculations.
>
> And space-time data do not have to be trajectory data.
>
> To be able to do distance calculations on data with M
> values, we need to be able to transform the M value into
> a "compatible" dimension (resulting in a Euclidean space).
> When M is time, this transform could be based on a
> user-specified velocity (d=v*t).  In general, a
> user-specified function (as suggested by Greg) that does
> this transformation would be useful.  Or perhaps some
> pre-defined functions with user-specified parameters
> could work (d=a*M).
>
> But this is probably too ambitious / complicated...
>
> Håvard
>
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