%%%% sphrmd01.txt
%%%% Created by Laurence D. Finston (LDF) Tue Jan 13 18:00:51 CET 2009


%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. 
%%%% Copyright (C) 2009, 2010, 2011, 2012, 2013 The Free Software Foundation
   
%%%% GNU 3DLDF is free software; you can redistribute it and/or modify 
%%%% it under the terms of the GNU General Public License as published by 
%%%% the Free Software Foundation; either version 3 of the License, or 
%%%% (at your option) any later version. 

%%%% GNU 3DLDF is distributed in the hope that it will be useful, 
%%%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the 
%%%% GNU General Public License for more details. 

%%%% You should have received a copy of the GNU General Public License 
%%%% along with GNU 3DLDF; if not, write to the Free Software 
%%%% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA

%%%% GNU 3DLDF is a GNU package.  
%%%% It is part of the GNU Project of the  
%%%% Free Software Foundation 
%%%% and is published under the GNU General Public License. 
%%%% See the website http://www.gnu.org 
%%%% for more information.   
%%%% GNU 3DLDF is available for downloading from 
%%%% http://www.gnu.org/software/3dldf/LDF.html. 

%%%% Please send bug reports to Laurence.Finston@gmx.de.
%%%% The mailing list help-3dldf@gnu.org is available for people to 
%%%% ask other users for help.  
%%%% The mailing list info-3dldf@gnu.org is for the maintainer of 
%%%% GNU 3DLDF to send announcements to users. 
%%%% To subscribe to these mailing lists, send an 
%%%% email with ``subscribe <email-address>'' as the subject.  

%%%% The author can be contacted at: 

%%%% Laurence D. Finston 
%%%% c/o Free Software Foundation, Inc. 
%%%% 51 Franklin St, Fifth Floor 
%%%% Boston, MA  02110-1301  
%%%% USA

%%%% Laurence.Finston@gmx.de



%% * (1)

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%% *** (3) Title page

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\begingroup
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\centerline{Sphere Model 1}
\vskip\baselineskip
\centerline{Laurence D. Finston}
\vskip\baselineskip
\centerline{Created:  October 20, 2009}
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\centerline{\hskip 1cm Last updated:  June 4, 2010}
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%
{\small
\hsize=.75\hsize
%\hskip1cm
\vbox{\vskip2\baselineskip
This document is part of GNU 3DLDF, a package for three-dimensional
drawing.
\vskip\baselineskip

Copyright (C) 2009, 2010, 2011, 2012, 2013 The Free Software Foundation
\vskip\baselineskip

GNU 3DLDF is free software; you can redistribute it and/or modify 
it under the terms of the GNU General Public License as published by 
the Free Software Foundation; either version 3 of the License, or 
(at your option) any later version. 
\vskip\baselineskip

GNU 3DLDF is distributed in the hope that it will be useful, 
but WITHOUT ANY WARRANTY; without even the implied warranty of 
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the 
GNU General Public License for more details. 
\vskip\baselineskip

You should have received a copy of the GNU General Public License 
along with GNU 3DLDF; if not, write to the Free Software 
Foundation, Inc.,\hfil\break
51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
\vskip\baselineskip

See the GNU Free Documentation License for the copying conditions 
that apply to this document.
\vskip\baselineskip

You should have received a copy of the GNU Free Documentation License 
along with GNU 3DLDF; if not, write to the Free Software 
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
\vskip\baselineskip

The mailing list {\smalltt info-3dldf@gnu.org} is for sending 
announcements to users. To subscribe to this mailing list, send an 
email with ``subscribe $\langle$email-address$\rangle$'' as the subject.  
\vskip\baselineskip

The webpages for GNU 3DLDF are here:
{\smalltt http://www.gnu.org/software/3dldf/LDF.html}
\vskip\baselineskip

The author can be contacted at:\vskip\baselineskip 

Laurence D. Finston\hfil\break
c/o Free Software Foundation, Inc.\hfil\break
51 Franklin St, Fifth Floor \hfil\break
Boston, MA  02110-1301 \hfil\break 
USA
\vskip\baselineskip

{\smalltt Laurence.Finston@gmx.de}}}
\par


%% *** (3)

\begingroup

\parskip=\baselineskip


\centerline{{\largebx Instructions}}
\vskip 1.5\baselineskip

{\bf PLEASE NOTE!}  The author has tried to ensure that the following
plans are correct.  As mentioned above, this material is distributed 
{\bf without a warranty}.  I recommend that users check it themselves before
investing a lot of time and effort into cutting out the paper model.

Any corrections will be gratefully received by the author.  Contact
information can be found on the title page.

These plans represent a ``development'' of a sphere:  The individual figures
are ``flattened-out'' spherical biangles corresponding to $1/8$ of a sphere.

To use these plans, tape, tack or otherwise attach them to a sheet of
paper which should be robust, but not too thick.  I generally prefer tacking
to taping, where possible.

Fairly light, smooth watercolor paper might be a good choice.  Bristol board
or cardboard cannot be used for this model, because the pieces need to be able to bend.  

First, prick out the holes for the stitches and then use a cutting knife to
cut out the {\it outer\/} lines of the plan.  {\bf Please note}:  The {\it
inner\/} lines are only for reference and should not be scored!  
%%
%% LDF 2010.06.02.
%%
Crosshairs in black mark the places where holes should be pricked.  Toward the
ends where the curves get very close to the edges, holes should not be pricked.
I have added numbers and tick-marks beside the even-numbered crosshairs and
also further along the curves beyond where holes should be pricked.
The numbers and tick marks should be written on both sides of the
pieces when they are cut out;  otherwise, it is nearly impossible to align the pieces correctly
when assembling the model.

There are two additional crosshairs at tick mark 15 at each end.  Here, holes
should be pricked and a thread run through them for pulling the ends together
{\it carefully\/} to finish assembling the model.

{\bf Please Note}:  This is not an ideal solution for the ends.  A better idea
would be some kind of ``polar cap''.  I will try to work on this as soon as
possible.  (2010.06.04.)

Felt mats are available at hobby supply stores.  I find they work well for
pricking out the holes.

%% Added.  LDF 2010.06.04.
%% 
The numbers on the spherical biangles and the letters ``L'' and ``R'' (for
``Left'' and ``Right'') are merely for reference.  Once the pieces are cut
out, and especially during assembly when the pieces are bent, it becomes
difficult to tell which side is which.

The knife must be sharp as watercolor paper (or other heavy papers) will dull
the blade quickly.  I have been using knives with disposable blades.  I've
been meaning to try sharpening them but haven't done so yet.  I therefore
can't say whether this will work.  It seems a shame to waste so many blades,
which is why I have a jar full of them.  They must be good for something.

It will be necessary to reattach the plans parts of them are cut out.

Make sure that the plan is attached smoothly or you will introduce
inaccuracies.  {\it Do not detach it or let it slip until you are
done!\/}  You will never get it back where it's supposed to go. 
However, with this model, this is only important for an individual piece,
since they aren't attached to each other.

If you use tape, please use the removable kind.  Ordinary masking tape will
damage the paper when it is removed.  Be aware that ``removable tape'' isn't
completely reliable, especially if left too long on the drawing.  Sometimes
it's possible to reuse pieces of it, which avoids wasting large amounts of
it. 

Each figure contains 5 curves:  From left-to-right:  1. the left edge of the
spherical biangle, 2.  an inner curve for stitches, 3. the right edge of the
spherical biangle, 4., an outer curve for stitches, 5. a curve that's even
further out to provide an offset so that holes can be punched for the stitches
in curve number four.

Once they are punched and cut out, two pieces A and B should be joined so that
the outer curve for stitches on A (4) should be placed over the inner curve
for stitches on B (2).  Then, curve 4 of B should be placed over curve 2 of a
third piece, C, and so forth.  As the sphere closes, it will probably be
necessary to pre-thread the holes in such a way that the threads can be pulled
tight without having to reach inside the (partial) sphere.  However, it may be
possible to use a curved needle, such as an upholsterer's needle.  
While the author has partially assembled the model, he hasn't gotten to
this point yet (as of 2010.06.02). 
\par
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%% *** (3) Headline

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\headline={\hskip 2cm Sphere Model 1\quad %
           Copyright {\copyright} 2009, 2010, 2011, 2012, 2013 The Free Software Foundation\hfil %
           \folio\hfil Author:  Laurence D. Finston\hfil}

%% *** (3) Page 2

\vbox to \vsize{%
\vskip1cm
\centerline{{\huge Spherical Biangles}}\vskip 1cm
\line{\hskip 2cm\epsffile{sphrmd01.1}\hss}
\vss}

%% *** (3) End here

\bye



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