[Algorithms] Diatribe Re: decompose onto non-orthogonal vectors

[Jonathan B. <jo...@bo...>]

In advance I'll say that this diatribe is not directed straight at Ben;
it's to everyone on this list who isn't eager to learn math.


Ben Discoe wrote:

> I was asking if somebody knew the solution, not for how to do the math,
> which i'm willing to leave to people who enjoy re-deriving solutions to math
> problems.

The problem here is that modern graphics programming is *all about* math.
If you don't know the math, you can't play ball.

You shouldn't think of the question you asked as some isolated problem
that you ought to be able to look up in a book.  If this were the best
way to learn how to do things, then you'd need to look up hundreds of
little special-case problems in order to write a modern 3D program
that does interesting things.  And as you've seen, it's often hard
to find a lucid explanation of even one of these problems, even though
lots of people know how to do them.

To understand graphics publications and implement them, and
especially to do new work, you need to be fluent enough in certain
areas of math (linear algebra being a major one) that you just instinctively
know answers to problems like the one you posed.  Once you have this 
knowledge, you'll find that you look at problems in a different way.  
You'll skip over whole truckloads of questions that would have been really 
perplexing before, because now they're non-issues.  Months of programming
work that would have been misguided can now be eliminated.  The scope of things 
you can do will be vastly expanded.

Trying to do 3D graphics without linear algebra is like this: You want to
be a sculptor and create this cool statue called The Thinker, and you've
got the big block of stone, your hammer and chisel are sitting
there on the table... but unfortunately you cut your hands off last
month, so you're squeezing the chisel between two wrist-stumps and
holding the hammer in your mouth and trying to bang away.

It's not good for your dental work.

    -J.