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devel/lib/MyPlanar.pm  view on Meta::CPAN

  if (($c1||$c2) && ($c3||$c4)) {
    ### partial overlap ...
    return [$c1 ? $p1 : $p2,
            $c3 ? $p3 : $p4];
  }

  foreach my $a ($p1,$p2) {
    foreach my $b ($p3,$p4) {
      if ($a->[0]==$b->[0] && $a->[1]==$b->[1]) {
        ### endpoint in common ...
        return [$a,$a];
      }
    }
  }

  ### try point intersection ...
  if (my $p = Math::Geometry::Planar::SegmentIntersection($points)) {
    return [$p,$p];
  }
  return 0;
}

sub distance_segment_to_segment {
  my ($points) = @_;
  my ($p1,$p2, $p3,$p4) = @$points;

  # DistanceToSegment() is +ve on the left and -ve on the right.
  # Here want absolute value.
  # 
  # Shortest distance is always attained going to the endpoint of one
  # segment, since straight lines.

  my $ret;
  foreach (0,1) {
    foreach my $i (2,3) {
      my $d = abs(DistanceToSegment([$points->[0],$points->[1],$points->[$i]]));
      $ret = min($ret // $d, $d)
        or return $ret;  # if 0
    }
    $points = [reverse @$points];

lib/Graph/Maker/Catalans.pm  view on Meta::CPAN

length are a row of the Catalan triangle.

     T              rotate_rightarm
    / \
       *            only rotate edges
      / \           on the right-most arm
         *          extending down
        / \

In terms of balanced binary, right arm means rotate at "1aaaa0 1" where the
0 there is a return to the zero line.  The graph endpoints
(C<$graph-E<gt>successorless_vertices>) have no such returns to zero.  They
are "1 balanced(N-1) 0", and hence Catalan(N-1) many.

In terms of C<Ldepths>, right arm vertices have Ldepth=0 and the x,y
vertices of the rotate are consecutive Ldepth=0 (and other non-zeros in
between).  The rotate increases the depth of the second.

Csar, Sengupta, and Suksompong get various rightarm results too, as
X<comb poset>"comb poset" of bracketings.