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	   and (not defined $A or abs($A - $L->[0][1]) < 0.0001) and (not defined $B or abs($B - $L->[0][2]) < 0.0001) ;
  # @$dirs are for the join-the-centers broken line (1 for 45 degrees, 0 for horizontal)
  for my $l (@$L) {
    $l->[$_] = 1+sprintf "%.12g", $l->[$_]-1 for 1, 2;	# Round also values close to 0
  }
  print "\\doCase{$P}{$PRE@SIDES$POST}{", (join ', ', map +(join '/', @$_), @$L), "}{$Perp}{$minDir16\\dots $maxDir16}	% (@DIRS) [@SIDES] (", !!$addL,", ", !!$addR, ")\n";
  print "%\\doSlopes{$SL}{$SLint}	%\n" unless @$lines <= 2;
}

sub test_encodes_line_prologue {
  <<'EOP';
\documentclass{amsart}
\usepackage[margin=0.4in,landscape,nohead,nofoot]{geometry}	% may need a4paper/letterpaper
\usepackage{tikz}

\newcommand\doCase[5]{%		1: points (X/Y) 2: descr 3: lines (A/B/x0/x1/extend_dotted_left_dx/extend_dotted_right_dx)  y=A*x+B
  \fbox{\tikz[scale=0.3]{%	4: perpendiculars X Y dX dY len
    \foreach \X/\Y/\how in {#1} {%
      \draw[gray!75,densely dotted] (\X-0.5,\Y-0.5) rectangle ++(1,1);%
      \pgfmathsetmacro\DIR{\how<0?-1:1}%
%      \pgfmathsetmacro\isVERT{\how==0}%
      \ifnum \how=0 %
        \fill[blue] (\X,\Y-0.5) circle (0.2em);%
        \fill[red] (\X,\Y+0.5) circle (0.2em);%
      \else		% \how=-1: decreasing; lower bound on the left, upper on the right; 1: opposite
        \fill[blue] (\X+\DIR/2,\Y) circle (0.2em);% lower
        \fill[red]  (\X-\DIR/2,\Y) circle (0.2em);% upper
      \fi
    }%
    \foreach [count=\c] \inv/\A/\B/\x/\X/\pre/\post in {#3} {%
      \pgfmathsetmacro\COL{{"orange","purple"}[mod(\c,2)]}%
      \pgfmathtruncatemacro\DO{\pre>0}%
      \pgfmathtruncatemacro\DOii{\post>0}%
      \ifnum \inv=0 %
        \draw[\COL] (\x,\x*\A+\B) -- (\X,\X*\A+\B);%
        \ifnum \DO > 0 %
          \draw[\COL,densely dotted] (\x-\pre,\x*\A-\pre*\A+\B) -- (\x,\x*\A+\B);%
        \fi
        \ifnum \DOii > 0 %
          \draw[\COL,densely dotted] (\X+\post,\X*\A+\post*\A+\B) -- (\X,\X*\A+\B);%
        \fi
      \else		% exchange 1st and 2nd coordinate
        \draw[\COL] (\x*\A+\B,\x) -- (\X*\A+\B,\X);%
        \ifnum \DO > 0 %
          \draw[\COL,densely dotted] (\x*\A-\pre*\A+\B,\x-\pre) -- (\x*\A+\B,\x);%
        \fi
        \ifnum \DOii > 0 %
          \draw[\COL,densely dotted] (\X*\A+\post*\A+\B,\X+\post) -- (\X*\A+\B,\X);%
        \fi
      \fi
    }%
    \foreach [count=\c] \x/\y/\dx/\dy/\len/\X/\Y/\i/\XX/\YY in {#4} {%
      \pgfmathtruncatemacro\DO{\len<30}%
      \ifnum \DO > 0 %
        \draw[] (\x,\y) -- ++(\dx,\dy) coordinate (e);%
        \fill[] (e) circle (0.28em);%			vs thickness of "thick"
        \draw[violet,thick] (e) -- (\XX,\YY) coordinate (ee);%
        \fill[violet] (ee) circle (0.28em);%
      \fi
    }%
  \node[below left, overlay] at (current bounding box.north east) {#5};%
  }}\llap{\small #2 }\hfil}


\newcommand\doSlopes[2]{%		points (X/Ymin/Ymax)
  {\color{blue}\fbox{\tikz[scale=0.3]{%
    \foreach \Z/\ZZ/\slope/\inv in {#2} {%
      \draw[gray!66,very thick] (\Z,\slope*5) -- (\ZZ,\slope*5);%
    }%
    \foreach \Z/\Umin/\Umax in {#1} {%
      \fill[blue] (\Z,\Umin*5) circle (0.2em);%
      \fill[red] (\Z,\Umax*5) circle (0.2em);%
    }%
    }}}\hfil}

\begin{document}

\noindent
EOP
}

sub _decode_expectations ($) {
  my $in = shift;
  return $in, undef unless ref $in;
  $in->[0], $in->[1]
}

# Encoding: numbers>=0 --> adjacent "horizontal" runs of this many tiles (1 level above the previous reference height, and change 
# this height); [N]: rotate whatever "increments" follow N * 90 degrees clockwise; numbers<0: change the reference height so that 
# the next run of tiles is that much below the preceding one.
sub _test_encodes_lines($$$$) {	# Need to check incredible amount of branches...
  my($how, $rot, $maxDx, $maxRoAng) = (shift, shift, shift, shift);
  print test_encodes_line_prologue;
  # Actually, the slopes below are for the old algorithm; the new one gives slightly different fits.
  my @exp;
  (@exp = _decode_expectations $_->[0]), test_encodes_line($rot, $exp[0], $exp[1], $_->[1], $_->[2], $_->[3], $how, $maxDx, $maxRoAng) 
#    for [undef, [7, 5], 0, 1]; 0
#    for [undef, [3,3,4,4,3], 1]; 0
#    for [[1, 0], [1,1]]; 0
#    for [undef, [1,3,1,1,3,1]]; 0
#    for [3, [3], 0, 1]; 0
#    for [undef, [7, 9], 1, 1]; 0
#    for [undef, [7, 9], 1]; 0
#    for [undef, [9, 7], 1, 1]; 0
#    for [undef, [1,1,1,2,2,2,5], 1]; 0
#    for [1,     [1,1]]; 0
#    for [undef, [4,4,4,3,3], 0, 1], ; 0
#    for [undef, [1,-2,1,-1,1,-1,2,-1,5,2,1,1,0,1]], [undef, [[1], 1,[],1,[-1],-1,1,-1,2,-1,5,2,1,1,0,1]], ; 0
#    for [undef, [[1], 2,1]], ; 0
#    for [undef, [[1], 1, 2,1]], ; 0
#    for [undef, [[1], 1,2]], [undef, [[1], 1,2,1]], [undef, [[1], 1,2,1,1]], ; 0
#    for [undef, [[1], 1,2, [-1], -1,1,-1,2,-1,5,2,1,1,0,1]], ; 0
#    for [undef, [[1], 1,2, [-1], -1,1,-1,2,-1, 5]], ; 0
#    for [undef, [[1], 1,2, [-1], -1,1,-1,2]], ; 0
#    for [undef, [[1], 1,2, [-1], -1,1,-1,2,-1,5,2,1,[-1],-1,2,-1,1]], ; 0
#    for [undef, [[1], 5, 1]], [-1/5, [[1], 5, 2]], ; 0
#    for [undef, [[1], 5, 1]], ; 0
#    for [-1/5, [[1], 5, 2]], ; 0
    for [7, [7], 1, 1], [7, [7], 0, 1], 
        [7, [7], 1], [undef, [7, 9], 1, 1], [undef, [7,9], 1], [undef, [5,7], 1], [undef, [7, 5], 0, 1], 
        [9, [7, 9], 0, 1], [9, [7,9]], [5.5, [5,6], 1], [5.5, [6, 5], 0, 1],