[futurebasic] [X-FB] Elliptical sine waves--follow-up

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From: Mark Goodes <wave@...>
Date: Sat, 21 Aug 1999 11:03:45 -0500
Thanks to everyone who replied to my request for information about how
to draw an elliptical sine wave.  It was nice to have a number of
alternate solutions.  I haven't tested any of the ideas yet but hope to
get on the project soon.  I just have a couple of follow-up comments and

Joe wrote:

>  Second; Your request fascinates me. As an architect, anything dealing with
> shapes really catches my attention. First of all, why - assuming you are able to
> do this - would you want to do something like this? The general equation for a
> circle with the center at the origin is:  x^2 + y^2 = r^2; and for an ellipse:
> x^2/a^2 + y^2/b^2 = 1.  Therefore...
> For a given x and y there can be only 1 circle; but it seems to me that there
> could be a whole multitude of ellipses; so it would seem to me that (if you can
> do it at all) you would have to have a sine wave based on a specific ellipse
> rather than on a general one as you might with a circle.
I'm taking a course which requires me to analyse a natural system and
look for periodicity.  Everyone tends to look for evenly spaced wave
peaks in natural systems, but to my knowledge nature uses ellipses as
often as it uses circles (e.g. orbits of planets and electrons).  So I
hope to get a good sense of what an elliptical wave looks like and be
able to eyeball one in my graphical data.  It may not work, but will at
the very least be interesting.

Herbie wrote:

> What you get is no longer a harmonic function. Actually it is a
> distorted sine-wave and I am sure it is quite easy to determine the
> Fourier coefficients and thus the distortion!
Herbie, your solution is much appreciated, but now I'm at a loss--where
would I look to get information on how to determine the Fourier
coefficients?  Also is there some place I could look to learn more about
the solution that you gave me?  I'm sure I could learn all this
reasonably quickly, but the world of higher mathematics is unfamiliar to
me and I have little idea of the basic topics and references.