Path: chuka.playstation.co.uk!news1.scei.co.jp!scea!greg_labrec@interactive.sony.com
From: Nick Porcino <Nick_Porcino@bc.sympatico.ca>
Newsgroups: scea.yaroze.programming.3d_graphics
Subject: A wacky trick for normalization
Date: Wed, 27 Aug 1997 22:14:47 -0800
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Normalization of a vector normally looks like -

mag = pow(x*x + y*y , 0.5)
x /= mag;
y /= mag;

However, if you're trying to do everything in integer math, it gets ugly
because n*n can overflow, and / and sqrt are somewhat slow.
I came up with a wacky trick in 2D that will actually allow
normalization of a vector in 2D using table lookups (thanks to however
wrote the lovely atan functions in the 3d demos):

theta = atan2(x, y);
x = cos(theta);
y = sin(theta);

presto, chango, no loss of precision, no integer overflow, supremely
fast integer based vector normalization.

My question -
can anyone think of a way to extend this idea to 3D? My solution looks
like

theta = atan2(x, y);
x1 = cos(theta);
y1 = sin(theta);
rotate vector around z axis by theta degrees
phi = atan2(x, z);
z = sin(theta);
x = x1 * cos(theta);
y = y1 * sin(theta);

(That's probably all messed up BTW, but you get the idea). The problem
is that this version with its 3D rotation is gonna be slower than the
pow(n, 0.5) version, methinks.

Anyone got any insights?

- nick