$rot_90_about_z = PDL->pdl([0,1,0], [-1,0,0], [0,0,1]);

$boat = PDL::3Space->new;
print "boat=$boat";
$bird = PDL::3Space->new($boat);
print "bird=$bird";
# boat=
# [
#  [1 0 0]
#  [0 1 0]
#  [0 0 1]
#  [0 0 0]
# ]
# bird=
# [
#  [1 0 0]
#  [0 1 0]
#  [0 0 1]
#  [0 0 0]
# ]

$boat->basis_update($rot_90_about_z);
print "after boat rot:\nboat=$boat";
print "bird=$bird";
# after boat rot:
# boat=
# [
#  [ 0  1  0]
#  [-1  0  0]
#  [ 0  0  1]
#  [ 0  0  0]
# ]
# bird=
# [
#  [ 0  1  0]
#  [-1  0  0]
#  [ 0  0  1]
#  [ 0  0  0]
# ]

$boat->origin_move(PDL->pdl(1,0,0));
print "after boat move:\nboat=$boat";
print "bird=$bird";
print "bird local=".$bird->local;
# after boat move:
# boat=
# [
#  [ 0  1  0]
#  [-1  0  0]
#  [ 0  0  1]
#  [ 0  1  0]
# ]
# bird=
# [
#  [ 0  1  0]
#  [-1  0  0]
#  [ 0  0  1]
#  [ 0  1  0]
# ]
# bird local=
# [
#  [1 0 0]
#  [0 1 0]
#  [0 0 1]
#  [0 0 0]
# ]

$bird->basis_update($rot_90_about_z);
$bird->origin_move(PDL->pdl(1,0,1));
print "after bird rot and move:\nbird=$bird";
print "bird local=".$bird->local;
# after bird rot and move:
# bird=
# [
#  [-1  0  0]
#  [ 0 -1  0]
#  [ 0  0  1]
#  [-1  1  1]
# ]
# bird local=
# [
#  [ 0  1  0]
#  [-1  0  0]
#  [ 0  0  1]
#  [ 0  1  1]
# ]

$boat->basis_update(PDL::MatrixOps::identity(3) * 2);
print "after boat expand:\nboat=$boat";
print "bird=$bird";
# after boat expand:
# boat=
# [
#  [ 0  2  0]
#  [-2  0  0]
#  [ 0  0  2]
#  [ 0  2  0]
# ]
# bird=
# [
#  [-2  0  0]
#  [ 0 -2  0]
#  [ 0  0  2]
#  [-2  2  2]
# ]