"Bald Eagle" <cre### [at] netscapenet> wrote:
>
> I can attest that there are an amazing number of things that can be done with
> the simplest of "tricks" - just using vcross, vdot, matrix determinants,
> eigenvalues, and vector swizzling.

About the only thing I truly grasp from that bunch is vector swizzling. :-( I
have lots more learnin' to do...
>
> And while that may all sound complicated and "out of reach" - the point
> is that you don't have to understand a damned thing about how any of it
> is "done" - you just need to understand the significance of the result.
> What it means.
>
> And then you can go on to code some pretty amazing stuff, that's easy to
> write (as a result of knowing the "tricks"), and is FAST - compared to
> the usual "I'm going to write my code in the exact same way as I went about
> figuring this out the long way" that we all do so often.
>

Well-said. Fortunately or unfortunately, I always think in terms of 'visual
images' regarding math stuff-- I have to construct a step-by-step mental picture
of the particular process that I'm dealing with...as well as for the particular
math 'tool' that I'm trying to use, before putting it to work. Only then do I
have a clear understanding of what the result will be. It's a plodding and
cautious process, admittedly. But at some point I'll (hopefully) have a
'Eureka!' moment, when all is clear. :-)

But then there are times that I'll just *experiment*-- using renders, one after
another-- with no clear idea of what's happening or what to expect, until I see
some kind of result that helps me learn. That's usually a lot of fun, because
unexpected things arise! I should do more of that, instead of trying to do so
much 'pre-thinking'.

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