Path: utzoo!attcan!uunet!husc6!psuvax1!psuvm!cunyvm!ndsuvm1.bitnet!nu113738
From: NU113738@NDSUVM1.BITNET
Newsgroups: comp.graphics
Subject: Re: Line Math
Message-ID: <2601NU113738@NDSUVM1>
Date: 28 Jul 89 05:37:48 GMT
References: <QYmDXdy00W0HE1u0ZG@andrew.cmu.edu> <2578NU113738@NDSUVM1>
Organization: North Dakota Higher Education Computer Network, Fargo, ND
Lines: 33
Disclaimer: Author bears full responsibility for contents of this article.

Ok, I was pointed out a problem in my last response, as sloppy as it was.

I indicated no division was required but then went on to suggest the
formula r = x / cos0.  Obviously a division.  But this is also equal to
r = x * 1/cos0 and of course 1/cos0 = csc0.  So by using csc and sec instead
of sin/cos, division can be removed.

Along this thought line, another item occurs in trying to speed up equation,
mainly, to calculate csc0 or sec0, floating point math is required.

What I did, in a situation where a sin/cos table of the values for each
degree were required, is to create it as such, say the value of 23 degress
is .3907311.....  After calculation of this value for storage in the lookup
table, I then used the idea that .390xxx = 390 x 10^-3.  But instead of base
10, I used base 2.  So I would take .3907311 x 4096 or 2048 or some power
of 2 and store that value as an integer.  Now, when I retrieve the value from
the storage table, say I need (3*sin23) then the math is performed as:
      (3 *(lookup(23)) >> 11.  The arthmethic shift by 11 is performed instead
of a division by 2048... A much faster method and it required no floating point
mathematics.  Although, to store the intial value of .3907311, if you want
a fairly accurate estimation, you need to use long integers since a word
(assuming a IBMPC size word) is insufficient to store the value with out
an overflow condition.  In timing the differences in this elongated and
somewhat sloppy method of division/multiplication/storage, it still kicks
a floating point arithmetic time.  (although, I don't know what would
be the result with a coprocessor, so don't take my word in that case.)

These are just some suggestions.  I hope they help or give someone some
ideas.


Jeff Bakke
NU113738@NDSUVM1.BITNET