I posted my request under “News and discussion” with nearly no result. So I want to give it a new try. Perhaps this is the right place to post my request.
Rewriting an article for german Blenderbook concerning Mapinput I´m would like to become more knowledgeable about this theme. The explanations in the Blenderwiki Manual doesn`t give many backgroundinformations and Blenderguide 2.3 is nearly the same. Any links or suggestions?
I need more informations about
- reflection vector
- tangent vector
*how does the renderer calculate x,y,z / u,v,w coordinates in combination with sticky coordinates or per-vertex UV coordinates. - The rendered image window coordinates
In the wikimanual all these items were used and none was explaned. Normaly people read this articles in Wikibooks, they read the words but don`t understand (cannot understand) and at the end it´s like allways: People are forced to find practical solution by “trial and error” to get the funktion to work - somehow.
I would be very pleased, if somebody had further informations. And please remember, I only had twelve years mathematics at school and this was long time ago… 
Stuff like this is very interesting - sorry, only german. It`s a paper written as homwork for a Proseminar at the “fakultät for Informatik” in munich/germany, but thank god with many pictures and not only mathematic. I think, to understand this functions I need more detailed informations about how the renderer in Blender is working.
http://www14.in.tum.de/lehre/1998WS/proseminar/krause/#1.%20TextureMapping