NAME¶
Math::Vec - Object-Oriented Vector Math Methods in Perl
SYNOPSIS¶
use Math::Vec;
$v = Math::Vec->new(0,1,2);
or
use Math::Vec qw(NewVec);
$v = NewVec(0,1,2);
@res = $v->Cross([1,2.5,0]);
$p = NewVec(@res);
$q = $p->Dot([0,1,0]);
or
use Math::Vec qw(:terse);
$v = V(0,1,2);
$q = ($v x [1,2.5,0]) * [0,1,0];
NOTICE¶
This module is still somewhat incomplete. If a function does nothing, there is
likely a really good reason. Please have a look at the code if you are trying
to use this in a production environment.
AUTHOR¶
Eric L. Wilhelm <ewilhelm at cpan dot org>
http://scratchcomputing.com
DESCRIPTION¶
This module was adapted from Math::Vector, written by Wayne M. Syvinski.
It uses most of the same algorithms, and currently preserves the same names as
the original functions, though some aliases have been added to make the
interface more natural (at least to the way I think.)
The "object" for the object oriented calling style is a blessed array
reference which contains a vector of the form [x,y,z]. Methods will typically
return a list.
COPYRIGHT NOTICE¶
Copyright (C) 2003-2006 Eric Wilhelm
portions Copyright 2003 Wayne M. Syvinski
NO WARRANTY¶
Absolutely, positively NO WARRANTY, neither express or implied, is offered with
this software. You use this software at your own risk. In case of loss,
neither Wayne M. Syvinski, Eric Wilhelm, nor anyone else, owes you anything
whatseover. You have been warned.
Note that this includes NO GUARANTEE of MATHEMATICAL CORRECTNESS. If you are
going to use this code in a production environment, it is YOUR RESPONSIBILITY
to verify that the methods return the correct values.
LICENSE¶
You may use this software under one of the following licenses:
(1) GNU General Public License
(found at http://www.gnu.org/copyleft/gpl.html)
(2) Artistic License
(found at http://www.perl.com/pub/language/misc/Artistic.html)
SEE ALSO¶
Math::Vector
Constructor¶
new
Returns a blessed array reference to cartesian point ($x, $y, $z), where $z is
optional. Note the feed-me-list, get-back-reference syntax here. This is the
opposite of the rest of the methods for a good reason (it allows nesting of
function calls.)
The z value is optional, (and so are x and y.) Undefined values are silently
translated into zeros upon construction.
$vec = Math::Vec->new($x, $y, $z);
NewVec
This is simply a shortcut to Math::Vec->new($x, $y, $z) for those of you who
don't want to type so much so often. This also makes it easier to nest / chain
your function calls. Note that methods will typically output lists (e.g. the
answer to your question.) While you can simply [bracket] the answer to make an
array reference, you need that to be blessed in order to use the
$object->method(@args) syntax. This function does that blessing.
This function is exported as an option. To use it, simply use Math::Vec
qw(NewVec); at the start of your code.
use Math::Vec qw(NewVec);
$vec = NewVec($x, $y, $z);
$diff = NewVec($vec->Minus([$ovec->ScalarMult(0.5)]));
Terse Functions¶
These are all one-letter shortcuts which are imported to your namespace with the
:terse flag.
use Math::Vec qw(:terse);
V
This is the same as Math::Vec->new($x,$y,$z).
$vec = V($x, $y, $z);
U
Shortcut to V($x,$y,$z)->
UnitVector()
$unit = U($x, $y, $z);
This will also work if called with a vector object:
$unit = U($vector);
X
Returns an x-axis unit vector.
$xvec = X();
Y
Returns a y-axis unit vector.
$yvec = Y();
Z
Returns a z-axis unit vector.
$zvec = Z();
Overloading¶
Best used with the :terse functions, the Overloading scheme introduces an
interface which is unique from the Methods interface. Where the methods take
references and return lists, the overloaded operators will return references.
This allows vector arithmetic to be chained together more easily. Of course,
you can easily dereference these with @{$vec}.
The following sections contain equivelant expressions from the longhand and
terse interfaces, respectively.
Negation:
@a = NewVec->(0,1,1)->ScalarMult(-1);
@a = @{-V(0,1,1)};
Stringification:
This also performs concatenation and other string operations.
print join(", ", 0,1,1), "\n";
print V(0,1,1), "\n";
$v = V(0,1,1);
print "$v\n";
print "$v" . "\n";
print $v, "\n";
Addition:
@a = NewVec(0,1,1)->Plus([2,2]);
@a = @{V(0,1,1) + V(2,2)};
# only one argument needs to be blessed:
@a = @{V(0,1,1) + [2,2]};
# and which one is blessed doesn't matter:
@a = @{[0,1,1] + V(2,2)};
Subtraction:
@a = NewVec(0,1,1)->Minus([2,2]);
@a = @{[0,1,1] - V(2,2)};
Scalar Multiplication:
@a = NewVec(0,1,1)->ScalarMult(2);
@a = @{V(0,1,1) * 2};
@a = @{2 * V(0,1,1)};
Scalar Division:
@a = NewVec(0,1,1)->ScalarMult(1/2);
# order matters!
@a = @{V(0,1,1) / 2};
Cross Product:
@a = NewVec(0,1,1)->Cross([0,1]);
@a = @{V(0,1,1) x [0,1]};
@a = @{[0,1,1] x V(0,1)};
Dot Product:
Also known as the "Scalar Product".
$a = NewVec(0,1,1)->Dot([0,1]);
$a = V(0,1,1) * [0,1];
Note: Not using the '.' operator here makes everything more efficient. I know,
the * is not a dot, but at least it's a mathematical operator (perl does some
implied string concatenation somewhere which drove me to avoid the dot.)
Comparison:
The == and != operators will compare vectors for equal direction and magnitude.
No attempt is made to apply tolerance to this equality.
Length:
$a = NewVec(0,1,1)->Length();
$a = abs(V(0,1,1));
Vector Projection:
This one is a little different. Where the method is written $a->Proj($b) to
give the projection of $b onto $a, this reads like you would say it (b
projected onto a): $b>>$a.
@a = NewVec(0,1,1)->Proj([0,0,1]);
@a = @{V(0,0,1)>>[0,1,1]};
Chaining Operations¶
The above examples simply show how to go from the method interface to the
overloaded interface, but where the overloading really shines is in chaining
multiple operations together. Because the return values from the overloaded
operators are all references, you dereference them only when you are done.
Unit Vector left of a line
This comes from the
CAD::Calc::line_to_rectangle() function.
use Math::Vec qw(:terse);
@line = ([0,1],[1,0]);
my ($a, $b) = map({V(@$_)} @line);
$unit = U($b - $a);
$left = $unit x -Z();
Length of a cross product
$length = abs($va x $vb);
Vectors as coordinate axes
This is useful in drawing eliptical arcs using dxf data.
$val = 3.14159; # the 'start parameter'
@c = (14.15973317961194, 6.29684276451746); # codes 10, 20, 30
@e = (6.146127847120538, 0); # codes 11, 21, 31
@ep = @{V(@c) + \@e}; # that's the axis endpoint
$ux = U(@e); # unit on our x' axis
$uy = U($ux x -Z()); # y' is left of x'
$center = V(@c);
# autodesk gives you this:
@pt = ($a * cos($val), $b * sin($val));
# but they don't tell you about the major/minor axis issue:
@pt = @{$center + $ux * $pt[0] + $uy * $pt[1]};;
Precedence¶
The operator precedence is going to be whatever perl wants it to be. I have not
yet investigated this to see if it matches standard vector arithmetic
notation. If in doubt, use parentheses.
One item of note here is that the 'x' and '*' operators have the same
precedence, so the leftmost wins. In the following example, you can get away
without parentheses if you have the cross-product first.
# dot product of a cross product:
$v1 x $v2 * $v3
($v1 x $v2) * $v3
# scalar crossed with a vector (illegal!)
$v3 * $v1 x $v2
Methods¶
The typical theme is that methods require array references and return lists.
This means that you can choose whether to create an anonymous array ref for
use in feeding back into another function call, or you can simply use the list
as-is. Methods which return a scalar or list of scalars (in the mathematical
sense, not the Perl SV sense) are exempt from this theme, but methods which
return what could become one vector will return it as a list.
If you want to chain calls together, either use the NewVec constructor, or
enclose the call in square brackets to make an anonymous array out of the
result.
my $vec = NewVec(@pt);
my $doubled = NewVec($vec->ScalarMult(0.5));
my $other = NewVec($vec->Plus([0,2,1], [4,2,3]));
my @result = $other->Minus($doubled);
$unit = NewVec(NewVec(@result)->UnitVector());
The vector objects are simply blessed array references. This makes for a fairly
limited amount of manipulation, but vector math is not complicated stuff.
Hopefully, you can save at least two lines of code per calculation using this
module.
Dot
Returns the dot product of $vec 'dot' $othervec.
$vec->Dot($othervec);
DotProduct
Alias to
Dot()
$number = $vec->DotProduct($othervec);
Cross
Returns $vec x $other_vec
@list = $vec->Cross($other_vec);
# or, to use the result as a vec:
$cvec = NewVec($vec->Cross($other_vec));
CrossProduct
Alias to
Cross() (should really strip out all of this clunkiness and go
to operator overloading, but that gets into other hairiness.)
$vec->CrossProduct();
Length
Returns the length of $vec
$length = $vec->Length();
Magnitude
$vec->Magnitude();
UnitVector
$vec->UnitVector();
ScalarMult
Factors each element of $vec by $factor.
@new = $vec->ScalarMult($factor);
Minus
Subtracts an arbitrary number of vectors.
@result = $vec->Minus($other_vec, $another_vec?);
This would be equivelant to:
@result = $vec->Minus([$other_vec->Plus(@list_of_vectors)]);
VecSub
Alias to
Minus()
$vec->VecSub();
InnerAngle
Returns the acute angle (in radians) in the plane defined by the two vectors.
$vec->InnerAngle($other_vec);
DirAngles
$vec->DirAngles();
Plus
Adds an arbitrary number of vectors.
@result = $vec->Plus($other_vec, $another_vec);
PlanarAngles
If called in list context, returns the angle of the vector in each of the
primary planes. If called in scalar context, returns only the angle in the xy
plane. Angles are returned in radians counter-clockwise from the primary axis
(the one listed first in the pairs below.)
($xy_ang, $xz_ang, $yz_ang) = $vec->PlanarAngles();
Ang
A simpler alias to
PlanarAngles() which eliminates the concerns about
context and simply returns the angle in the xy plane.
$xy_ang = $vec->Ang();
VecAdd
$vec->VecAdd();
UnitVectorPoints
Returns a unit vector which points from $A to $B.
$A->UnitVectorPoints($B);
InnerAnglePoints
Returns the
InnerAngle() between the three points. $Vert is the vertex of
the points.
$Vert->InnerAnglePoints($endA, $endB);
PlaneUnitNormal
Returns a unit vector normal to the plane described by the three points. The
sense of this vector is according to the right-hand rule and the order of the
given points. The $Vert vector is taken as the vertex of the three points.
e.g. if $Vert is the origin of a coordinate system where the x-axis is $A and
the y-axis is $B, then the return value would be a unit vector along the
positive z-axis.
$Vert->PlaneUnitNormal($A, $B);
TriAreaPoints
Returns the angle of the triangle formed by the three points.
$A->TriAreaPoints($B, $C);
Comp
Returns the scalar projection of $B onto $A (also called the component of $B
along $A.)
$A->Comp($B);
Proj
Returns the vector projection of $B onto $A.
$A->Proj($B);
PerpFoot
Returns a point on line $A,$B which is as close to $pt as possible (and
therefore perpendicular to the line.)
$pt->PerpFoot($A, $B);
Incomplete Methods¶
The following have yet to be translated into this interface. They are shown here
simply because I intended to fully preserve the function names from the
original Math::Vector module written by Wayne M. Syvinski.
TripleProduct
$vec->TripleProduct();
IJK
$vec->IJK();
OrdTrip
$vec->OrdTrip();
STV
$vec->STV();
Equil
$vec->Equil();