Date: Tue, 4 Feb 1997 10:14:44 +0000 ( ) From: Gurunandan R Bhat To: Benjamin D Chambers Cc: djgpp AT delorie DOT com Subject: Re: ellipses at an angle In-Reply-To: <19970203.183342.4575.2.chambersb@juno.com> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII On Mon, 3 Feb 1997, Benjamin D Chambers wrote: > (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 :) check out arthur koestler's "sleepwalkers" - history of man's conception of the universe. you might begin to like history. > 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 [snipped equation] > The point is, computers don't run on equations - they run on algorithms. how true! there is a way however to get "shapes" out of equations: its called the "parametric equation". the advantage of these parametric equation is that the solution is built into the expressions. (sorry to bore people who know..) an example is a circle: x^2 + y^2 == a^2, to plot that, use some optimised version of the two expressions: x = a * cos(t) y = a * sin(t) with these expressions (not equations, mind! note the == in the equation as opposed to = in the expression) the equation for the circle comes "presolved". one can get a parametric expression for the ellipse too and i had posted it a few days ago (with a mistake, later corrected). in any case here it is again: x = r1 * cos(t) y = r2 * sin(t) these expressions are designed to "presolve" the equation for the ellipse for any value of t (the angle actually). rotation expressions were given in my earlier mail which i cannot locate now. but if you are interested, i would be happy to send them to you. with warmest regards