Add invert() method and tests and perform some cleanup.

Thanks to Kevin Ryde for the invert() implementation.

Geometry-AffineTransform/lib/Geometry/AffineTransform.pm

@@ -1,6 +1,6 @@
 package Geometry::AffineTransform;
 
-our $VERSION = '1.3';
+our $VERSION = '1.4';
 
 use strict;
 use warnings;
@@ -9,8 +9,6 @@ use Carp;
 use Hash::Util;
 use Math::Trig ();
 
-# $Id$
-
 =head1 NAME
 
 Geometry::AffineTransform - Affine Transformation to map 2D coordinates to other 2D coordinates
@@ -86,7 +84,7 @@ In other words, invoking the constructor without arguments is equivalent to this
 =cut
 
 sub new {
-	my $self = shift @_;
+	my $self = shift;
 	my (%args) = @_;
 
 	my $class = ref($self) || $self;
@@ -112,12 +110,39 @@ Returns a clone of the instance.
 =cut
 
 sub clone {
-	my $self = shift @_;
+	my $self = shift;
 	return $self->new()->set_matrix_2x3($self->matrix_2x3());
 }
 
 
 
+=head2 invert
+
+Inverts the state of the transformation.
+
+    my $inverted_clone = $t->clone()->invert();
+
+=cut
+
+sub invert {
+	my $self = shift;
+
+    my $det = $self->determinant();
+
+  	croak "Unable to invert this transform (zero determinant)" unless $det;
+
+    return $self->set_matrix_2x3(
+        $self->{m22} / $det, # 11
+        -$self->{m12} / $det, # 12
+        -$self->{m21} / $det, # 21
+        $self->{m11} / $det, # 22
+        ($self->{m21} * $self->{ty} - $self->{m22} * $self->{tx}) / $det,
+        ($self->{m12} * $self->{tx} - $self->{m11} * $self->{ty}) / $det,
+    );
+}
+
+
+
 =head2 transform
 
 Transform one or more coordinate pairs according to the current state.
@@ -127,6 +152,8 @@ representing the x and y coordinates of a point.
 
 Returns the transformed list of coordinates in the same form as the input list.
 
+    my @output = $t->transform(2, 4, 10, 20);
+
 =cut
 
 sub transform {
@@ -275,6 +302,14 @@ sub matrix_2x3 {
 	return $self->{m11}, $self->{m12}, $self->{m21}, $self->{m22}, $self->{tx}, $self->{ty};
 }
 
+
+# returns the determinant of the matrix
+sub determinant {
+	my $self = shift;
+	return $self->{m11} * $self->{m22} - $self->{m12} * $self->{m21};
+}
+
+
 # sets the 6 specifiable parts of the transformation matrix
 sub set_matrix_2x3 {
 	my $self = shift;

Geometry-AffineTransform/t/lib/Geometry/AffineTransform/Test.pm

@@ -10,7 +10,7 @@ use Test::More;
 use List::Util qw(max min);
 use Data::Dumper;
 
-sub identity : Test(2) {
+sub identity : Test(6) {
 	my $self = shift;
 
 	my $t = Geometry::AffineTransform->new();
@@ -19,27 +19,70 @@ sub identity : Test(2) {
 	is_deeply(\@result, [10, 5], "identity transform");
 	@result = $t->transform(0, 0);
 	is_deeply(\@result, [0, 0], "identity transform");
+
+	my $inverse = $t->clone()->invert();
+	ok(ref($inverse), "clone()->invert()");
+	isnt($inverse, $t, "clone()->invert() returns different instance");
+
+	@result = $inverse->transform(10, 5);
+	is_deeply(\@result, [10, 5], "reverse identity transform");
+	@result = $inverse->transform(0, 0);
+	is_deeply(\@result, [0, 0], "reverse identity transform");
 
 }
 
 
+sub inverse : Test(2) {
+	my $self = shift;
 
-sub rotate : Test(3) {
+	my $t = Geometry::AffineTransform->new();
+	my @result;
+	$t->scale(0, 1)->translate(7, 7);
+	@result = $t->transform(10, 5, 20, 6);
+	is_deeply(\@result, [7, 12, 7, 13], "to line");
+
+    eval {
+    	$t->invert();
+    };
+
+    like($@, qr/^Unable to invert this transform .zero determinant./, "exception for zero determinant");	
+}
+
+
+sub determinant : Test(2) {
 	my $self = shift;
 
 	my $t = Geometry::AffineTransform->new();
-	is($t->rotate(180), $t);
 	my @result;
+	$t->scale(10, 5);
+	is($t->determinant(), 50, "determinant()");
+
+    $t->scale(0, 1);
+	is($t->determinant(), 0, "determinant()");
+}
+
+
+
+sub rotate : Test(5) {
+	my $self = shift;
+
+	my $t = Geometry::AffineTransform->new();
+	is($t->rotate(180), $t);
+    my $inverse = $t->clone()->invert();
+
 	is_deeply([$t->transform(10, 5)], [-10, -5], "rotate 180");
+	is_deeply([$inverse->transform(-10, -5)], [10, 5], "rotate 180");
 
 	$t->rotate(90)->rotate(90);
 	is_deeply([$t->transform(10, 5)], [10, 5], "rotate 360");
+
+	$inverse = $t->clone()->invert();
+	is_deeply([$inverse->transform(10, 5)], [10, 5], "rotate 360 inverse");
 
 }
 
 
 
-
 sub matrix_2x3 : Test(4) {
 	my $self = shift @_;
 	my $t = Geometry::AffineTransform->new();