From: "Bill T." 
To: atm{at}shore.net
Reply-To: "Bill T." 


>ooh, cardioids

Can't be much help with cardioid math, but I do know those babies can be
downright vicious.

http://www.kupercontrols.com/misc/modulus2.jpg

I use a machine where the table rotation and stroke are arbitrarily
programmable.  The .jpg in the URL shows a graphic representation of the
paths of the center of a 75% tool over a mirror.  The black circle is the
mirror, the violet circle is the 70% zone, the white circle is the tool.
The red dots show the position of the mirror rotation at the start of each
stroke.  The cardioid patterns show the path of the center of the tool over
about 3 minutes.  The stroke is a narrow, 3 stroke W pattern offset
slightly from center.

The path at the left is every optician's worst nightmare.  After a few
minutes of that, the star test would look like the effects of a really bad
mirror cell.

On the right, we have the same stroke and pattern, but with the lap speed
modified by only 2.5% from 4.2 inches/second to 4.1 ips.  The result is
good stroke distribution.

The moral: it pays to test the stroke pattern with a pencil!

This is an especially extreme example.  In general, the transition from an
ultra-repeateable stroke to a more random stroke is not so pronounced.

Bill T.


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