"Kenneth" <kdw### [at] gmailcom> wrote:
> I must now
> cast the runes, to see if the auspices are favorable...

Make sure you stir the chicken entrails in the proper direction.  POV-Ray use
the left-hand coordinate system.


> 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.

Hey, listen, the POV-Ray docs...   :|   Nevermind.

> 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.)

Didn't have time to read through all of that - but it looks a lot like the
stereographic 4D-->3D projection stuff I'd like to do.

> 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 basis vectors are just the "axis vectors" you're using.

Suppose you applied a shear transform to an entire scene.
If you had the original x, y, and z vectors defined as "user-defined" vectors,
and applied that shear transformation, then the resulting output would be the
basis vectors for that new sheared scene-space.

So If you used THOSE vectors as the axes, then you'd be able to traverse all
around THAT space without having to apply any transformations - it would be
_native_.

Look over the 3brown1blue video channel I posted - he does a GREAT job at
explaining it all - look at the linear algebra series - he specifically focuses
on basis vectors in one video.

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