Thread Subject: Assigning Property to Space Points

Hi,

I would like to assign scalar property to 3D space points, the problem
is;

1) How does the non uniform property (Pi) store as their related space
points (Xi,Yi,Zi)?
2) How could the property called back by entering its coordinates?
3) Is there any possibility to use some function in this regards?


Thank you very much in advance
Arash

Arash wrote:

> I would like to assign scalar property to 3D space points, the problem
> is;

> 1) How does the non uniform property (Pi) store as their related space
> points (Xi,Yi,Zi)?
> 2) How could the property called back by entering its coordinates?
> 3) Is there any possibility to use some function in this regards?

Some crucial questions about this:

A) is the scalar property a single number? For example, from one point
of view, strings such as 'Fred' and 'Brenda' are scalar properties, and
from another point of view, a vector of numbers is sometimes considered
a scalar property.

B) When you want to recall by coordinates, it is almost certain that the
coordinates that arrive at the recall routine will not be _exactly_ the
same as the original coordinates, due to floating point round-off if
nothing else. What do you want to have happen if there is not an exact
match for the coordinates?

C) Continuing the above: suppose the coordinates provided for recall are
a non-negligible distance away from the original coordinates, then what
do you want to have happen? Do you want the scalar value returned to be
interpolated from the scalar values of the original coordinates "near
by" to the provided coordinates?

Walter Roberson wrote:
> Arash wrote:
>
>> I would like to assign scalar property to 3D space points, the problem
>> is;
>
>> 1) How does the non uniform property (Pi) store as their related space
>> points (Xi,Yi,Zi)?
>> 2) How could the property called back by entering its coordinates?
>> 3) Is there any possibility to use some function in this regards?
>
> Some crucial questions about this:
>
> A) is the scalar property a single number? For example, from one point
> of view, strings such as 'Fred' and 'Brenda' are scalar properties, and
> from another point of view, a vector of numbers is sometimes considered
> a scalar property.
>
> B) When you want to recall by coordinates, it is almost certain that the
> coordinates that arrive at the recall routine will not be _exactly_ the
> same as the original coordinates, due to floating point round-off if
> nothing else. What do you want to have happen if there is not an exact
> match for the coordinates?
>
> C) Continuing the above: suppose the coordinates provided for recall are
> a non-negligible distance away from the original coordinates, then what
> do you want to have happen? Do you want the scalar value returned to be
> interpolated from the scalar values of the original coordinates "near
> by" to the provided coordinates?

The original poster replied to me by email and indicated that the
"properties" are indeed single numbers, and that interpolation would be
a "fantastic" idea. (Note: it is better to reply to me here rather than
in email, so that others can see the developing ideas and contribute,
especially since other people are available at different times, such as
while I am working.)


Okay, so the next question: what _kind_ of interpolation is desired?
What is the "neighbourhood" of points considered to contribute to the
interpolation (as I gather that the data is irregularly spaced, not on a
grid.)

Another question: is the range of the points in each dimension
sufficiently small that it would be practical to fit a three-dimensional
grid that could then be used for fast-lookup reference, and perhaps also
to provide the fixed nodes for the interpolation? If so, then John
D'Errico's FEX contribution "gridfit" could be quite useful for this
purpose.