To:	djgpp AT delorie DOT com
Subject:	Re: ellipses at an angle
Message-ID:	<19970203.183342.4575.2.chambersb@juno.com>
References:	<199702030225 DOT UAA22378 AT mail DOT texoma DOT net>
From:	chambersb AT juno DOT com (Benjamin D Chambers)
Date:	Mon, 03 Feb 1997 21:32:45 EST

On Sun, 2 Feb 1997 20:28:15 -0600 "Mark S. Teel" <mteel AT texoma DOT net>
writes:

>No!  This is not even the definition of an ellipse parallel to a 
>coordinate
>axis!
Wasn't it Galileo who used ellipses like this to model the solar system? 
(Might of been Newton, I was sleeping through that part... the general
equations and such get a lot more fun than a bunch of history :)

>The general equation for an ellipse is:
>
>Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, B^2 - 4*A*C < 0.
>
>If B == 0, then this reduces to an ellipse parallel to a coordinate 
>axis.
>
>MST
>
Uhh.... Hello?  Looks like you're spending a little too much time
indoors, to do that math off the top of your head.
The point is, shapes aren't mathematical equations - they're shapes. 
However, they CAN be modelled with math (by the way, it's easier {IMHO}
to use
(X+A)^2   (Y+B)^2
------- + ------- = 1
  C         D
)
The point is, computers don't run on equations - they run on algorithms. 
You can do all sorts of stuff with algorithms that you can't with
equations - look at any word processor.  Because of this, you can model
shapes by their actual definitions, rather than their mathematical
equations (for a hyperbola, the difference between the distances from the
two foci equals 1 - for a parabola, etc etc)...

...Chabers

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