Vector
Manipulate 3D vectors
PhilipRBrenan@yahoo.com, 2004, Perl licence
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));Description
Manipulate 3 dimensional vectors via operators.
package Math::Zap::Vector;
$VERSION=1.07;
use Math::Trig;
use Carp;
use constant debug => 0; # Debugging levelConstructors
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], $_[2])}units
Unit vectors
sub units() {($x, $y, $z)}Methods
check
Check its a vector
sub check(@)
{if (debug)
{for my $v(@_)
{confess "$v is not a vector" unless ref($v) eq __PACKAGE__;
}
}
return (@_)
}is
Test its a vector
sub is(@)
{for my $v(@_)
{return 0 unless ref($v) eq __PACKAGE__;
}
'vector';
}accuracy
Get/Set accuracy for comparisons
my $accuracy = 1e-10;
sub accuracy
{return $accuracy unless scalar(@_);
$accuracy = shift();
}round
Round: round to nearest integer if within accuracy of that integer
sub round($)
{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 $a;
}
}x,y,z
x,y,z components of vector
sub x($) {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);
$z = new(0,0,1);clone
Create a vector from another vector
sub clone($)
{my ($v) = check(@_); # Vectors
round bless {x=>$v->x, y=>$v->y, z=>$v->z};
}length
Length of a vector
sub length($)
{my ($v) = check(@_[0..0]); # Vectors
sqrt($v->x**2+$v->y**2+$v->z**2);
} Print vector
sub print($)
{my ($v) = check(@_); # Vectors
my ($x, $y, $z) = ($v->x, $v->y, $v->z);
"vector($x, $y, $z)";
} norm
Normalize vector
sub norm($)
{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;
} dot
Dot product
sub dot($$)
{my ($a, $b) = check(@_); # Vectors
$a->x*$b->x+$a->y*$b->y+$a->z*$b->z;
} angle
Angle between two vectors
sub angle($$)
{my ($a, $b) = check(@_); # Vectors
acos($a->norm->dot($b->norm));
} cross
Cross product
sub cross($$)
{my ($a, $b) = check(@_); # Vectors
new
((($a->y * $b->z) - ($a->z * $b->y)),
(($a->z * $b->x) - ($a->x * $b->z)),
(($a->x * $b->y) - ($a->y * $b->x))
);
}add
Add vectors
sub add($$)
{my ($a, $b) = check(@_); # Vectors
new($a->x+$b->x, $a->y+$b->y, $a->z+$b->z);
}subtract
Subtract vectors
sub subtract($$)
{check(@_) if debug; # Vectors
new($_[0]->{x}-$_[1]->{x}, $_[0]->{y}-$_[1]->{y}, $_[0]->{z}-$_[1]->{z});
}multiply
Vector times a scalar
sub multiply($$)
{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);
}divide
Vector divided by a non zero scalar
sub divide($$)
{my ($a) = check(@_[0..0]); # Vector
my ($b) = @_[1..1]; # Scalar
confess "$b is not a scalar" if ref($b);
confess "$b is zero" if $b == 0;
new($a->x/$b, $a->y/$b, $a->z/$b);
}equals
Equals to within accuracy
sub equals($$)
{my ($a, $b) = check(@_); # Vectors
abs($a->x-$b->x) < $accuracy and
abs($a->y-$b->y) < $accuracy and
abs($a->z-$b->z) < $accuracy;
}Operator Overloads
Operator overloads
use overload
'+' => \&add3, # Add two vectors
'-' => \&subtract3, # Subtract one vector from another
'*' => \&multiply3, # Times by a scalar, or vector dot product
'/' => \÷3, # Divide by a scalar
'x' => \&cross3, # BEWARE LOW PRIORITY! Cross product
'<' => \&angle3, # Angle in radians between two vectors
'>' => \&angle3, # Angle in radians between two vectors
'==' => \&equals3, # Equals
'""' => \&print3, # Print
'!' => \&length, # Length
'fallback' => FALSE;Add operator
Add operator, see "add"
sub add3
{my ($a, $b) = @_;
$a->add($b);
}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});
}Multiply Operator
Multiply operator, see "multiply"
sub multiply3
{my ($a, $b) = @_;
return $a->dot ($b) if ref($b);
return $a->multiply($b);
}Divide Operator
Divide operator, see "divide"
sub divide3
{my ($a, $b, $c) = @_;
return $a->divide($b);
}Cross Operator
Cross operator, see "cross"
sub cross3
{my ($a, $b, $c) = @_;
return $a->cross($b);
}Angle Operator
Angle operator, see "angle"
sub angle3
{my ($a, $b, $c) = @_;
return $a->angle($b);
}Equals Operator
Equals operator, see "equals"
sub equals3
{my ($a, $b, $c) = @_;
return $a->equals($b);
}Print Operator
Print a vector, see "print"
sub print3
{my ($a) = @_;
return $a->print;
}Export Definitions
Export "vector", "units", "check", "is"
use Math::Zap::Exports qw(
vector ($$$)
units ()
check (@)
is (@)
);
#______________________________________________________________________
# Package loaded successfully
#______________________________________________________________________
1;Credits
Author
philiprbrenan@yahoo.com
Copyright
philiprbrenan@yahoo.com, 2004
License
Perl License.