Yes, Thinking about it we've probably seen these 4x4 matrices before in
the mesh files. The book I've got on 3-D graphics has this to say for
homogeneous co-ordinates (but my words not the book's):
You can do rotations in 3D: R v = x
You can do scalings in 3D: Sv = y
but to do translations you have to do v = x + T
No longer a matrix multiplication but a vector add. Once you have adds and
multiplications you have a ring structure (abstract algebra) but not a group
structure (just adds or multiplications, depending on what you are doing.)
Rings have less known about them so groups are better. The cool part, and
the part I missed at university is that in projective geometry you can make
4x4 matrices like:
Code:
( R Tvec) ( v ) = ( x )
( 0 1 ) ( 1 ) ( y )
and make translations obey matrix multiplications and so be a group. (This
won't work out well in HTML but this is all I can do right now.) These are
called homogeneous co-ordinates and are probably known to all the modellers
\but where news to me. (My Linear Algebra course skimped on projective
geometry.)
I've seen these in the settlement files but, like you said, there's a 17th float
which doesn't fit (rotations and translations and then an overall scaling?).
At any rate, I have found some overall logic to the .world file. The header
says 40 so you can read the first part: that part defines 31 entries that
have a sequence number/ There happen to be 31 complexes so maybe
that is the magic number. Then come 867 entries. Total mystery except
the header/footers contain a count of the number of homogeneous data
segments but also contain a secondary count of somethingh else. At the
end that number turns out to be 867. Wish I knew what it meant.
I've been refactorizing the code and, except for these oddities, it is almost
suitable for putting in for loops. Maybe a little more study will unlock the
inexplicable. (Or make me buy an X-box: Mario bros. was entertaining when I
played it against my daughter.) 
Apologies, I should be fixing animation difficulties but I can't do
that at lunch time; unemployment would result if I installed the game.
@GOM, I've copied almost all of that interesting chapter, just a few pages
more. Sorry, been kinda' rattled with contractors and getting lawn stuff done.
Regards,
KE
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