def test_construction(self):
# Valid
RotateYpr(10, 20, 30)
# Invalid
with self.assertRaises(TypeError):
RotateYpr(1, 2, "3")
def test_equality(self):
# Same object
self.assertEqualToItself(RotateYpr(10, 20, 30))
# Equal objects
self.assertEqual(RotateYpr(10, 20, 30), RotateYpr(10, 20, 30)) # Equal
# Different objects
self.assertNotEqual(RotateYpr(10, 20, 30),
RotateYpr(10, 20, 40)) # Different values
def test_rotate(self):
# Canonical axis/angle
self.assertEqual(rotate(axis = Vector(1, 2, 3), angle = 45), RotateAxisAngle(Vector(1, 2, 3), 45)) # Vector
self.assertEqual(rotate(axis = [1, 2, 3], angle = 45), RotateAxisAngle(Vector(1, 2, 3), 45)) # List
# Canonical from/to
self.assertEqual(rotate(frm = Vector(1, 2, 3), to = Vector(4, 5, 6)), RotateFromTo(Vector(1, 2, 3), Vector(4, 5, 6))) # Vectors
self.assertEqual(rotate(frm = [1, 2, 3], to = [4, 5, 6]), RotateFromTo(Vector(1, 2, 3), Vector(4, 5, 6))) # Lists
# Canonical XYZ
self.assertEqual(rotate(xyz = [45, 0, 30]), RotateXyz(45, 0, 30))
# Canonical yaw/pitch/roll
self.assertEqual(rotate(ypr = [90, -20, 5]), RotateYpr(90, -20, 5))
# Convenience axis/angle (implicit)
self.assertEqual(rotate(Vector(1, 2, 3), 45), RotateAxisAngle(Vector(1, 2, 3), 45)) # Vector
self.assertEqual(rotate( [1, 2, 3], 45), RotateAxisAngle(Vector(1, 2, 3), 45)) # List
# Convenience axis/angle (explicit)
self.assertEqual(rotate(Vector(1, 2, 3), angle = 45), RotateAxisAngle(Vector(1, 2, 3), 45)) # Vector
self.assertEqual(rotate( [1, 2, 3], angle = 45), RotateAxisAngle(Vector(1, 2, 3), 45)) # List
# Convenience from/to (implicit)
self.assertEqual(rotate(X , Y ), RotateFromTo(X, Y)) # Vectors
self.assertEqual(rotate([1, 0, 0], [0, 1, 0]), RotateFromTo(X, Y)) # Lists
# Convenience from/to (explicit)
self.assertEqual(rotate(X , to = Y ), RotateFromTo(X, Y)) # Vectors
self.assertEqual(rotate([1, 0, 0], to = [0, 1, 0]), RotateFromTo(X, Y)) # Lists
def test_str(self):
self.assertStr(RotateYpr(0, 0, 0), "Yaw, pitch, and roll by 0°")
self.assertStr(RotateYpr(1, 0, 0), "Yaw 1°")
self.assertStr(RotateYpr(0, 2, 0), "Pitch 2°")
self.assertStr(RotateYpr(0, 0, 3), "Roll 3°")
self.assertStr(RotateYpr(1, 2, 0), "Yaw 1°, pitch 2°")
self.assertStr(RotateYpr(1, 0, 3), "Yaw 1°, roll 3°")
self.assertStr(RotateYpr(0, 2, 3), "Pitch 2°, roll 3°")
self.assertStr(RotateYpr(1, 2, 3), "Yaw 1°, pitch 2°, roll 3°")
def test_rotate_shortcuts(self):
self.assertEqual(shortcuts.yaw_left(1), RotateYpr(1, 0, 0))
self.assertEqual(shortcuts.yaw_right(2), RotateYpr(-2, 0, 0))
self.assertEqual(shortcuts.pitch_up(3), RotateYpr(0, 3, 0))
self.assertEqual(shortcuts.pitch_down(4), RotateYpr(0, -4, 0))
self.assertEqual(shortcuts.roll_right(5), RotateYpr(0, 0, 5))
self.assertEqual(shortcuts.roll_left(6), RotateYpr(0, 0, -6))
def test_to_scad(self):
self.ignore_scad_comments = True
# Since OpenSCAD does not have YPR rotations, they have to translated to
# corresponding XYZ rotations.
# A zero YPR transform is a zero XYZ transform (not an empty ScadObject,
# which would also be possible).
self.assertEqual(
RotateYpr(0, 0, 0).to_scad(None),
ScadObject("rotate", [[0, 0, 0]], None, None))
# A single-axis YPR rotation can be expressed as a single-axis YPR
# rotation.
# Yaw - Z axis
self.assertEqual(
RotateYpr(1, 0, 0).to_scad(None),
ScadObject("rotate", [[0, 0, 1]], None, None))
# Pitch - X axis
self.assertEqual(
RotateYpr(0, 2, 0).to_scad(None),
ScadObject("rotate", [[2, 0, 0]], None, None))
# Roll - Y axis
self.assertEqual(
RotateYpr(0, 0, 3).to_scad(None),
ScadObject("rotate", [[0, 3, 0]], None, None))
# A dual-axis YPR rotation must be expressed as a chain of two single-
# axis XYZ rotations (except in the case of yaw and pitch, which can be
# combined).
self.assertEqual(
RotateYpr(0, 2, 3).to_scad(None),
ScadObject("rotate", [[2, 0, 0]], None,
[ScadObject("rotate", [[0, 3, 0]], None, None)]))
self.assertEqual(
RotateYpr(1, 0, 3).to_scad(None),
ScadObject("rotate", [[0, 0, 1]], None,
[ScadObject("rotate", [[0, 3, 0]], None, None)]))
self.assertEqual(
RotateYpr(1, 2, 0).to_scad(None),
ScadObject("rotate", [[2, 0, 1]], None, None))
# A tripel-axis YPR rotation must be expressed as a chain of two
# single-axis XYZ rotations (yaw and pitch can be combined).
self.assertEqual(
RotateYpr(1, 2, 3).to_scad(None),
ScadObject("rotate", [[2, 0, 1]], None,
[ScadObject("rotate", [[0, 3, 0]], None, None)]))
def test_inequality(self):
# Different-type transformations are not equal (even if the values are identical)
transforms = [
RotateAxisAngle(X, 0),
RotateFromTo(X, X),
RotateXyz(0, 0, 0),
RotateYpr(0, 0, 0),
ScaleAxisFactor(X, 1),
ScaleUniform(1),
ScaleAxes (1, 1, 1),
Translate([0, 0, 0]),
]
for t1 in transforms:
for t2 in transforms:
if t1 is not t2:
self.assertNotEqual(t1, t2)
def test_transform_shortcuts(self):
a = Cuboid(11, 11, 11)
self.assertEqual(a.up (1), Transformed(Translate([ 0, 0, 1]), a))
self.assertEqual(a.down (2), Transformed(Translate([ 0, 0, -2]), a))
self.assertEqual(a.left (3), Transformed(Translate([-3, 0, 0]), a))
self.assertEqual(a.right (4), Transformed(Translate([ 4, 0, 0]), a))
self.assertEqual(a.forward(5), Transformed(Translate([ 0, 5, 0]), a))
self.assertEqual(a.back (6), Transformed(Translate([ 0, -6, 0]), a))
self.assertEqual(a.yaw_left (1), Transformed(RotateYpr( 1, 0, 0), a))
self.assertEqual(a.yaw_right (2), Transformed(RotateYpr(-2, 0, 0), a))
self.assertEqual(a.pitch_up (3), Transformed(RotateYpr( 0, 3, 0), a))
self.assertEqual(a.pitch_down(4), Transformed(RotateYpr( 0, -4, 0), a))
self.assertEqual(a.roll_right(5), Transformed(RotateYpr( 0, 0, 5), a))
self.assertEqual(a.roll_left (6), Transformed(RotateYpr( 0, 0, -6), a))
def roll_left(r):
return RotateYpr(0, 0, -r)
def roll_right(r):
return RotateYpr(0, 0, r)
def pitch_down(p):
return RotateYpr(0, -p, 0)
def pitch_up(p):
return RotateYpr(0, p, 0)
def yaw_right(y):
return RotateYpr(-y, 0, 0)
def yaw_left(y):
return RotateYpr(y, 0, 0)
def rotate(axis_or_frm = None, angle_or_to = None, axis = None, angle = None, frm = None, to = None, xyz = None, ypr = None, ignore_ambiguity = False):
"""Generate a rotation around an axis through the origin.
Signatures (canonical forms):
* rotate(axis = x, angle = 45)
* rotate(frm = x, to = y)
* rotate(xyz = [45, 0, 30])
* rotate(ypr = [45, -30, 10])
Signatures (convenience forms):
* rotate(x, 45)
* rotate(x, angle = 45)
* rotate(x, y)
* rotate(x, to = y)
"""
# Canonical forms:
# axis_or_axmag_or_frm angle_or_to axis angle frm to xyz ypr
# - - vec num - - - - # Axis/angle
# - - - - vec vec - - # From/to
# - - - - - - list - # XYZ
# - - - - - - - list # Yaw/pitch/roll
# Convenience forms (-: must be None, *: overwritten)
# vec num * * - - - - # Axis/angle (implicit)
# vec - * num - - - - # Axis/angle (explicit)
# vec vec - - * * - - # From/to (implicit)
# vec - - - * vec - - # From/to (explicit)
#
# "Vector type" is Vector, list, or tuple
# Make sure that there are no conflicts between convenience parameters and canonical parameters
if both(axis_or_frm, axis ): raise TypeError("axis" " cannot be specified together with axis_or_frm")
if both(axis_or_frm, frm ): raise TypeError("frm" " cannot be specified together with axis_or_frm")
if both(angle_or_to, angle): raise TypeError("angle" " cannot be specified together with angle_or_to")
if both(angle_or_to, to ): raise TypeError("to" " cannot be specified together with angle_or_to")
# Transform the convenience forms to canonical form
if axis_or_frm is not None:
if not Vector.valid_type(axis_or_frm):
raise TypeError("axis must be a vector type")
if angle_or_to is not None:
if number.valid(angle_or_to):
# Axis/angle (implicit)
axis = axis_or_frm
angle = angle_or_to
elif Vector.valid_type(angle_or_to):
# From/to (implicit)
frm = axis_or_frm
to = angle_or_to
else:
raise TypeError("angle_or_to must be a number or a vector type")
elif angle is not None:
# Axis/angle (explicit)
axis = axis_or_frm
elif to is not None:
# From/to (explicit)
frm = axis_or_frm
# Check the parameters that must appear in pairs
if axis is not None and angle is None: raise TypeError("angle" " is required when " "axis" " is given")
if angle is not None and axis is None: raise TypeError("axis" " is required when " "angle" " is given")
if frm is not None and to is None: raise TypeError("to" " is required when " "frm" " is given")
if to is not None and frm is None: raise TypeError("frm" " is required when " "to" " is given")
# Handle the different cases
if axis is not None:
# Check that no other specification is given
if frm is not None: raise TypeError("frm" " cannot be specified together with axis")
if xyz is not None: raise TypeError("xyz" " cannot be specified together with axis")
if ypr is not None: raise TypeError("ypr" " cannot be specified together with axis")
return RotateAxisAngle(axis, angle)
elif frm is not None:
# Check that no other specification is given
if axis is not None: raise TypeError("axis" " cannot be specified together with frm")
if xyz is not None: raise TypeError("xyz" " cannot be specified together with frm")
if ypr is not None: raise TypeError("ypr" " cannot be specified together with frm")
return RotateFromTo(frm, to, ignore_ambiguity)
elif xyz is not None:
# Check that no other specification is given
if axis is not None: raise TypeError("axis" " cannot be specified together with frm")
if frm is not None: raise TypeError("frm" " cannot be specified together with axis")
if ypr is not None: raise TypeError("ypr" " cannot be specified together with axis")
return RotateXyz(*xyz)
elif ypr is not None:
# Check that no other specification is given
if axis is not None: raise TypeError("axis" " cannot be specified together with frm")
if frm is not None: raise TypeError("frm" " cannot be specified together with axis")
if xyz is not None: raise TypeError("xyz" " cannot be specified together with axis")
return RotateYpr(*ypr)
else:
raise TypeError("Invalid call signature")
def test_inverse(self):
self.assertInverse(RotateYpr(10, 20, 30),
RotateYpr(0, 0, -30) * RotateYpr(0, -20, 0) *
RotateYpr(-10, 0, 0),
symmetric=False)
def test_to_matrix(self):
# No rotation
self.assertAlmostEqual(
RotateYpr(0, 0, 0).to_matrix(), affine_matrix(X, Y, Z))
# 90 degrees around a single axis
self.assertAlmostEqual(
RotateYpr(90, 0, 0).to_matrix(), affine_matrix(Y, -X,
Z)) # Yaw left
self.assertAlmostEqual(
RotateYpr(0, 90, 0).to_matrix(), affine_matrix(X, Z,
-Y)) # Pitch up
self.assertAlmostEqual(
RotateYpr(0, 0, 90).to_matrix(), affine_matrix(-Z, Y,
X)) # Roll right
# 180 degrees around a single axis
self.assertAlmostEqual(
RotateYpr(180, 0, 0).to_matrix(), affine_matrix(-X, -Y, Z)) # Yaw
self.assertAlmostEqual(
RotateYpr(0, 180, 0).to_matrix(), affine_matrix(X, -Y,
-Z)) # Pitch
self.assertAlmostEqual(
RotateYpr(0, 0, 180).to_matrix(), affine_matrix(-X, Y, -Z)) # Roll
# 90 degrees each around two axes
self.assertAlmostEqual(
RotateYpr(90, 90, 0).to_matrix(),
affine_matrix(Y, Z, X)) # Yaw left, pitch up
self.assertAlmostEqual(
RotateYpr(90, 0, 90).to_matrix(),
affine_matrix(-Z, -X, Y)) # Yaw left, roll right
self.assertAlmostEqual(
RotateYpr(0, 90, 90).to_matrix(),
affine_matrix(Y, Z, X)) # Pitch up, roll right
# 90 degrees each around all three axes
self.assertAlmostEqual(
RotateYpr(90, 90, 90).to_matrix(),
affine_matrix(-X, Z, Y)) # Yaw left, pitch up, roll right
def test_repr(self):
self.assertRepr(RotateYpr(1, 2, 3), "RotateYpr(1, 2, 3)")
