Path: chuka.playstation.co.uk!scea!greg_labrec@interactive.sony.com
From: "Chris Blackwell" <bespeed@smartt.com>
Newsgroups: scea.yaroze.programming.3d_graphics
Subject: A reply to one of Nick's questions.
Date: 8 Sep 1997 12:01:01 GMT
Organization: SCEA News Server
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Hey Nick! You know, one of the reasons people may not be replying to your
messages is that your crazy Mac newsreader does something wierd so that
when I try to reply to your messages, the reply text I type in comes out in
symbol font. It's an extremely peculiar behavior. What newsreader are you
using????

Anyway, here's an idea to solve your problem. You still could perform the
formula listed below, but do it using fixed point series expansions. I
don't know what kind of gain you'd get, but it's worth a look. You could
use series expansions converted into fixed point, and then reduce the
equations to come up with an expansion that will cover your formula.

You formula would break down to 

z = sin(atan(x/y))
x = cos(atan(x/y)) ^ 2
y = sin(atan(x/y)) ^ 2

These could then be reduced using the the following expansions:

sin(x) = x - 1/6x^3 + 1/120x^5 - 1/5040x^7 + 1/362880x^9
cos(x) = 1 - 1/2x^2 + 1/24x^4 - 1/720x^6 + 1/40320x^8
atan(x) = x - 1/3x^3 + 1/5x^5 - 1/7x^7 + 1/9 x^9

I leave it to you to plug these in and do the  reductions. After doing the
reductions you'll have an idea of how many multiply and divides this leads
to. It may be rediculous, but hey, it's an idea.

-Chris

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

ChrisB Notes: Did you mean to use phi in the next calcs?? :-) If so, my
formula's above will need to be adjusted.

>phi = atan2(x, z);
>z = sin(theta);
>x = x1 * cos(theta);
>y = y1 * sin(theta);