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From: kadickey@phoenix.Princeton.EDU (Kent Andrew Dickey)
Newsgroups: comp.sys.apple
Subject: Re: 3-D vector graphics in assembly
Summary: A better way
Message-ID: <7899@phoenix.Princeton.EDU>
Date: 22 Apr 89 02:00:08 GMT
References: <23400@agate.BERKELEY.EDU> <722@ultb.UUCP>
Reply-To: kadickey@phoenix.Princeton.EDU (Kent Andrew Dickey)
Organization: Princeton University, NJ
Lines: 43

In article <722@ultb.UUCP> lmb7421@ultb.UUCP (L.M. Barstow (674SPS)) writes:
>In article <23400@agate.BERKELEY.EDU> labc-3dc@web-4b.berkeley.edu (Andy McFadden) writes:
>>Question is, does anybody have source/object/vague general notions of
>>how to do 3-D transformations in assembly language?
>>
>>I have a couple of old Nibble magazines, but those requires some transcen-
>>dental functions and square roots (the latter of which is not well handled
>>in the GS toolbox... +/- 3...).  Is there a better/faster way?
>>
>How about taking the transcendentals and changing them into series
>expansions...then all you have to do is run about 3-4 terms of the
>series expansion through the computer (something that, if programmed
>with care, can be done without too much reliance on SANE)
>
>I make no claims on the ability of this method, as I have never actually
>programmed it, but it should be faster than using SANE.  Using tricks
>like multiplying by bit-shifting, and storing polynomials in
>bit-patterns, you should be able to create some fairly fast code.

Most commercial games don't actually do the 3-D computation on the fly--
instead, they compute the actual bit-image of the shape rotated at
various angles and store those directly into memory.  There could be
dozens of different rotations all stored in memory at once.  They can
then 'rotate' the object by just copying directly to the screen the
bit-image of the correct rotation.  All of the calculations for the
proper shapes can be computed before-hand using BASIC if so desired.

For 'on-the-fly' type graphics, you are probably best off computing a
table of approximate sines and cosines, and using that with a fixed
point representation.  If possible, look into how Applesoft does shape
table rotations...it's a pretty good method. 

I also don't understand what the storing polynomials in bit-patterns
means exactly...what polynomials???

NEVER USE SANE!!  You must be joking if you were seriously considering
using that!  Find the actual code that does integer multiplications, and
recode that directly into your programs...it's an efficient routine, but
calls through the tool manager slow it down a lot.

                        Kent Dickey
			KADICKEY@phoenix.arpa
			KADICKEY@PUCC.Bitnet