RE: [ATM] Which stroke ?

[Jim Burrows <burrjaw@earthlink.net>]

At 2004-05-04 19:43 -0400, Jerry wrote:

>No matter which program you are using for a Texereau type reduction program,
>it will boil your test numbers down to the difference from one zone to the
>next.

Nope.  Look at Texereau, p. 103, "That is, the distance HH' is the integral 
of the slope error u taken from the mirror center to point H."  So TEX, in 
particular, uses each Foucault reading to obtain the slope of the 
corresponding mirror surface patch and does a "simple graphical integration."

Sixtests is slightly more precise and sets up a differential equation for 
the mirror surface height x as a function of zone radius y:

         dx/dy = y/(f - x),

f being the (moving-source) Foucault reading (mirror vertex to KE).  The 
differential equation is numerically solved for height x(y) using the 
Runge-Kutta formula which in turn requires interpolating the readings, not 
differencing them.

         -- Jim Burrows
         -- mailto://burrjaw@earthlink.net
         -- http://home.earthlink.net/~burrjaw
         -- Seattle N47.4723 W122.3662 (WGS84) 

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