Who has greater proximity,

i) the point 1 mm from the tip of the flagpole atop a skyscaper,
or
ii) the point 2 mm from three surfaces inside a groove in the facade on the
middle story of the skyscraper
?

ABX's formula measures ii).

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In article <f91a9v40mae692tpohmiaha5dg92al80l8@4ax.com>,
 ABX <abx### [at] abxartpl> wrote:

> I think you misunderstand me. My understanding is that proximity 
> (closeness, nearness) can be any function which is growing in 
> direction to nearest point of object. Not necessary linear like 
> distance returned from intersection test. I do not exclude distance, 
> just allow other characteristics to express that something is more 
> near.

But your function doesn't measure distance. Again, it measures the 
amount of local volume occupied by the object, some objects have no 
volume but definitely have proximity. A point is the simplest example of 
this, examples of POV primitives would include triangles, bezier 
patches, and polygons.


> That's why I'm looking for reference where it is stated that in
> mathematical english proximity _is_ linear distance.

Falloff rate doesn't matter, it is the "distance" part that does. Your 
function isn't distance related. It is corellated with distance in many 
cases, but it is not a function of distance.


> Can you provide me such a reference?

Any half-decent English dictionary is a sufficient reference. If you are 
looking for a published paper on it, I doubt any such paper exists. I 
used "proximity" because the word seemed to be the closest match to what 
my pattern computed ("closeness" to the object), not because somebody 
else used it. I would not have chosen it for your pattern, because it 
isn't proximity.

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/

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