
=head1 Vector


Manipulate 3D vectors

PhilipRBrenan@yahoo.com, 2004, Perl licence


=head2 Synopsis


Example t/vector.t

 #_ Vector _____________________________________________________________
 # Test 3d vectors    
 # philiprbrenan@yahoo.com, 2004, Perl License    
 #______________________________________________________________________
 
 use Math::Zap::Vector vector=>'v', units=>'u';
 use Test::Simple tests=>7;
 
 my ($x, $y, $z) = u();
 
 ok(!$x                            == 1);
 ok(2*$x+3*$y+4*$z                 == v( 2,  3,   4));
 ok(-$x-$y-$z                      == v(-1, -1,  -1));
 ok((2*$x+3*$y+4*$z) + (-$x-$y-$z) == v( 1,  2,   3));
 ok((2*$x+3*$y+4*$z) * (-$x-$y-$z) == -9);  
 ok($x*2                           == v( 2,  0,   0));
 ok($y/2                           == v( 0,  0.5, 0));
 


=head2 Description


Manipulate 3 dimensional vectors via operators.

 
 package Math::Zap::Vector; 
 $VERSION=1.03;
 use Math::Trig;
 use Carp;
 use constant debug => 0; # Debugging level
 


=head3 Constructors



=head4 new


Create a vector from numbers

 
 sub new($$$)
  {return round(bless({x=>$_[0], y=>$_[1], z=>$_[2]})) if debug; 
   bless {x=>$_[0], y=>$_[1], z=>$_[2]}; 
  }
 
 sub vector($$$) {new($_[0], $_[1], $_[2])}
 


=head4 units


Unit vectors              

 
 sub units() {($x, $y, $z)}
 


=head3 Methods



=head4 check


Check its a vector

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


=head4 is


Test its a vector

 
 sub is(@)
  {for my $v(@_)
    {return 0 unless ref($v) eq __PACKAGE__;
    }
   'vector';
  }
 


=head4 accuracy


Get/Set accuracy for comparisons

 
 my $accuracy = 1e-10;
 
 sub accuracy
  {return $accuracy unless scalar(@_);
   $accuracy = shift();
  }
 


=head4 round


Round: round to nearest integer if within accuracy of that integer 

 
 sub round($)
  {unless (debug)
    {return $_[0];
    }
   else
    {my ($a) = @_;
     for my $k(keys(%$a))
      {my $n = $a->{$k};
       my $N = int($n);
       $a->{$k} = $N if abs($n-$N) < $accuracy;
      }
     return $a;
    }
  }
 


=head4 x,y,z


x,y,z components of vector

 
 sub x($) {check(@_) if debug; $_[0]->{x}}
 sub y($) {check(@_) if debug; $_[0]->{y}}
 sub z($) {check(@_) if debug; $_[0]->{z}}
 
 $x = new(1,0,0);
 $y = new(0,1,0);
 $z = new(0,0,1);
 


=head4 clone


Create a vector from another vector

 
 sub clone($)
  {my ($v) = check(@_); # Vectors
   round bless {x=>$v->x, y=>$v->y, z=>$v->z}; 
  }
 


=head4 length


Length of a vector

 
 sub length($)
  {my ($v) = check(@_[0..0]); # Vectors
   sqrt($v->x**2+$v->y**2+$v->z**2);
  } 
 


=head4 print


Print vector

 
 sub print($)
  {my ($v) = check(@_); # Vectors
   my ($x, $y, $z) = ($v->x, $v->y, $v->z);
 
   "vector($x, $y, $z)";
  } 
 


=head4 norm


Normalize vector

 
 sub norm($)
  {my ($v) = check(@_); # Vectors
      $v = $v->clone;   # Copy vector
   my $l = $v->length;
 
   $l > 0 or confess "Cannot normalize zero length vector $v";
 
   $v->{x} /= $l;
   $v->{y} /= $l;
   $v->{z} /= $l;
   $v;
  } 
 


=head4 dot


Dot product

 
 sub dot($$)
  {my ($a, $b) = check(@_); # Vectors
   $a->x*$b->x+$a->y*$b->y+$a->z*$b->z;
  } 
 


=head4 angle


Angle between two vectors

 
 sub angle($$)
  {my ($a, $b) = check(@_); # Vectors
   acos($a->norm->dot($b->norm));
  } 
 


=head4 cross


Cross product

 
 sub cross($$)
  {my ($a, $b) = check(@_); # Vectors
 
 	new
   ((($a->y * $b->z) - ($a->z * $b->y)),
 	 (($a->z * $b->x) - ($a->x * $b->z)),
 	 (($a->x * $b->y) - ($a->y * $b->x))
   );
  }
 


=head4 add


Add vectors

 
 sub add($$)
  {my ($a, $b) = check(@_); # Vectors
   new($a->x+$b->x, $a->y+$b->y, $a->z+$b->z);
  }
 


=head4 subtract


Subtract vectors

 
 sub subtract($$)
  {check(@_) if debug; # Vectors
   new($_[0]->{x}-$_[1]->{x}, $_[0]->{y}-$_[1]->{y}, $_[0]->{z}-$_[1]->{z});
  }
 


=head4 multiply


Vector times a scalar

 
 sub multiply($$)
  {my ($a) = check(@_[0..0]); # Vector 
   my ($b) =       @_[1..1];  # Scalar
   
   confess "$b is not a scalar" if ref($b);
   new($a->x*$b, $a->y*$b, $a->z*$b);
  }
 


=head4 divide


Vector divided by a non zero scalar

 
 sub divide($$)
  {my ($a) = check(@_[0..0]); # Vector 
   my ($b) =       @_[1..1];  # Scalar
 
   confess "$b is not a scalar" if ref($b);
   confess "$b is zero"         if $b == 0;
   new($a->x/$b, $a->y/$b, $a->z/$b);
  }
 


=head4 equals


Equals to within accuracy

 
 sub equals($$)
  {my ($a, $b) = check(@_); # Vectors
   abs($a->x-$b->x) < $accuracy and
   abs($a->y-$b->y) < $accuracy and
   abs($a->z-$b->z) < $accuracy;
  }
 


=head4 Operator Overloads


Operator overloads

 
 use overload
  '+'        => \&add3,      # Add two vectors
  '-'        => \&subtract3, # Subtract one vector from another
  '*'        => \&multiply3, # Times by a scalar, or vector dot product 
  '/'        => \&divide3,   # Divide by a scalar
  'x'        => \&cross3,    # BEWARE LOW PRIORITY! Cross product
  '<'        => \&angle3,    # Angle in radians between two vectors
  '>'        => \&angle3,    # Angle in radians between two vectors
  '=='       => \&equals3,   # Equals
  '""'       => \&print3,    # Print
  '!'        => \&length,    # Length
  'fallback' => FALSE;
 


=head4 Add operator


Add operator, see L</add>

 
 sub add3
  {my ($a, $b) = @_;
   $a->add($b);
  }
 


=head4 Subtract Operator


Subtract operator.

 
 sub subtract3
  {return new($_[0]->{x}-$_[1]->{x}, $_[0]->{y}-$_[1]->{y}, $_[0]->{z}-$_[1]->{z}) if ref($_[1]);
   new(-$_[0]->{x}, -$_[0]->{y}, -$_[0]->{z});
  }
 


=head4 Multiply Operator


Multiply operator, see L</multiply>

 
 sub multiply3
  {my ($a, $b) = @_;
   return $a->dot     ($b) if ref($b);
   return $a->multiply($b);
  }
 


=head4 Divide Operator


Divide operator, see L</divide>

 
 sub divide3
  {my ($a, $b, $c) = @_;
   return $a->divide($b);
  }
 


=head4 Cross Operator


Cross operator, see L</cross>

 
 sub cross3
  {my ($a, $b, $c) = @_;
   return $a->cross($b);
  }
 


=head4 Angle Operator


Angle operator, see L</angle>

 
 sub angle3
  {my ($a, $b, $c) = @_;
   return $a->angle($b);
  }
 


=head4 Equals Operator


Equals operator, see L</equals>

 
 sub equals3
  {my ($a, $b, $c) = @_;
   return $a->equals($b);
  }
 


=head4 Print Operator


Print a vector, see L</print>

 
 sub print3
  {my ($a) = @_;
   return $a->print;
  }
 


=head2 Export Definitions


Export L</vector>, L</units>, L</check>, L</is>

 
 use Math::Zap::Exports qw(
   vector ($$$)
   units  ()
   check  (@)
   is     (@)
  );
 
 #______________________________________________________________________
 # Package loaded successfully
 #______________________________________________________________________
 
 1;
 
 


=head2 Credits




=head3 Author



philiprbrenan@yahoo.com


=head3 Copyright



philiprbrenan@yahoo.com, 2004


=head3 License



Perl License.



