Re: [ATM] Another Math Question

["Richard F.L.R. Snashall" <rflrs@rcn.com>]

Richard F.L.R. Snashall wrote:
> I'm trying to solve a problem in R^3.  I have a point P0 and
> a [unit] direction P0'.  I also have another point P1.  I want
> to find the minimal distance of P1 from the ray path given by
> P0 and P0'.  I create R1, the relative position of P1, equal
> to P1 - P0.  Then, the dot product R1 . P0' represents the
> [signed] component of the relative position in the direction
> of propagation, since the norm of P0' is unity.  Then,
> R1 - R1.P0' * P0' gives the rest of the relative position not
> in the direction of propagation.  Its norm should then give
> the minimal distance between P1 and the ray. -- Right?
Thank you all.  Yes, it works; what I had forgotten to say here
was that I already needed R1.P0' as I used it to judge whether
there was any possible interference at all (the pass point
could be out-of-bounds, anyway).  Anyway, I used it to
design a ZPL macro to check the clearances.  Yes, it can be
done within the merit function itself, but, with five cones and
four interference points each, the code was getting quite
lengthy.  I then used the macro to help design this 200.4 mm
f/11 Tetra-Schiefspiegel:

    http://users.rcn.com/rflrs/schiefsp01-89x.atm   ATMOS input file
    http://users.rcn.com/rflrs/schiefsp01-89x.len   OSLO input file
    http://users.rcn.com/rflrs/schiefsp01-89x.sp    WINSPOT input file
    http://users.rcn.com/rflrs/schiefsp01-89x.txt   TEXT prescription
    http://users.rcn.com/rflrs/schiefsp01-89x.zmx   ZEMAX input file

This one is an adaptation of one of John Francis' designs:

    http://bhs.broo.k12.wv.us/homepage/alumni/dstevick/novel.htm

Another feature with this design is that it has low anamorphism.
This term was new to me -- anamorphism is considered to be the
difference between the image scales perpendicular to and parallel
to the paper, in case anyone else is unfamiliar with it.  It
seems this can be a problem with tilted component telescopes,
even though, technically, it is just a first-order distortion.

The design ended up being relatively compact, too.

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