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 }


=head3 triangle

Create a triangle from 3 vectors specifying the coordinates of each
corner in space coordinates - synonym for L</new>.

=cut


sub triangle($$$) {new($_[0],$_[1],$_[2])};


=head2 Methods


=head3 narrow

Narrow (colinear) triangle?

=cut


sub narrow($$)
 {my $t = shift;  # Triangle
  my $a = 1e-2;   # Accuracy
  my $A = shift;  # Action 0: return indicator, 1: confess 
  
  my $n = (($t->b-$t->a) x ($t->c-$t->a))->length < $a;
  
  confess "Narrow triangle" if $n and $A;
  $n;      
 }


=head3 check

Check its a triangle

=cut


sub check(@)
 {if (debug)
   {for my $t(@_)
     {confess "$t is not a triangle" unless ref($t) eq __PACKAGE__;
     }
   } 
  return (@_)
 }


=head3 is

Test its a triangle

=cut


sub is(@)
 {for my $t(@_)
   {return 0 unless ref($t) eq __PACKAGE__;
   }
  'triangle';
 }


=head3 components

Components of a triangle

=cut


sub a($)   {check(@_) if debug; $_[0]->{a}}
sub b($)   {check(@_) if debug; $_[0]->{b}}
sub c($)   {check(@_) if debug; $_[0]->{c}}

sub ab($)  {check(@_) if debug; ($_[0]->{b}-$_[0]->{a})}
sub ac($)  {check(@_) if debug; ($_[0]->{c}-$_[0]->{a})}
sub ba($)  {check(@_) if debug; ($_[0]->{a}-$_[0]->{b})}
sub bc($)  {check(@_) if debug; ($_[0]->{c}-$_[0]->{b})}
sub ca($)  {check(@_) if debug; ($_[0]->{a}-$_[0]->{c})}
sub cb($)  {check(@_) if debug; ($_[0]->{b}-$_[0]->{c})}

sub abc($) {check(@_) if debug; ($_[0]->{a}, $_[0]->{b}, $_[0]->{c})}
sub area($){check(@_) if debug; ($_[0]->ab x $_[0]->ac)->length}


=head3 clone

Create a triangle from another triangle 

=cut


sub clone($)
 {my ($t) = check(@_); # Triangle   
  bless {a=>$t->a, b=>$t->b, c=>$t->c};
 }


=head3 permute

Cyclically permute the points of a triangle

=cut


sub permute($)
 {my ($t) = check(@_); # Triangle   
  bless {a=>$t->b, b=>$t->c, c=>$t->a};
 }


=head3 center

Center 

=cut


sub center($)
 {my ($t) = check(@_); # Triangle   
  ($t->a + $t->b + $t->c) / 3;
 }


=head3 add

Add a vector to a triangle               

=cut


sub add($$)
 {my ($t) =         check(@_[0..0]); # Triangle   
  my ($v) = vectorCheck(@_[1..1]); # Vector     
  new($t->a+$v, $t->b+$v, $t->c+$v);                         
 }


=head3 subtract