def test_assert_rotation_matrix_normalized_preset(self, dtype):
"""Checks that assert_normalized function works as expected."""
angles = test_helpers.generate_preset_test_euler_angles().astype(dtype)
matrix = rotation_matrix_3d.from_euler(angles)
matrix_rescaled = matrix * 1.01
matrix_normalized = rotation_matrix_3d.assert_rotation_matrix_normalized(
matrix)
self.evaluate(matrix_normalized)
with self.assertRaises(tf.errors.InvalidArgumentError): # pylint: disable=g-error-prone-assert-raises
self.evaluate(rotation_matrix_3d.assert_rotation_matrix_normalized(
matrix_rescaled))
def test_assert_rotation_matrix_normalized_passthrough(self):
"""Checks that the assert is a passthrough when the flag is False."""
angles = test_helpers.generate_preset_test_euler_angles()
matrix_input = rotation_matrix_3d.from_euler(angles)
matrix_output = rotation_matrix_3d.assert_rotation_matrix_normalized(
matrix_input)
self.assertTrue(matrix_input is matrix_output) # pylint: disable=g-generic-assert
def from_rotation_matrix(rotation_matrix: type_alias.TensorLike,
name: str = "axis_angle_from_rotation_matrix"
) -> Tuple[tf.Tensor, tf.Tensor]:
"""Converts a rotation matrix to an axis-angle representation.
Note:
In the current version the returned axis-angle representation is not unique
for a given rotation matrix. Since a direct conversion would not really be
faster, we first transform the rotation matrix to a quaternion, and finally
perform the conversion from that quaternion to the corresponding axis-angle
representation.
Note:
In the following, A1 to An are optional batch dimensions.
Args:
rotation_matrix: A tensor of shape `[A1, ..., An, 3, 3]`, where the last two
dimensions represent a rotation matrix.
name: A name for this op that defaults to "axis_angle_from_rotation_matrix".
Returns:
A tuple of two tensors, respectively of shape `[A1, ..., An, 3]` and
`[A1, ..., An, 1]`, where the first tensor represents the axis, and the
second represents the angle. The resulting axis is a normalized vector.
Raises:
ValueError: If the shape of `rotation_matrix` is not supported.
"""
with tf.name_scope(name):
rotation_matrix = tf.convert_to_tensor(value=rotation_matrix)
shape.check_static(
tensor=rotation_matrix,
tensor_name="rotation_matrix",
has_rank_greater_than=1,
has_dim_equals=((-2, 3), (-1, 3)))
rotation_matrix = rotation_matrix_3d.assert_rotation_matrix_normalized(
rotation_matrix)
quaternion = quaternion_lib.from_rotation_matrix(rotation_matrix)
return from_quaternion(quaternion)
def from_rotation_matrix(rotation_matrix, name=None):
"""Converts a rotation matrix representation to a quaternion.
Warning:
This function is not smooth everywhere.
Note:
In the following, A1 to An are optional batch dimensions.
Args:
rotation_matrix: A tensor of shape `[A1, ..., An, 3, 3]`, where the last two
dimensions represent a rotation matrix.
name: A name for this op that defaults to "quaternion_from_rotation_matrix".
Returns:
A tensor of shape `[A1, ..., An, 4]`, where the last dimension represents
a normalized quaternion.
Raises:
ValueError: If the shape of `rotation_matrix` is not supported.
"""
with tf.compat.v1.name_scope(name, "quaternion_from_rotation_matrix",
[rotation_matrix]):
rotation_matrix = tf.convert_to_tensor(value=rotation_matrix)
shape.check_static(
tensor=rotation_matrix,
tensor_name="rotation_matrix",
has_rank_greater_than=1,
has_dim_equals=((-1, 3), (-2, 3)))
rotation_matrix = rotation_matrix_3d.assert_rotation_matrix_normalized(
rotation_matrix)
trace = tf.linalg.trace(rotation_matrix)
eps_addition = asserts.select_eps_for_addition(rotation_matrix.dtype)
rows = tf.unstack(rotation_matrix, axis=-2)
entries = [tf.unstack(row, axis=-1) for row in rows]
def tr_positive():
sq = tf.sqrt(trace + 1.0) * 2. # sq = 4 * qw.
qw = 0.25 * sq
qx = safe_ops.safe_unsigned_div(entries[2][1] - entries[1][2], sq)
qy = safe_ops.safe_unsigned_div(entries[0][2] - entries[2][0], sq)
qz = safe_ops.safe_unsigned_div(entries[1][0] - entries[0][1], sq)
return tf.stack((qx, qy, qz, qw), axis=-1)
def cond_1():
sq = tf.sqrt(1.0 + entries[0][0] - entries[1][1] - entries[2][2] +
eps_addition) * 2. # sq = 4 * qx.
qw = safe_ops.safe_unsigned_div(entries[2][1] - entries[1][2], sq)
qx = 0.25 * sq
qy = safe_ops.safe_unsigned_div(entries[0][1] + entries[1][0], sq)
qz = safe_ops.safe_unsigned_div(entries[0][2] + entries[2][0], sq)
return tf.stack((qx, qy, qz, qw), axis=-1)
def cond_2():
sq = tf.sqrt(1.0 + entries[1][1] - entries[0][0] - entries[2][2] +
eps_addition) * 2. # sq = 4 * qy.
qw = safe_ops.safe_unsigned_div(entries[0][2] - entries[2][0], sq)
qx = safe_ops.safe_unsigned_div(entries[0][1] + entries[1][0], sq)
qy = 0.25 * sq
qz = safe_ops.safe_unsigned_div(entries[1][2] + entries[2][1], sq)
return tf.stack((qx, qy, qz, qw), axis=-1)
def cond_3():
sq = tf.sqrt(1.0 + entries[2][2] - entries[0][0] - entries[1][1] +
eps_addition) * 2. # sq = 4 * qz.
qw = safe_ops.safe_unsigned_div(entries[1][0] - entries[0][1], sq)
qx = safe_ops.safe_unsigned_div(entries[0][2] + entries[2][0], sq)
qy = safe_ops.safe_unsigned_div(entries[1][2] + entries[2][1], sq)
qz = 0.25 * sq
return tf.stack((qx, qy, qz, qw), axis=-1)
def cond_idx(cond):
cond = tf.expand_dims(cond, -1)
cond = tf.tile(cond, [1] * (rotation_matrix.shape.ndims - 2) + [4])
return cond
where_2 = tf.compat.v1.where(
cond_idx(entries[1][1] > entries[2][2]), cond_2(), cond_3())
where_1 = tf.compat.v1.where(
cond_idx((entries[0][0] > entries[1][1])
& (entries[0][0] > entries[2][2])), cond_1(), where_2)
quat = tf.compat.v1.where(cond_idx(trace > 0), tr_positive(), where_1)
return quat
def from_rotation_matrix(rotation_matrix, name=None):
"""Converts rotation matrices to Euler angles.
The rotation matrices are assumed to have been constructed by rotation around
the $$x$$, then $$y$$, and finally the $$z$$ axis.
Note:
There is an infinite number of solutions to this problem. There are
Gimbal locks when abs(rotation_matrix(2,0)) == 1, which are not handled.
Note:
In the following, A1 to An are optional batch dimensions.
Args:
rotation_matrix: A tensor of shape `[A1, ..., An, 3, 3]`, where the last two
dimensions represent a rotation matrix.
name: A name for this op that defaults to "euler_from_rotation_matrix".
Returns:
A tensor of shape `[A1, ..., An, 3]`, where the last dimension represents
the three Euler angles.
Raises:
ValueError: If the shape of `rotation_matrix` is not supported.
"""
def general_case(rotation_matrix, r20, eps_addition):
"""Handles the general case."""
theta_y = -tf.asin(r20)
sign_cos_theta_y = safe_ops.nonzero_sign(tf.cos(theta_y))
r00 = rotation_matrix[..., 0, 0]
r10 = rotation_matrix[..., 1, 0]
r21 = rotation_matrix[..., 2, 1]
r22 = rotation_matrix[..., 2, 2]
r00 = safe_ops.nonzero_sign(r00) * eps_addition + r00
r22 = safe_ops.nonzero_sign(r22) * eps_addition + r22
# cos_theta_y evaluates to 0 on Gimbal locks, in which case the output of
# this function will not be used.
theta_z = tf.atan2(r10 * sign_cos_theta_y, r00 * sign_cos_theta_y)
theta_x = tf.atan2(r21 * sign_cos_theta_y, r22 * sign_cos_theta_y)
angles = tf.stack((theta_x, theta_y, theta_z), axis=-1)
return angles
def gimbal_lock(rotation_matrix, r20, eps_addition):
"""Handles Gimbal locks."""
r01 = rotation_matrix[..., 0, 1]
r02 = rotation_matrix[..., 0, 2]
sign_r20 = safe_ops.nonzero_sign(r20)
r02 = safe_ops.nonzero_sign(r02) * eps_addition + r02
theta_x = tf.atan2(-sign_r20 * r01, -sign_r20 * r02)
theta_y = -sign_r20 * tf.constant(math.pi / 2.0, dtype=r20.dtype)
theta_z = tf.zeros_like(theta_x)
angles = tf.stack((theta_x, theta_y, theta_z), axis=-1)
return angles
with tf.compat.v1.name_scope(name, "euler_from_rotation_matrix",
[rotation_matrix]):
rotation_matrix = tf.convert_to_tensor(value=rotation_matrix)
shape.check_static(tensor=rotation_matrix,
tensor_name="rotation_matrix",
has_rank_greater_than=1,
has_dim_equals=((-1, 3), (-2, 3)))
rotation_matrix = rotation_matrix_3d.assert_rotation_matrix_normalized(
rotation_matrix)
r20 = rotation_matrix[..., 2, 0]
eps_addition = asserts.select_eps_for_addition(rotation_matrix.dtype)
general_solution = general_case(rotation_matrix, r20, eps_addition)
gimbal_solution = gimbal_lock(rotation_matrix, r20, eps_addition)
is_gimbal = tf.equal(tf.abs(r20), 1)
gimbal_mask = tf.stack((is_gimbal, is_gimbal, is_gimbal), axis=-1)
return tf.compat.v1.where(gimbal_mask, gimbal_solution,
general_solution)
def from_rotation_matrix(rotation_matrix, name=None):
"""Converts a rotation matrix representation to a quaternion.
Warning:
This function is not smooth everywhere.
Note:
In the following, A1 to An are optional batch dimensions.
Args:
rotation_matrix: A tensor of shape `[A1, ..., An, 3, 3]`, where the last two
dimensions represent a rotation matrix.
name: A name for this op that defaults to "quaternion_from_rotation_matrix".
Returns:
A tensor of shape `[A1, ..., An, 4]`, where the last dimension represents
a normalized quaternion.
Raises:
ValueError: If the shape of `rotation_matrix` is not supported.
"""
with tf.compat.v1.name_scope(name, "quaternion_from_rotation_matrix",
[rotation_matrix]):
rotation_matrix = tf.convert_to_tensor(value=rotation_matrix)
shape.check_static(
tensor=rotation_matrix,
tensor_name="rotation_matrix",
has_rank_greater_than=1,
has_dim_equals=((-1, 3), (-2, 3)))
rotation_matrix = rotation_matrix_3d.assert_rotation_matrix_normalized(
rotation_matrix)
eps_addition = asserts.select_eps_for_addition(rotation_matrix.dtype)
def tr_positive(matrix, trace):
sq = tf.sqrt(trace + 1.0) * 2. # sq = 4 * qw.
qw = 0.25 * sq
qx = safe_ops.safe_unsigned_div(matrix[2, 1] - matrix[1, 2], sq)
qy = safe_ops.safe_unsigned_div(matrix[0, 2] - matrix[2, 0], sq)
qz = safe_ops.safe_unsigned_div(matrix[1, 0] - matrix[0, 1], sq)
return tf.convert_to_tensor([qx, qy, qz, qw], dtype=tf.float32)
def cond_1(matrix):
sq = tf.sqrt(1.0 + matrix[0, 0] - matrix[1, 1] - matrix[2, 2] +
eps_addition) * 2. # sq = 4 * qx.
qw = safe_ops.safe_unsigned_div(matrix[2, 1] - matrix[1, 2], sq)
qx = 0.25 * sq
qy = safe_ops.safe_unsigned_div(matrix[0, 1] + matrix[1, 0], sq)
qz = safe_ops.safe_unsigned_div(matrix[0, 2] + matrix[2, 0], sq)
return tf.convert_to_tensor([qx, qy, qz, qw], dtype=tf.float32)
def cond_2(matrix):
sq = tf.sqrt(1.0 + matrix[1, 1] - matrix[0, 0] - matrix[2, 2] +
eps_addition) * 2. # sq = 4 * qy.
qw = safe_ops.safe_unsigned_div(matrix[0, 2] - matrix[2, 0], sq)
qx = safe_ops.safe_unsigned_div(matrix[0, 1] + matrix[1, 0], sq)
qy = 0.25 * sq
qz = safe_ops.safe_unsigned_div(matrix[1, 2] + matrix[2, 1], sq)
return tf.convert_to_tensor([qx, qy, qz, qw], dtype=tf.float32)
def cond_3(matrix):
sq = tf.sqrt(1.0 + matrix[2, 2] - matrix[0, 0] - matrix[1, 1] +
eps_addition) * 2. # sq = 4 * qz.
qw = safe_ops.safe_unsigned_div(matrix[1, 0] - matrix[0, 1], sq)
qx = safe_ops.safe_unsigned_div(matrix[0, 2] + matrix[2, 0], sq)
qy = safe_ops.safe_unsigned_div(matrix[1, 2] + matrix[2, 1], sq)
qz = 0.25 * sq
return tf.convert_to_tensor([qx, qy, qz, qw], dtype=tf.float32)
def quat_from_matrix(matrix):
trace = tf.linalg.trace(matrix)
where_2 = tf.cond(matrix[1, 1] > matrix[2, 2], lambda: cond_2(matrix),
lambda: cond_3(matrix))
where_1 = tf.cond(
(matrix[0, 0] > matrix[1, 1]) & (matrix[0, 0] > matrix[2, 2]),
lambda: cond_1(matrix), lambda: where_2)
return tf.cond(trace > 0, lambda: tr_positive(matrix, trace),
lambda: where_1)
return tf.map_fn(quat_from_matrix, rotation_matrix)
