%% radius_templates_2.txt
%% Created by Laurence D. Finston (LDF) Sun 03 Jul 2022 04:55:34 AM CEST

%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing. 
%%%% Copyright (C) 2022, 2023 The Free Software Foundation, Inc.
   
%%%% 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 
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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)

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%% * (1)


\footline={\hfil \folio\hfil}

%% Uncomment for A4 portrait
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%% *** (3) 

\def\epsfsize#1#2{#1}

%% *** (3)

\headline={\hfil {\tt \timestamp}\hskip2cm}

\pageno=-1

\begingroup
\advance\hsize by -2.5cm
\parskip=.5\baselineskip
\centerline{{\largebx Radius Templates 2}}
\vskip\baselineskip

\small
This document is part of GNU 3DLDF, a package for three-dimensional drawing. 

!Copyright (C) 2022, 2023 The Free Software Foundation

\setbox0=\hbox{Last updated:\quad}

\leavevmode\hbox to \wd0{Created:\hfil}July 3, 2022

\leavevmode\box0 July 6, 2022 %% Updated

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 Publibfgfor 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

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

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

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.  

The author can be contacted at:

Laurence D. Finston\hfil\break
c/o Free Software Foundation, Inc.\hfil\break
51 Franklin St, Fifth Floor \hfil\break
Boston, MA  02110-1301 USA\hfil\break
{\smalltt Laurence.Finston@gmx.de}
\vskip\baselineskip
\centerline{{\largebx Table of Contents}}
\advance\baselineskip by 2pt
%\advance\parskip by 2pt
\readtocfile
\vskip1.5\baselineskip
\endgroup
\vskip\baselineskip
\hldest{xyz}{}{introduction}\vskip.125cm
\Chapter{introduction}{Introduction}
\centerline{{\largebx Introduction}}

\begingroup
\advance\hsize by -1in
\advance\hoffset by 2cm
\parskip=.5\baselineskip

\leftskip=.5cm
The following radius templates may be printed out onto or otherwise transferred to paper, cardboard
or some other material and cut out.  They can then be used to test whether surfaces have the
required camber.  I believe the best way to cut them would be to use a cutting plotter or a
{\Small CNC} machine, however, I have not tested this myself yet.  {\Small PLEASE NOTE} that there is
{\Small NO WARRANTY} for these drawings (see license information above)!

As the radius $r_n$ of circles $c_n$ increases, the circumference of $c_n$ increases proportionately.
In order to keep the radius templates more or less the same size, the magnitude of the angle $\phi_n$
subtended by the arc must decrease as $r_n$ increases.  This is done in the ``Section 1'' sections in
the chapters ``Concave'' and ``Convex''.

In the ``Section 2'' sections, constant $\phi = 10^\circ$ is used, in order to show the
increasing arc length as $r_n$ increases.

The ending angle $\phi_e$ is dependent on the starting angle $\phi_s$ such that
$\phi_e = 180^\circ - \phi_s$.
The starting angle  is arbitrary:  due to the symmetry properties of the circle, any two arcs
of the circle subtended by the same angle are congruent.  In the following figures, $90^\circ$
is taken to be the center of the arc.  However, with $0^\circ$, $30.75^\circ$ or any other value,
the results would have been identical.
\par
\endgroup
\vfil\eject

%% ** (2)



%% * (1)

\headline={\hfil{Radius Templates}\hfil\llap{{\tt \timestamp}\hskip2cm}}
\pageno=1

%% ** (2) Concave

%% *** (3) Section 1

\vbox to \vsize{\hldest{xyz}{}{concave}\vskip.125cm
\Chapter{concave}{Concave}
\centerline{{\largebx Concave}}
\vskip.25cm
\hldest{xyz}{}{concavesectionone}\vskip.125cm
\Section{concavesectionone}{Section 1}
\centerline{{\largebx Section 1}}
\vskip.75cm
\hbox{\epsffile{radius_templates_2_001.eps}\hskip.333cm\epsffile{radius_templates_2_002.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_003.eps}\hskip.333cm\epsffile{radius_templates_2_004.eps}\hss}\vss}
\vfil\eject


\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_005.eps}\hskip.333cm\epsffile{radius_templates_2_006.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_007.eps}\hskip.333cm\epsffile{radius_templates_2_008.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_009.eps}\hskip.333cm\epsffile{radius_templates_2_010.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_011.eps}\hskip.333cm\epsffile{radius_templates_2_012.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_013.eps}\hskip.333cm\epsffile{radius_templates_2_014.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_015.eps}\hskip.333cm\epsffile{radius_templates_2_016.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_017.eps}\hskip.333cm\epsffile{radius_templates_2_018.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_019.eps}\hskip.333cm\epsffile{radius_templates_2_020.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_021.eps}\hskip.333cm\epsffile{radius_templates_2_022.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_023.eps}\hskip.333cm\epsffile{radius_templates_2_024.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_025.eps}\hskip.333cm\epsffile{radius_templates_2_026.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_027.eps}\hskip.333cm\epsffile{radius_templates_2_028.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_029.eps}\hskip.333cm\epsffile{radius_templates_2_030.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_031.eps}\hskip.333cm\epsffile{radius_templates_2_032.eps}\hss}\vss}
\vfil\eject



%% *** (3) Section 2

\vbox to \vsize{\hldest{xyz}{}{concavesectiontwo}\vskip.125cm
\Section{concavesectiontwo}{Section 2}
\centerline{{\largebx Section 2}}
\vskip.75cm
\hbox{\epsffile{radius_templates_2_101.eps}\hskip2cm\epsffile{radius_templates_2_102.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_103.eps}\hskip2cm\epsffile{radius_templates_2_104.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\epsffile{radius_templates_2_105.eps}\hskip1.5cm\epsffile{radius_templates_2_106.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
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\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox{\hskip-.25cm\epsffile{radius_templates_2_109.eps}\hskip.25cm\epsffile{radius_templates_2_110.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_111.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_112.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_113.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_114.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
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\hbox to \hsize{\hss\epsffile{radius_templates_2_115.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_116.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_117.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_118.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_119.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_120.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_121.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_122.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_123.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_124.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_125.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_126.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_127.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_128.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_129.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_130.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_131.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip.125cm
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_132.eps}\hss}\vss}
\vfil\eject

%% ** (2) Convex

%% *** (3) Section 1

\newskip\convexskip
\convexskip=0pt

\vbox to \vsize{\hldest{xyz}{}{convex}\vskip\convexskip
\Chapter{convex}{Convex}
\centerline{{\largebx Convex}}
\vskip.25cm
\hldest{xyz}{}{convexsectionone}\vskip\convexskip
\Section{convexsectionone}{Section 1}
\centerline{{\largebx Section 1}}
\vskip.75cm
\hbox{\epsffile{radius_templates_2_201.eps}\hskip.333cm\epsffile{radius_templates_2_202.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_203.eps}\hskip.333cm\epsffile{radius_templates_2_204.eps}\hss}\vss}
\vfil\eject


\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_205.eps}\hskip.333cm\epsffile{radius_templates_2_206.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_207.eps}\hskip.333cm\epsffile{radius_templates_2_208.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_209.eps}\hskip.333cm\epsffile{radius_templates_2_210.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_211.eps}\hskip.333cm\epsffile{radius_templates_2_212.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_213.eps}\hskip.333cm\epsffile{radius_templates_2_214.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_215.eps}\hskip.333cm\epsffile{radius_templates_2_216.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_217.eps}\hskip.333cm\epsffile{radius_templates_2_218.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_219.eps}\hskip.333cm\epsffile{radius_templates_2_220.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_221.eps}\hskip.333cm\epsffile{radius_templates_2_222.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_223.eps}\hskip.333cm\epsffile{radius_templates_2_224.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_225.eps}\hskip.333cm\epsffile{radius_templates_2_226.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_227.eps}\hskip.333cm\epsffile{radius_templates_2_228.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_229.eps}\hskip.333cm\epsffile{radius_templates_2_230.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_231.eps}\hskip.333cm\epsffile{radius_templates_2_232.eps}\hss}\vss}
\vfil\eject


%% *** (3) Section 2

\vbox to \vsize{\hldest{xyz}{}{convexsectiontwo}\vskip\convexskip
\Section{convexsectiontwo}{Section 2}
\centerline{{\largebx Section 2}}
\vskip.75cm
\hbox{\epsffile{radius_templates_2_301.eps}\hskip2cm\epsffile{radius_templates_2_302.eps}\hss}\vss}
\vfil\eject


\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_303.eps}\hskip2cm\epsffile{radius_templates_2_304.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_305.eps}\hskip1.5cm\epsffile{radius_templates_2_306.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\epsffile{radius_templates_2_307.eps}\hskip.5cm\epsffile{radius_templates_2_308.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox{\hskip-.25cm\epsffile{radius_templates_2_309.eps}\hskip.25cm\epsffile{radius_templates_2_310.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_311.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_312.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_313.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_314.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_315.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_316.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_317.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_318.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_319.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_320.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
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\hbox to \hsize{\hss\epsffile{radius_templates_2_321.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
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\hbox to \hsize{\hss\epsffile{radius_templates_2_322.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_323.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_324.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_325.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_326.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_327.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_328.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_329.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_330.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_331.eps}\hss}\vss}
\vfil\eject

\vbox to \vsize{\vskip\convexskip
\vskip.75cm
\hbox to \hsize{\hss\epsffile{radius_templates_2_332.eps}\hss}\vss}
\vfil\eject


%% *** (3) End here

\bye

%% ** (2)

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