%%%% sphrmd02.txt
%%%% Created by Laurence D. Finston (LDF) Mon May 31 19:23:37 CEST 2010


%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. 
%%%% Copyright (C) 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 
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%%%% 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. 
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%%%% for more information.   
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%%%% Please send bug reports to Laurence.Finston@gmx.de.
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%%%% 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)

\special{papersize=297mm, 420mm} %% DIN A3 Portrait
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%% !! TODO:  LDF 2012.08.05.  Fix spacing or make another page for instructions.

\begingroup
\hsize=27cm
%\pageno=0
\vbox{}\vskip-1cm
\advance\parskip by -4pt %% LDF 2012.08.05.
%\advance\baselineskip by -.75pt
\centerline{Sphere Model 2}
\vskip\baselineskip
\centerline{Version With Separate Tabs}
\vskip\baselineskip
\centerline{Laurence D. Finston}
\vskip\baselineskip
\centerline{Created:  May 31, 2010}
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\centerline{\hskip 1cm Last updated:  August 6, 2012}
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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) 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 NEW!} 2012.08.06.  Added pyramids for attachment to the octagonal caps.

{\bf NEW!} 2012.08.05.  Added octagonal caps.  They are attached to the
spherical biangles at number 12, where I've added markings for the tab
traces.   The plan for the cap and the tabs are on the page for the 
separate tabs.  The spherical biangles and the tabs will need to be cut off 
beyond the places where the caps are attached.  
accordingly, as soon as I get a chance.  {\bf PLEASE NOTE!}  It may not be
possible to remove the ends of the spherical biangles from the plans, because
this might cause the resulting paths to be drawn inaccurately:  I was working
on subpaths at some time in this past, but I'm not sure if it's possible to draw
portions of paths.  I remember working on this feature, but I don't know
whether I finished it and it certainly hasn't been tested thoroughly.

{\bf PLEASE NOTE!}  The author has tried to ensure that the following
plans are correct, but as of May 31, 2010, he has not tested them
yet himself.  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.

This version of the model consists of separate pieces which must be joined by
using tabs placed under the spherical biangles.  They will not be visible when
the model is assembled.

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.  In addition,
if the paper is too thick, it may be difficult to attach the tabs.  For better
accuracy, it would be necessary to account for the thickness of the paper when
calculating the shape of the tabs.

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 2010.06.04.
%%
Crosshairs in black mark the places where holes should be pricked, on both the
pieces and the tabs.  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 and tabs when they are cut out;  otherwise, it is nearly
impossible to align them correctly when assembling the model.

There are two additional crosshairs at tick mark 15 at the ends of the pieces.
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.

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 has three curves on the left and right sides:  
1. the edge of the spherical biangle, 2.  an inner curve for stitches, 
3. the trace of the edge of the tab used to join each piece with its neighbour.

\par
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%% *** (3) Page 2

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%% *** (3) Headline

\pageno=2

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

%% *** (3) Page 2

\vbox to \vsize{%
\vskip1.5cm
\centerline{{\huge Spherical Biangles}}\vskip 1cm
\line{\hskip 2cm\epsffile{sphrmd02.1}\hss}
\vss}

%% *** (3) Page 3

\vbox to \vsize{%
\centerline{{\huge Tabs}}\vskip.5cm
\line{\hskip 1cm\epsffile{sphrmd02.2}\hss}\vskip.5cm
\centerline{\Large{Octagonal cap}}\vskip1cm
\centerline{\epsffile{sphrmd02.3}}%
\vss}

%% *** (3) Page 4

\vbox to \vsize{\vskip0pt
\centerline{\Large{Octagonal Pyramids for Caps}}\vskip1cm
%\centerline{\epsffile{sphrmd02.4}}
\centerline{\epsffile{sphrmd02.1004}\hfil\epsffile{sphrmd02.2004}}\vskip-1cm
\centerline{\hskip4cm\epsffile{sphrmd02.1004}\hfil\epsffile{sphrmd02.2004}}\vskip-1cm
\centerline{\epsffile{sphrmd02.1004}\hfil\epsffile{sphrmd02.2004}}\vskip.5cm
\line{\hskip5.5cm\epsffile{sphrmd02.3004}\hfil}\vskip1cm
\centerline{\epsffile{sphrmd02.4004}\hfil\epsffile{sphrmd02.4004}\hfil\epsffile{sphrmd02.4004}}\vss}


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