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mttroot/mtt/lib/examples/Dia/robotrain/robotrain_desc.tex @@ -0,0 +1,31 @@ +% -*-latex-*- Put EMACS into LaTeX-mode +% Verbal description for system robotrain (robotrain_desc.tex) +% Generated by MTT on Sun Sep 12 20:03:30 BST 2004. + +The acausal bond graph of system \textbf{robotrain} is +displayed in Figure \Ref{fig:robotrain_abg.ps}. +The model is based on an off-hooked design of a passive multiple +trailer system for indoor service robots +\footnote{{Jaehyoung Lee, Woojin Chung, Munsang Kim, Chongwon Lee and Jeabok-Song, + A passive multiple trailer system for indoor service robots, + \emph{Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems}, + Maui, Hawaii, USA, 2001}} +The equations of motion for each trailer are given by: +\begin{align} + v_i &= v_{i-1}\cos \phi_i+D_{i-1}\dot\theta_{i-1}\sin \phi_i\\ + \dot\theta_i &= \frac{1}{L_i}\left(v_{i-1}\sin \phi_i+D_{i-1}\dot\theta_{i-1}\cos \phi_i\right)\\ + \phi_i &= \theta_{i-1}-\theta_i +\end{align} +where $v$ and $\dot\theta$ are the translational and rotational velocity of each trailer (in the body axis system), $L$ and $D$ are the lengths of the front and rear moment arms, and the subscripts $_i$ and $_{i-1}$ refer to any trailer and the one in front of it. + +The label file is listed in Section \Ref{sec:robotrain_lbl} and the +subsystems are listed in Section \Ref{sec:robotrain_sub}. + +\subsection{Trajectory} +The trajectory of each of the trailer hooks in response to a constant forward and rotational velocity is shown in figure \Ref{fig:trajectory.ps}. +\fig{trajectory}{trajectory.ps}{0.9}{Trajectory of trailer links} +The plot was generated with the following script: +\footnotesize +\verbatiminput{make_trajectory.sh} +\normalsize + ADDED mttroot/mtt/lib/examples/Dia/robotrain/robotrain_input.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/robotrain_input.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/robotrain_input.txt @@ -0,0 +1,13 @@ +## -*-octave-*- Put Emacs into octave-mode ## + +## +## System robotrain, representation input, language txt; +## File robotrain_input.txt; +## Generated by MTT on Fri Sep 10 00:39:34 BST 2004; + + + +robotrain__Fx = 0.0; +robotrain__Fy = 0.0; +robotrain__tractor__omega__u = 1.0; +robotrain__tractor__v__u = 1.0; ADDED mttroot/mtt/lib/examples/Dia/robotrain/robotrain_lbl.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/robotrain_lbl.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/robotrain_lbl.txt @@ -0,0 +1,36 @@ +#SUMMARY robotrain +#DESCRIPTION Detailed description here + +## System robotrain, representation lbl, language txt +## File robotrain_lbl.txt +## Generated by MTT on Sun Sep 12 19:26:13 BST 2004 + + ###################################### + ##### Model Transformation Tools ##### + ###################################### + +## Port aliases + +## Argument aliases +#ALIAS $1 D +#ALIAS $2 L + +## Each line should be of one of the following forms: +## a comment (ie starting with #) +## component-name cr_name arg1,arg2,..argn +## blank + +## ---- Component labels ---- + +## Component type SS + Fx SS external,external + Fy SS external,external + +## Component type tractor + tractor lin D + +## Component type trailer + front lin D;L + middle lin D;L + rear lin D;L + ADDED mttroot/mtt/lib/examples/Dia/robotrain/robotrain_rep.pdf Index: mttroot/mtt/lib/examples/Dia/robotrain/robotrain_rep.pdf ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/robotrain_rep.pdf cannot compute difference between binary files ADDED mttroot/mtt/lib/examples/Dia/robotrain/robotrain_rep.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/robotrain_rep.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/robotrain_rep.txt @@ -0,0 +1,25 @@ +## -*-octave-*- Put Emacs into octave-mode +## Outline report file for system robotrain (robotrain_rep.txt) +## Generated by MTT on" Sun Sep 12 20:02:40 BST 2004. + +mtt robotrain abg tex # The system description +#mtt robotrain cbg ps # The causal bond graph +mtt robotrain struc tex # The system structure +mtt robotrain sympar tex # The system parameters +## Uncomment the following lines or add others +## mtt robotrain dae tex # The system dae +## mtt robotrain ode tex # The system ode +## mtt robotrain sspar tex # Steady-state parameters +## mtt robotrain ss tex # Steady state +## mtt robotrain dm tex # Descriptor matrices (of linearised system) +## mtt robotrain sm tex # State matrices (of linearised system) +## mtt robotrain tf tex # Transfer function (of linearised system) +## mtt robotrain lmfr ps # log modulus of frequency response (of linearised system) +## mtt robotrain simpar txt # Simulation parameters +## mtt robotrain numpar txt # Numerical simulation parameters +mtt robotrain state txt # Simulation initial state +mtt robotrain input txt # Simulation input +## mtt robotrain logic txt # Logic control +## mtt robotrain odeso ps # Simulation output + +## mtt robotrain rep txt # This file ADDED mttroot/mtt/lib/examples/Dia/robotrain/robotrain_simpar.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/robotrain_simpar.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/robotrain_simpar.txt @@ -0,0 +1,12 @@ +# -*-octave-*- Put Emacs into octave-mode +# Simulation parameters for system robotrain (robotrain_simpar.txt) +# Generated by MTT on Sun Sep 12 18:45:47 BST 2004. + +FIRST = 0.0; # First time in simulation output +DT = 0.1; # Print interval +LAST = 10.0; # Last time in simulation +STEPFACTOR = 10; # Integration steps per print interval +WMIN = -1; # Minimum frequency = 10^WMIN +WMAX = 2; # Maximum frequency = 10^WMAX +WSTEPS = 100; # Number of frequency steps +INPUT = 1; # Index of the input ADDED mttroot/mtt/lib/examples/Dia/robotrain/robotrain_state.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/robotrain_state.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/robotrain_state.txt @@ -0,0 +1,17 @@ +## -*-octave-*- Put Emacs into octave-mode ## + +## +## System robotrain, representation state, language txt; +## File robotrain_state.txt; +## Generated by MTT on Sun Sep 12 18:46:40 BST 2004; + +robotrain__tractor__yaw__mttC = 0.0; +robotrain__front__mttINTF__mttC = -D; +robotrain__front__mttINTF_2__mttC = 0.0; +robotrain__front__yaw__mttC = 0.0; +robotrain__middle__mttINTF__mttC = -(D+L+D); +robotrain__middle__mttINTF_2__mttC = 0.0; +robotrain__middle__yaw__mttC = 0.0; +robotrain__rear__mttINTF__mttC = -(D+L+D+L+D); +robotrain__rear__mttINTF_2__mttC = 0.0; +robotrain__rear__yaw__mttC = 0.0; ADDED mttroot/mtt/lib/examples/Dia/robotrain/rotate_z.cr Index: mttroot/mtt/lib/examples/Dia/robotrain/rotate_z.cr ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/rotate_z.cr @@ -0,0 +1,43 @@ +operator rotate_z; + +let rotate_z (R,~out_causality,1, + ~x1,~causality1,1, + ~y1,~causality2,2, + ~x2,~causality3,3, + ~y2,~causality4,4, + ~psi,~causality5,5) => % x1 + x2*cos(psi)-y2*sin(psi); + +let rotate_z (R,~out_causality,2, + ~x1,~causality1,1, + ~y1,~causality2,2, + ~x2,~causality3,3, + ~y2,~causality4,4, + ~psi,~causality5,5) => % y1 + x2*sin(psi)+y2*sin(psi); + +let rotate_z (R,~out_causality,3, + ~x1,~causality1,1, + ~y1,~causality2,2, + ~x2,~causality3,3, + ~y2,~causality4,4, + ~psi,~causality5,5) => % x2 + x1*cos(psi)+y1*sin(psi); + +let rotate_z (R,~out_causality,4, + ~x1,~causality1,1, + ~y1,~causality2,2, + ~x2,~causality3,3, + ~y2,~causality4,4, + ~psi,~causality5,5) => % y2 + -x1*sin(psi)+y1*cos(psi); + +let rotate_z (R,~out_causality,5, + ~x1,~causality1,1, + ~y1,~causality2,2, + ~x2,~causality3,3, + ~y2,~causality4,4, + ~psi,~causality5,5) => % x1 + 0; + +;end; ADDED mttroot/mtt/lib/examples/Dia/robotrain/rotate_z.pm Index: mttroot/mtt/lib/examples/Dia/robotrain/rotate_z.pm ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/rotate_z.pm @@ -0,0 +1,132 @@ +#------------------------------------------------------------------------------- +# Model Transformation Tools +#------------------------------------------------------------------------------- + + +package rotate_z; + +#------------------------------------------------------------------------------- +# rotation of x-y plane about z +#------------------------------------------------------------------------------- + +use strict; +use warnings; + +#------------------------------------------------------------------------------- +# standard module header (see perlmod for explanation) +#------------------------------------------------------------------------------- +BEGIN { + use Exporter (); + our ($VERSION, @ISA, @EXPORT, @EXPORT_OK, %EXPORT_TAGS); + + $VERSION = 1.00; + + @ISA = qw(Exporter); + @EXPORT = qw(&rotate_z); # CR name + %EXPORT_TAGS = ( ); +} + +#------------------------------------------------------------------------------- +# declaration of specific component implementations +#------------------------------------------------------------------------------- +sub rotate_z_R(@); # R + +#------------------------------------------------------------------------------- +# main function: selects which subfunction to call +#------------------------------------------------------------------------------- +sub rotate_z (@) { + + my $retval; + + $_ = $_[0]; + + s/\((.*)\)/$1/; # strip brackets + my @args = split (/,/); # split arguments + + $_ = $args[0]; # get component type + + # select rule to use + if (/^R|r$/) { $retval = rotate_z_R (@args); } + + # if a substitution has been made ($retval) + if ($retval) + { + return $retval; # return substituted expression + } + else # return nothing + { + return; + } +} + +#------------------------------------------------------------------------------- +# R +#------------------------------------------------------------------------------- +sub rotate_z_R (@) { + + my @args = @_; + my $retval = ''; + + if ($#args == 18-1) + { + my ($component, + $out_causality, + $out_port, + $x1, + $causality1, + $port1, + $y1, + $causality2, + $port2, + $x2, + $causality3, + $port3, + $y2, + $causality4, + $port4, + $psi, + $causality5, + $port5) = @args; + + # [ x2 ] [ +cos(psi) +sin(psi) 0 ] [ x1 ] + # [ y2 ] = [ -sin(psi) +cos(psi) 0 ] [ y1 ] + # [ z2 ] [ 0 0 1 ] [ z1 ] + + # for reverse transformation (x2->x1) use psi=-psi + # note that cos(-psi)=cos(psi) and sin(-psi)=-sin(psi) + + if ($out_port == 1) # x1 + { + $retval = "(($x2)*(+cos($psi))+($y2)*(-sin($psi)))"; + } + elsif ($out_port == 2) # y1 + { + $retval = "(($x2)*(+sin($psi))+($y2)*(+cos($psi)))"; + } + elsif ($out_port == 3) # x2 + { + $retval = "(($x1)*(+cos($psi))+($y1)*(+sin($psi)))"; + } + elsif ($out_port == 4) # y2 + { + $retval = "(($x1)*(-sin($psi))+($y1)*(+cos($psi)))"; + } + elsif ($out_port == 5) + { + $retval = "(0)"; + } + } + + if ($retval) + { + return $retval; + } + else + { + return; + } +} + +#------------------------------------------------------------------------------- +1; # return true + ADDED mttroot/mtt/lib/examples/Dia/robotrain/rotation_abg.dia Index: mttroot/mtt/lib/examples/Dia/robotrain/rotation_abg.dia ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/rotation_abg.dia @@ -0,0 +1,1251 @@ + + + + + + + + + + + + + #A4# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + #Rotation about Z# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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18.453096 13.906937 l s +n 18.453096 13.906937 m 19.205155 15.204785 l s +n 18.453096 13.906937 m 17.705157 15.207163 l s +showpage ADDED mttroot/mtt/lib/examples/Dia/robotrain/rotation_desc.tex Index: mttroot/mtt/lib/examples/Dia/robotrain/rotation_desc.tex ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/rotation_desc.tex @@ -0,0 +1,22 @@ +% -*-latex-*- Put EMACS into LaTeX-mode +% Verbal description for system rotation (rotation_desc.tex) +% Generated by MTT on Sun Sep 12 22:06:34 BST 2004. + +The acausal bond graph of system \textbf{rotation} is +displayed in Figure \Ref{fig:rotation_abg.ps} +. +The label file is listed in Section \Ref{sec:rotation_lbl} and the +subsystems are listed in Section \Ref{sec:rotation_sub}. + +\subsubsection{rotate\_z constitutive relationship} +The rotation between body and Earth axes is achieved using the ``rotate\_z'' constitutive relationship which is implemented as a Reduce file (.cr) and a Perl module (.pm) to permit the model to be built with or without MTT's -no-reduce option. + +\paragraph{rotate\_z.cr} +\footnotesize +\verbatiminput{rotate_z.cr} +\normalsize + +\paragraph{rotate\_z.pm} +\footnotesize +\verbatiminput{rotate_z.pm} +\normalsize ADDED mttroot/mtt/lib/examples/Dia/robotrain/rotation_lbl.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/rotation_lbl.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/rotation_lbl.txt @@ -0,0 +1,44 @@ +#SUMMARY rotation +#DESCRIPTION Detailed description here + +## System rotation, representation lbl, language txt +## File rotation_lbl.txt +## Generated by MTT on Tue Sep 7 16:59:01 BST 2004 + + ###################################### + ##### Model Transformation Tools ##### + ###################################### + +## Port aliases +#ALIAS in x_earth,y_earth +#ALIAS out x_body,y_body + +## Argument aliases + +## Each line should be of one of the following forms: +## a comment (ie starting with #) +## component-name cr_name arg1,arg2,..argn +## blank + +## ---- Component labels ---- + +## Component type 0 (anonymous => default parameters) + # 0 + # 0 + # 0 + # 0 + # 0 + +## Component type AF (anonymous => default parameters) + # AF + +## Component type R + rotation rotate_z + +## Component type SS + [psi] SS external,external + [x_body] SS external,external + [x_earth] SS external,external + [y_body] SS external,external + [y_earth] SS external,external + ADDED mttroot/mtt/lib/examples/Dia/robotrain/tractor_abg.dia Index: mttroot/mtt/lib/examples/Dia/robotrain/tractor_abg.dia ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/tractor_abg.dia @@ -0,0 +1,1458 @@ + + + + + + + + + + + + + #A4# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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22.457897 42.013896 m 21.061956 41.307830 l s +/Helvetica-latin1 ff 0.560000 scf sf +n 21.061956 41.307830 m 21.882638 42.563410 l s +n 21.061956 41.307830 m 22.559662 41.224889 l s +showpage ADDED mttroot/mtt/lib/examples/Dia/robotrain/tractor_lbl.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/tractor_lbl.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/tractor_lbl.txt @@ -0,0 +1,49 @@ +#SUMMARY tractor +#DESCRIPTION Detailed description here + +## System tractor, representation lbl, language txt +## File tractor_lbl.txt +## Generated by MTT on Wed Sep 8 00:42:45 BST 2004 + + ###################################### + ##### Model Transformation Tools ##### + ###################################### + +## Port aliases +#ALIAS out x2,y2 + +## Argument aliases +#ALIAS $1 D + +## Each line should be of one of the following forms: +## a comment (ie starting with #) +## component-name cr_name arg1,arg2,..argn +## 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+/Times-Roman-latin1 ff 0.700000 scf sf +(De:y) dup sw 2 div 48.321492 ex sub 29.353553 m gs 1 -1 sc sh gr +0.100000 slw +[] 0 sd +[] 0 sd +0 slc +0 slj +0 slc +0 slj +[] 0 sd +/Times-Roman-latin1 ff 0.700000 scf sf +(De:x) dup sw 2 div 47.421442 ex sub 45.253553 m gs 1 -1 sc sh gr +0.050000 slw +[] 0 sd +[] 0 sd +1 slc +n 45.333284 29.002269 m 45.570649 29.006347 l s +/Helvetica-latin1 ff 0.560000 scf sf +n 45.570649 29.006347 m 44.258922 29.733925 l s +n 45.570649 29.006347 m 44.284684 28.234146 l s +0.050000 slw +[] 0 sd +[] 0 sd +1 slc +n 47.429326 42.556219 m 47.427874 43.000981 l s +/Helvetica-latin1 ff 0.560000 scf sf +n 47.427874 43.000981 m 48.182111 41.704398 l s +n 47.427874 43.000981 m 46.682119 41.699501 l s +showpage ADDED mttroot/mtt/lib/examples/Dia/robotrain/trailer_lbl.txt Index: mttroot/mtt/lib/examples/Dia/robotrain/trailer_lbl.txt ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/trailer_lbl.txt @@ -0,0 +1,59 @@ +#SUMMARY trailer +#DESCRIPTION Detailed description here + +## System trailer, representation lbl, language txt +## File trailer_lbl.txt +## Generated by MTT on Wed Sep 8 00:41:53 BST 2004 + + ###################################### + ##### Model Transformation Tools ##### + ###################################### + +## Port aliases +#ALIAS in x1,y1 +#ALIAS out x2,y2 + +## Argument aliases +#ALIAS $1 D +#ALIAS $2 L + +## Each line should be of one of the following forms: +## a comment (ie starting with #) +## component-name cr_name arg1,arg2,..argn +## blank + +## ---- Component labels ---- + +## Component type 1 (anonymous => default parameters) + # 1 + # 1 + # 1 + +## Component type AE + negative lin effort,-1 + +## Component type De + x SS external + y SS external + +## Component type Df + omega SS external + v SS external + +## Component type INTF + yaw none + +## Component type SS + [x1] SS external,external + [x2] SS external,external + [y1] SS external,external + [y2] SS external,external + +## Component type TF + D lin flow,-D + L lin effort,L + +## Component type rotation + z1 rotate_z + z2 rotate_z + ADDED mttroot/mtt/lib/examples/Dia/robotrain/trajectory.ps Index: mttroot/mtt/lib/examples/Dia/robotrain/trajectory.ps ================================================================== --- /dev/null +++ mttroot/mtt/lib/examples/Dia/robotrain/trajectory.ps @@ -0,0 +1,927 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: trajectory.eps +%%Creator: gnuplot 4.0 patchlevel 0 +%%CreationDate: Sun Sep 12 19:59:53 2004 +%%DocumentFonts: (atend) +%%BoundingBox: 50 50 410 302 +%%Orientation: Portrait +%%EndComments +/gnudict 256 dict def +gnudict begin +/Color false def +/Solid false def +/gnulinewidth 5.000 def +/userlinewidth gnulinewidth def +/vshift -46 def +/dl {10.0 mul} def +/hpt_ 31.5 def +/vpt_ 31.5 def +/hpt hpt_ def +/vpt vpt_ def +/Rounded false def +/M {moveto} bind def +/L {lineto} bind def +/R {rmoveto} bind def +/V {rlineto} bind def +/N {newpath moveto} bind def +/C {setrgbcolor} bind def +/f {rlineto fill} bind def +/vpt2 vpt 2 mul def +/hpt2 hpt 2 mul def +/Lshow { currentpoint stroke M + 0 vshift R show } def +/Rshow { currentpoint stroke M + dup stringwidth pop neg vshift R show } def +/Cshow { currentpoint stroke M + dup stringwidth pop -2 div vshift R show } def +/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def + /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def +/DL { Color {setrgbcolor Solid {pop []} if 0 setdash } + {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def +/BL { stroke userlinewidth 2 mul setlinewidth + Rounded { 1 setlinejoin 1 setlinecap } if } def +/AL { stroke userlinewidth 2 div setlinewidth + Rounded { 1 setlinejoin 1 setlinecap } if } def +/UL { dup gnulinewidth mul /userlinewidth exch def + dup 1 lt {pop 1} if 10 mul /udl exch def } def +/PL { stroke userlinewidth setlinewidth + Rounded { 1 setlinejoin 1 setlinecap } if } def +/LTw { PL [] 1 setgray } def +/LTb { BL [] 0 0 0 DL } def +/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def +/LT0 { PL [] 1 0 0 DL } def +/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def +/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def +/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def +/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def +/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def +/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def +/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def +/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def +/Pnt { stroke [] 0 setdash + gsave 1 setlinecap M 0 0 V stroke grestore } def +/Dia { stroke [] 0 setdash 2 copy vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke + Pnt } def +/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V + currentpoint stroke M + hpt neg vpt neg R hpt2 0 V stroke + } def +/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke + Pnt } def +/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M + hpt2 vpt2 neg V currentpoint stroke M + hpt2 neg 0 R hpt2 vpt2 V stroke } def +/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke + Pnt } def +/Star { 2 copy Pls Crs } def +/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath fill } def +/TriUF { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath fill } def +/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke + Pnt } def +/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath fill} def +/DiaF { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath fill } def +/Pent { stroke [] 0 setdash 2 copy gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore Pnt } def +/PentF { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath fill grestore } def +/Circle { stroke [] 0 setdash 2 copy + hpt 0 360 arc stroke Pnt } def +/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def +/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def +/C1 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + vpt 0 360 arc closepath } bind def +/C2 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C3 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C4 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C5 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc + 2 copy moveto + 2 copy vpt 180 270 arc closepath fill + vpt 0 360 arc } bind def +/C6 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C7 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 270 arc closepath fill + vpt 0 360 arc closepath } bind def +/C8 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C9 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 270 450 arc closepath fill + vpt 0 360 arc closepath } bind def +/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill + 2 copy moveto + 2 copy vpt 90 180 arc closepath fill + vpt 0 360 arc closepath } bind def +/C11 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 180 arc closepath fill + 2 copy moveto + 2 copy vpt 270 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C12 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C13 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 0 90 arc closepath fill + 2 copy moveto + 2 copy vpt 180 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/C14 { BL [] 0 setdash 2 copy moveto + 2 copy vpt 90 360 arc closepath fill + vpt 0 360 arc } bind def +/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill + vpt 0 360 arc closepath } bind def +/Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } bind def +/Square { dup Rec } bind def +/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def +/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def +/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def +/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def +/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill + exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def +/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill + 2 copy vpt Square fill + Bsquare } bind def +/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def +/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def +/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare } bind def +/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare } bind def +/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def +/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare } bind def +/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def +/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def +/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def +/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def +/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def +/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def +/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def +/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def +/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def +/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def +/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def +/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def +/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def +/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def +/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def +/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def +/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def +/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def +/DiaE { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke } def +/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke } def +/TriUE { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke } def +/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke } def +/PentE { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore } def +/CircE { stroke [] 0 setdash + hpt 0 360 arc stroke } def +/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def +/DiaW { stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V Opaque stroke } def +/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V Opaque stroke } def +/TriUW { stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V Opaque stroke } def +/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V Opaque stroke } def +/PentW { stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + Opaque stroke grestore } def +/CircW { stroke [] 0 setdash + hpt 0 360 arc Opaque stroke } def +/BoxFill { gsave Rec 1 setgray fill grestore } def +/BoxColFill { + gsave Rec + /Fillden exch def + currentrgbcolor + /ColB exch def /ColG exch def /ColR exch def + /ColR ColR Fillden mul Fillden sub 1 add def + /ColG ColG Fillden mul Fillden sub 1 add def + /ColB ColB Fillden mul Fillden sub 1 add def + ColR ColG ColB setrgbcolor + fill grestore } def +% +% PostScript Level 1 Pattern Fill routine +% Usage: x y w h s a XX PatternFill +% x,y = lower left corner of box to be filled +% w,h = width and height of box +% a = angle in degrees between lines and x-axis +% XX = 0/1 for no/yes cross-hatch +% +/PatternFill { gsave /PFa [ 9 2 roll ] def + PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate + PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec + gsave 1 setgray fill grestore clip + currentlinewidth 0.5 mul setlinewidth + /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def + 0 0 M PFa 5 get rotate PFs -2 div dup translate + 0 1 PFs PFa 4 get div 1 add floor cvi + { PFa 4 get mul 0 M 0 PFs V } for + 0 PFa 6 get ne { + 0 1 PFs PFa 4 get div 1 add floor cvi + { PFa 4 get mul 0 2 1 roll M PFs 0 V } for + } if + stroke grestore } def +% +/Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont +dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall +currentdict end definefont pop +end +%%EndProlog +gnudict begin +gsave +50 50 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