"Bald Eagle" <cre### [at] netscapenet> wrote:
> I think what you need to do is define something like:
> X = x, Y = y, and Z = z, and use those as the basis vectors of your overall
> transform matrix composition.

        [..."then a miracle occurs"...]
>
> Then apply those sequential transforms to those vectors, and then, as an
> exercise for you, the alert reader, do trig to get the angles back.

        [..."and the final miracle happens here"...]
>
> This sounds pretty cool - it should be neat once it's worked out.  :)

:-P  I couldn't resist! It all seems like magic to me at present. I must now
cast the runes, to see if the auspices are favorable...

BTW, I had previously seen the Wikipedia article on "Transformation Matrix"
(with my eyes glazing over), but it's actually starting to make some sense now.
As is often the case with Wikipedia technical articles, there is just enough
detail to be maddening, with a fair amount of knowledge by the reader already
assumed.

I see that an important concept re: matrices is the use of "homogenous
coordinates", rather than the typical Cartesian coordinates, something I didn't
know about:

https://en.wikipedia.org/wiki/Homogeneous_coordinates#Use_in_computer_graphics

It helps explain why matrices use 1's and 0's, and what they represent. (I'm
still digesting that stuff though, so I'm not yet totally clear about the
concepts.)

The other mystery to me is what a 'basis vector' is (maybe specifically to
POV-Ray.) Am I correct in thinking that it's not a typical <...,...,...>-style
vector, but a matrix version of same? The Wiki article about that is way over my
head-- but I did come across this link, which is somewhat more human-readable
:-) ---

http://fourier.eng.hmc.edu/e102/lectures/orthogonaltransform/node3.html

I'm still a "babe in the woods" with this stuff, so any comments/corrections are
certainly appreciated. It's all *slowly* starting to sink in...

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