test, doc a perspective projection

Author: mohawk2

lib/PDL/Transform.pd

@@ -3888,9 +3888,17 @@ can continuously warp an image plane so that C<ncoords + 2> arbitrarily chosen
 points exactly map to the same number of other arbitrarily chosen points.  They
 have the property that straight lines remain straight after transformation.
 
+=for example
+
+  # perspective projection 3D -> 2D
+  $t_proj = t_projective(
+    src => pdl('1 1 1; -1 1 1; -1 -1 1; 1 -1 1; 2 2 2; -2 -2 2'),
+    dst => pdl('0 1000; 1000 1000; 1000 0; 0 0; 0 1000; 1000 0'),
+  );
+
 You can specify your projective transformation directly in homogeneous
 coordinates, or (as of 2.104, not just in 2 dimensions) as a set
-of C<ncoords + 2> unique points that
+of unique points that
 are mapped one to the other by the transformation.
 
 Projective transforms are quasi-linear because they are most easily
@@ -3936,8 +3944,7 @@ For example, specifying
 maps the origin and the point (0,1) to themselves, the point (5,9)
 to (5,8), and the point (9,4) to (9,3).
 
-Added in 2.104. Works on any number of dimensions, the same for
-C<src> and C<dst> (a homography).
+Added in 2.104. Works on any number of dimensions.
 
 =item p, point, points, Points
 
@@ -4007,9 +4014,7 @@ sub solve_DLT {
   my ($A, $T_src, $T_dst) = @_;
   my ($U, $S, $V) = svd($A, 1); # full SVD
   my $P_norm = $V->slice(-1)->reshape(map $_->dim(0), $T_src, $T_dst); # reshape smallest singular value vector
-  my $P = $T_dst->inv x $P_norm x $T_src; # Denormalize
-  my $div_value = $P->slice(($T_dst->dim(0)-1) x 2); # scaling for numerical stability
-  $P / $div_value;
+  $T_dst->inv x $P_norm x $T_src; # Denormalize
 }
 
 sub t_projective {

t/transform.t

@@ -38,14 +38,12 @@ use Test::Exception;
 
   my $t_points = pdl('[0 0; 1 0] [1 0; 2 1] [0 1; -1 3] [1 1; 0 4]'); # xy,io,npoints
   my $t_proj = t_projective(p=>$t_points);
-  is_pdl $t_proj->{params}{matrix}, my $exp_proj = pdl('1 -2 1; 1 3 0; 0 0 1');
   is_pdl +(my $p_in = pdl('0.5 0; 1 0.5; 0.5 1; 0 0.5'))->apply($t_proj), my $p_out = pdl('1.5 0.5; 1 2.5; -0.5 3.5; 0 1.5'), 't_projective works';
   is_pdl $p_out->invert($t_proj), $p_in, 't_projective inv';
   $t_proj = t_projective(
     src => my $src2 = $t_points->slice(",(0)"),
     dst => my $dst2 = $t_points->slice(",(1)"),
   );
-  is_pdl $t_proj->{params}{matrix}, $exp_proj;
   my ($A_2) = PDL::Transform::construct_DLT($src2, $dst2);
   is_pdl $A_2, pdl('
     -1 -1 1 0 0 0  0.365966  0.365966 -0.365966;
@@ -60,7 +58,12 @@ use Test::Exception;
   $t_proj = t_projective(
     m => pdl('-500 0 500 0; 0 500 500 0; 0 0 1 0'),
   );
-  is_pdl $t_proj->apply(my $in32 = pdl('0 -1 -1; 4 2 -10')), my $out32 = pdl('500 1000; 700 400'), 'project 3->2 with matrix';
+  is_pdl $t_proj->apply(my $in32 = pdl('0 -1 -1; 4 2 -10')), my $out32 = pdl('500 1000; 700 400'), 'project perspective 3->2 with matrix';
+  $t_proj = t_projective(
+    src => my $src32perspective = pdl('1 1 1; -1 1 1; -1 -1 1; 1 -1 1; 2 2 2; -2 -2 2'),
+    dst => my $dst32perspective = pdl('0 1000; 1000 1000; 1000 0; 0 0; 0 1000; 1000 0'),
+  );
+  is_pdl $t_proj->apply($in32), $out32, 'project perspective 3->2 with src/dst';
   $t_proj = t_projective(
     src => my $src3 = pdl('0 0 0; 1 0 0;  0 1 0; 1 1 0; 0 0 1'),
     dst => my $dst3 = pdl('1 0 0; 2 1 0; -1 3 0; 0 4 0; 1 0 1'),