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