From:	Martin Ambuhl <mambuhl AT earthlink DOT net>
Newsgroups:	comp.os.msdos.djgpp
Subject:	Re: sin(acos((float)i/1024))*0x10000L
Date:	Mon, 15 Mar 1999 14:19:13 -0500
References:	<36EBFD7D DOT 7D0FCB2C AT geocities DOT com> <36ecc7f2 DOT 50985511 AT news DOT snafu DOT de>
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To:	djgpp AT delorie DOT com
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Horst Kraemer wrote:

> Better get another tutorial. The formula sin(acos(x)) is ridiculous.
> 
> For x between 0 and 1
> 
>         sin(acos(x)) = sqrt(1-x*x)

Horst is obviously right, but it is worth remarking that if you want to
do graphics, you must learn some elementary trigonometry.  Among the the
things you should learn (or work our for your self) is that the
Pythagorean formula
   double sqr(double x) { return x*x; }  /* helper function */
   sqr(a) + sqr(b) == sqr(c);
on a unit circle is
   sqr(y) + sqr(x) == 1;
or
   sqr(cos(t)) + sqr(sin(t)) == 1;
When you know cos(t) == v, this leads to Horst's form
   sin(t) == sqrt(1-v*v);
This is the sort of thing you should learn now, before further graphics
programming.  It is not the sort of thing you ask in a newsgroup for a
programming language.


 

    

-- 
Martin Ambuhl (mambuhl AT earthlink DOT net)
Note: mambuhl AT tiac DOT net will soon be inactive

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