def test_euler_angles_equivalence_to_general_3D():
phi = 1
theta = 2
psi = 3
rot_euler = np.rotation_matrix_from_euler_angles(phi, theta, psi)
rot_manual = (
np.rotation_matrix_3D(psi, np.array([0, 0, 1])) @
np.rotation_matrix_3D(theta, np.array([0, 1, 0])) @
np.rotation_matrix_3D(phi, np.array([1, 0, 0]))
)
assert rot_euler == pytest.approx(rot_manual)
def xyz_te(self) -> np.ndarray:
"""
Returns the (wing-relative) coordinates of the trailing edge of the cross section.
"""
rot = np.rotation_matrix_3D(self.twist * pi / 180, self.twist_axis)
xyz_te = self.xyz_le + rot @ np.array([self.chord, 0, 0])
return xyz_te
def _compute_frame_of_WingXSec(self, index: int):
twist = self.xsecs[index].twist
if index == len(self.xsecs) - 1:
index = len(self.xsecs) - 2 # The last WingXSec has the same frame as the last section.
### Compute the untwisted reference frame
xg_local = np.array([1, 0, 0])
xyz_le_a = self.xsecs[index].xyz_le
xyz_le_b = self.xsecs[index + 1].xyz_le
vector_between = xyz_le_b - xyz_le_a
vector_between[0] = 0 # Project it onto the YZ plane.
yg_local = vector_between / np.linalg.norm(vector_between)
zg_local = np.cross(xg_local, yg_local)
### Twist the reference frame by the WingXSec twist angle
rot = np.rotation_matrix_3D(
twist * pi / 180,
yg_local
)
xg_local = rot @ xg_local
zg_local = rot @ zg_local
return xg_local, yg_local, zg_local
def _compute_frame_of_WingXSec(
self, index: int) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
"""
Computes the local reference frame associated with a particular cross section (XSec) of this wing.
Args:
index: Which cross section (as indexed in Wing.xsecs) should we get the frame of?
Returns:
A tuple of (xg_local, yg_local, zg_local), where each entry refers to the respective (normalized) axis of
the local reference frame of the WingXSec. Given in geometry axes.
"""
### Compute the untwisted reference frame
xg_local = np.array([1, 0, 0])
if index == 0:
span_vector = self.xsecs[1].xyz_le - self.xsecs[0].xyz_le
span_vector[0] = 0
yg_local = span_vector / np.linalg.norm(span_vector)
z_scale = 1
elif index == len(self.xsecs) - 1 or index == -1:
span_vector = self.xsecs[-1].xyz_le - self.xsecs[-2].xyz_le
span_vector[0] = 0
yg_local = span_vector / np.linalg.norm(span_vector)
z_scale = 1
else:
vector_before = self.xsecs[index].xyz_le - self.xsecs[index -
1].xyz_le
vector_after = self.xsecs[index +
1].xyz_le - self.xsecs[index].xyz_le
vector_before[0] = 0 # Project onto YZ plane.
vector_after[0] = 0 # Project onto YZ plane.
vector_before = vector_before / np.linalg.norm(vector_before)
vector_after = vector_after / np.linalg.norm(vector_after)
span_vector = (vector_before + vector_after) / 2
yg_local = span_vector / np.linalg.norm(span_vector)
cos_vectors = np.linalg.inner(vector_before, vector_after)
z_scale = np.sqrt(2 / (cos_vectors + 1))
zg_local = np.cross(xg_local, yg_local) * z_scale
### Twist the reference frame by the WingXSec twist angle
rot = np.rotation_matrix_3D(self.xsecs[index].twist * pi / 180,
yg_local)
xg_local = rot @ xg_local
zg_local = rot @ zg_local
return xg_local, yg_local, zg_local
def compute_rotation_matrix_wind_to_geometry(self) -> np.ndarray:
"""
Computes the 3x3 rotation matrix that transforms from wind axes to geometry axes.
Returns: a 3x3 rotation matrix.
"""
alpha_rotation = np.rotation_matrix_3D(angle=np.radians(self.alpha),
axis=np.array([0, 1, 0]),
_axis_already_normalized=True)
beta_rotation = np.rotation_matrix_3D(angle=np.radians(self.beta),
axis=np.array([0, 0, 1]),
_axis_already_normalized=True)
axes_flip = np.rotation_matrix_3D(
angle=np.pi,
axis=np.array([0, 1, 0]),
_axis_already_normalized=True
) # Since in geometry axes, X is downstream by convention, while in wind axes, X is upstream by convetion. Same with Z being up/down respectively.
r = axes_flip @ alpha_rotation @ beta_rotation # where "@" is the matrix multiplication operator
return r
def test_general_3D_shorthands():
rotx = np.rotation_matrix_3D(1, np.array([1, 0, 0]))
assert pytest.approx(rotx) == np.rotation_matrix_3D(1, "x")
roty = np.rotation_matrix_3D(1, np.array([0, 1, 0]))
assert pytest.approx(roty) == np.rotation_matrix_3D(1, "y")
rotz = np.rotation_matrix_3D(1, np.array([0, 0, 1]))
assert pytest.approx(rotz) == np.rotation_matrix_3D(1, "z")
def test_rotation_matrices(types):
for angle in types["scalar"]:
for axis in types["vector"]:
np.rotation_matrix_2D(angle)
np.rotation_matrix_3D(angle, np.array([axis[0], axis[1], axis[0]]))
def test_validity_of_general_3D():
rot = np.rotation_matrix_3D(
angle=1,
axis=[2, 3, 4]
)
assert np.is_valid_rotation_matrix(rot)
