[argyllcms] Re: Version 0.53 - Gamut mapping warning message.

Gerhard Fuernkranz wrote:

But I doubt that monotonicity with regard to such an "artificial" ordering of multi-dimensional numbers is useful for our desired purpose. As you said above, it's rather more interesting, whether the device -> PCS mapping is bijective or not. So we should probably not use the misleading term "monotonic" (which depends on the chosen ordering relation), but simply the term "bijective" to describe this property, at least for multi-dimensional spaces. 

According to these definitions:

Bijective: 
<http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=907&langcode=en>
Surjective: <http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=321>
Injective: <http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=828>

then what I'm calling "monotonic" is actual the Injective property,
but not Surjective (You can't reproduce all of PCS from a device),
therefore not Bijective.) This depends on the definition of
the ranges or course.

Unfortunately, I suspect even fewer people would understand what "Injective"
is, than understand what "non-monotonic" means ...

Graeme Gill.

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