Mail Archives: djgpp/1997/02/04/01:39:38
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
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