Classes | Functions | Variables
tf_quaternion.transformations Namespace Reference

Classes

class  Arcball
 

Functions

def _import_module (module_name, warn=True, prefix='_py_', ignore='_')
 
def arcball_constrain_to_axis (point, axis)
 
def arcball_map_to_sphere (point, center, radius)
 
def arcball_nearest_axis (point, axes)
 
def clip_matrix (left, right, bottom, top, near, far, perspective=False)
 
def compose_matrix (scale=None, shear=None, angles=None, translate=None, perspective=None)
 
def concatenate_matrices (matrices)
 
def decompose_matrix (matrix)
 
def euler_from_matrix (matrix, axes='sxyz')
 
def euler_from_quaternion (quaternion, axes='sxyz')
 
def euler_matrix (ai, aj, ak, axes='sxyz')
 
def identity_matrix ()
 
def inverse_matrix (matrix)
 
def is_same_transform (matrix0, matrix1)
 
def orthogonalization_matrix (lengths, angles)
 
def projection_from_matrix (matrix, pseudo=False)
 
def projection_matrix (point, normal, direction=None, perspective=None, pseudo=False)
 
def quaternion_about_axis (angle, axis)
 
def quaternion_conjugate (quaternion)
 
def quaternion_from_euler (ai, aj, ak, axes='sxyz')
 
def quaternion_from_matrix (matrix)
 
def quaternion_inverse (quaternion)
 
def quaternion_matrix (quaternion)
 
def quaternion_multiply (quaternion1, quaternion0)
 
def quaternion_slerp (quat0, quat1, fraction, spin=0, shortestpath=True)
 
def random_quaternion (rand=None)
 
def random_rotation_matrix (rand=None)
 
def random_vector (size)
 
def reflection_from_matrix (matrix)
 
def reflection_matrix (point, normal)
 
def rotation_from_matrix (matrix)
 
def rotation_matrix (angle, direction, point=None)
 
def scale_from_matrix (matrix)
 
def scale_matrix (factor, origin=None, direction=None)
 
def shear_from_matrix (matrix)
 
def shear_matrix (angle, direction, point, normal)
 
def superimposition_matrix (v0, v1, scaling=False, usesvd=True)
 
def translation_from_matrix (matrix)
 
def translation_matrix (direction)
 
def unit_vector (data, axis=None, out=None)
 
def vector_norm (data, axis=None, out=None)
 

Variables

string __docformat__ = "restructuredtext en"
 
dictionary _AXES2TUPLE
 
float _EPS = numpy.finfo(float).eps*4.0
 
list _NEXT_AXIS = [1, 2, 0, 1]
 
 _TUPLE2AXES = dict((v, k) for k, v in _AXES2TUPLE.items())
 

Function Documentation

def tf_quaternion.transformations._import_module (   module_name,
  warn = True,
  prefix = '_py_',
  ignore = '_' 
)
private
Try import all public attributes from module into global namespace.

Existing attributes with name clashes are renamed with prefix.
Attributes starting with underscore are ignored by default.

Return True on successful import.

Definition at line 1681 of file transformations.py.

def tf_quaternion.transformations.arcball_constrain_to_axis (   point,
  axis 
)
Return sphere point perpendicular to axis.

Definition at line 1485 of file transformations.py.

def tf_quaternion.transformations.arcball_map_to_sphere (   point,
  center,
  radius 
)
Return unit sphere coordinates from window coordinates.

Definition at line 1472 of file transformations.py.

def tf_quaternion.transformations.arcball_nearest_axis (   point,
  axes 
)
Return axis, which arc is nearest to point.

Definition at line 1501 of file transformations.py.

def tf_quaternion.transformations.clip_matrix (   left,
  right,
  bottom,
  top,
  near,
  far,
  perspective = False 
)
Return matrix to obtain normalized device coordinates from frustrum.

The frustrum bounds are axis-aligned along x (left, right),
y (bottom, top) and z (near, far).

Normalized device coordinates are in range [-1, 1] if coordinates are
inside the frustrum.

If perspective is True the frustrum is a truncated pyramid with the
perspective point at origin and direction along z axis, otherwise an
orthographic canonical view volume (a box).

Homogeneous coordinates transformed by the perspective clip matrix
need to be dehomogenized (devided by w coordinate).

>>> frustrum = numpy.random.rand(6)
>>> frustrum[1] += frustrum[0]
>>> frustrum[3] += frustrum[2]
>>> frustrum[5] += frustrum[4]
>>> M = clip_matrix(*frustrum, perspective=False)
>>> numpy.dot(M, [frustrum[0], frustrum[2], frustrum[4], 1.0])
array([-1., -1., -1.,  1.])
>>> numpy.dot(M, [frustrum[1], frustrum[3], frustrum[5], 1.0])
array([ 1.,  1.,  1.,  1.])
>>> M = clip_matrix(*frustrum, perspective=True)
>>> v = numpy.dot(M, [frustrum[0], frustrum[2], frustrum[4], 1.0])
>>> v / v[3]
array([-1., -1., -1.,  1.])
>>> v = numpy.dot(M, [frustrum[1], frustrum[3], frustrum[4], 1.0])
>>> v / v[3]
array([ 1.,  1., -1.,  1.])

Definition at line 572 of file transformations.py.

def tf_quaternion.transformations.compose_matrix (   scale = None,
  shear = None,
  angles = None,
  translate = None,
  perspective = None 
)
Return transformation matrix from sequence of transformations.

This is the inverse of the decompose_matrix function.

Sequence of transformations:
    scale : vector of 3 scaling factors
    shear : list of shear factors for x-y, x-z, y-z axes
    angles : list of Euler angles about static x, y, z axes
    translate : translation vector along x, y, z axes
    perspective : perspective partition of matrix

>>> scale = numpy.random.random(3) - 0.5
>>> shear = numpy.random.random(3) - 0.5
>>> angles = (numpy.random.random(3) - 0.5) * (2*math.pi)
>>> trans = numpy.random.random(3) - 0.5
>>> persp = numpy.random.random(4) - 0.5
>>> M0 = compose_matrix(scale, shear, angles, trans, persp)
>>> result = decompose_matrix(M0)
>>> M1 = compose_matrix(*result)
>>> is_same_transform(M0, M1)
True

Definition at line 786 of file transformations.py.

def tf_quaternion.transformations.concatenate_matrices (   matrices)
Return concatenation of series of transformation matrices.

>>> M = numpy.random.rand(16).reshape((4, 4)) - 0.5
>>> numpy.allclose(M, concatenate_matrices(M))
True
>>> numpy.allclose(numpy.dot(M, M.T), concatenate_matrices(M, M.T))
True

Definition at line 1649 of file transformations.py.

def tf_quaternion.transformations.decompose_matrix (   matrix)
Return sequence of transformations from transformation matrix.

matrix : array_like
    Non-degenerative homogeneous transformation matrix

Return tuple of:
    scale : vector of 3 scaling factors
    shear : list of shear factors for x-y, x-z, y-z axes
    angles : list of Euler angles about static x, y, z axes
    translate : translation vector along x, y, z axes
    perspective : perspective partition of matrix

Raise ValueError if matrix is of wrong type or degenerative.

>>> T0 = translation_matrix((1, 2, 3))
>>> scale, shear, angles, trans, persp = decompose_matrix(T0)
>>> T1 = translation_matrix(trans)
>>> numpy.allclose(T0, T1)
True
>>> S = scale_matrix(0.123)
>>> scale, shear, angles, trans, persp = decompose_matrix(S)
>>> scale[0]
0.123
>>> R0 = euler_matrix(1, 2, 3)
>>> scale, shear, angles, trans, persp = decompose_matrix(R0)
>>> R1 = euler_matrix(*angles)
>>> numpy.allclose(R0, R1)
True

Definition at line 700 of file transformations.py.

def tf_quaternion.transformations.euler_from_matrix (   matrix,
  axes = 'sxyz' 
)
Return Euler angles from rotation matrix for specified axis sequence.

axes : One of 24 axis sequences as string or encoded tuple

Note that many Euler angle triplets can describe one matrix.

>>> R0 = euler_matrix(1, 2, 3, 'syxz')
>>> al, be, ga = euler_from_matrix(R0, 'syxz')
>>> R1 = euler_matrix(al, be, ga, 'syxz')
>>> numpy.allclose(R0, R1)
True
>>> angles = (4.0*math.pi) * (numpy.random.random(3) - 0.5)
>>> for axes in _AXES2TUPLE.keys():
...    R0 = euler_matrix(axes=axes, *angles)
...    R1 = euler_matrix(axes=axes, *euler_from_matrix(R0, axes))
...    if not numpy.allclose(R0, R1): print axes, "failed"

Definition at line 1031 of file transformations.py.

def tf_quaternion.transformations.euler_from_quaternion (   quaternion,
  axes = 'sxyz' 
)
Return Euler angles from quaternion for specified axis sequence.

>>> angles = euler_from_quaternion([0.06146124, 0, 0, 0.99810947])
>>> numpy.allclose(angles, [0.123, 0, 0])
True

Definition at line 1089 of file transformations.py.

def tf_quaternion.transformations.euler_matrix (   ai,
  aj,
  ak,
  axes = 'sxyz' 
)
Return homogeneous rotation matrix from Euler angles and axis sequence.

ai, aj, ak : Euler's roll, pitch and yaw angles
axes : One of 24 axis sequences as string or encoded tuple

>>> R = euler_matrix(1, 2, 3, 'syxz')
>>> numpy.allclose(numpy.sum(R[0]), -1.34786452)
True
>>> R = euler_matrix(1, 2, 3, (0, 1, 0, 1))
>>> numpy.allclose(numpy.sum(R[0]), -0.383436184)
True
>>> ai, aj, ak = (4.0*math.pi) * (numpy.random.random(3) - 0.5)
>>> for axes in _AXES2TUPLE.keys():
...    R = euler_matrix(ai, aj, ak, axes)
>>> for axes in _TUPLE2AXES.keys():
...    R = euler_matrix(ai, aj, ak, axes)

Definition at line 968 of file transformations.py.

def tf_quaternion.transformations.identity_matrix ( )
Return 4x4 identity/unit matrix.

>>> I = identity_matrix()
>>> numpy.allclose(I, numpy.dot(I, I))
True
>>> numpy.sum(I), numpy.trace(I)
(4.0, 4.0)
>>> numpy.allclose(I, numpy.identity(4, dtype=numpy.float64))
True

Definition at line 180 of file transformations.py.

def tf_quaternion.transformations.inverse_matrix (   matrix)
Return inverse of square transformation matrix.

>>> M0 = random_rotation_matrix()
>>> M1 = inverse_matrix(M0.T)
>>> numpy.allclose(M1, numpy.linalg.inv(M0.T))
True
>>> for size in range(1, 7):
...     M0 = numpy.random.rand(size, size)
...     M1 = inverse_matrix(M0)
...     if not numpy.allclose(M1, numpy.linalg.inv(M0)): print size

Definition at line 1633 of file transformations.py.

def tf_quaternion.transformations.is_same_transform (   matrix0,
  matrix1 
)
Return True if two matrices perform same transformation.

>>> is_same_transform(numpy.identity(4), numpy.identity(4))
True
>>> is_same_transform(numpy.identity(4), random_rotation_matrix())
False

Definition at line 1665 of file transformations.py.

def tf_quaternion.transformations.orthogonalization_matrix (   lengths,
  angles 
)
Return orthogonalization matrix for crystallographic cell coordinates.

Angles are expected in degrees.

The de-orthogonalization matrix is the inverse.

>>> O = orthogonalization_matrix((10., 10., 10.), (90., 90., 90.))
>>> numpy.allclose(O[:3, :3], numpy.identity(3, float) * 10)
True
>>> O = orthogonalization_matrix([9.8, 12.0, 15.5], [87.2, 80.7, 69.7])
>>> numpy.allclose(numpy.sum(O), 43.063229)
True

Definition at line 838 of file transformations.py.

def tf_quaternion.transformations.projection_from_matrix (   matrix,
  pseudo = False 
)
Return projection plane and perspective point from projection matrix.

Return values are same as arguments for projection_matrix function:
point, normal, direction, perspective, and pseudo.

>>> point = numpy.random.random(3) - 0.5
>>> normal = numpy.random.random(3) - 0.5
>>> direct = numpy.random.random(3) - 0.5
>>> persp = numpy.random.random(3) - 0.5
>>> P0 = projection_matrix(point, normal)
>>> result = projection_from_matrix(P0)
>>> P1 = projection_matrix(*result)
>>> is_same_transform(P0, P1)
True
>>> P0 = projection_matrix(point, normal, direct)
>>> result = projection_from_matrix(P0)
>>> P1 = projection_matrix(*result)
>>> is_same_transform(P0, P1)
True
>>> P0 = projection_matrix(point, normal, perspective=persp, pseudo=False)
>>> result = projection_from_matrix(P0, pseudo=False)
>>> P1 = projection_matrix(*result)
>>> is_same_transform(P0, P1)
True
>>> P0 = projection_matrix(point, normal, perspective=persp, pseudo=True)
>>> result = projection_from_matrix(P0, pseudo=True)
>>> P1 = projection_matrix(*result)
>>> is_same_transform(P0, P1)
True

Definition at line 499 of file transformations.py.

def tf_quaternion.transformations.projection_matrix (   point,
  normal,
  direction = None,
  perspective = None,
  pseudo = False 
)
Return matrix to project onto plane defined by point and normal.

Using either perspective point, projection direction, or none of both.

If pseudo is True, perspective projections will preserve relative depth
such that Perspective = dot(Orthogonal, PseudoPerspective).

>>> P = projection_matrix((0, 0, 0), (1, 0, 0))
>>> numpy.allclose(P[1:, 1:], numpy.identity(4)[1:, 1:])
True
>>> point = numpy.random.random(3) - 0.5
>>> normal = numpy.random.random(3) - 0.5
>>> direct = numpy.random.random(3) - 0.5
>>> persp = numpy.random.random(3) - 0.5
>>> P0 = projection_matrix(point, normal)
>>> P1 = projection_matrix(point, normal, direction=direct)
>>> P2 = projection_matrix(point, normal, perspective=persp)
>>> P3 = projection_matrix(point, normal, perspective=persp, pseudo=True)
>>> is_same_transform(P2, numpy.dot(P0, P3))
True
>>> P = projection_matrix((3, 0, 0), (1, 1, 0), (1, 0, 0))
>>> v0 = (numpy.random.rand(4, 5) - 0.5) * 20.0
>>> v0[3] = 1.0
>>> v1 = numpy.dot(P, v0)
>>> numpy.allclose(v1[1], v0[1])
True
>>> numpy.allclose(v1[0], 3.0-v1[1])
True

Definition at line 438 of file transformations.py.

def tf_quaternion.transformations.quaternion_about_axis (   angle,
  axis 
)
Return quaternion for rotation about axis.

>>> q = quaternion_about_axis(0.123, (1, 0, 0))
>>> numpy.allclose(q, [0.06146124, 0, 0, 0.99810947])
True

Definition at line 1157 of file transformations.py.

def tf_quaternion.transformations.quaternion_conjugate (   quaternion)
Return conjugate of quaternion.

>>> q0 = random_quaternion()
>>> q1 = quaternion_conjugate(q0)
>>> q1[3] == q0[3] and all(q1[:3] == -q0[:3])
True

Definition at line 1245 of file transformations.py.

def tf_quaternion.transformations.quaternion_from_euler (   ai,
  aj,
  ak,
  axes = 'sxyz' 
)
Return quaternion from Euler angles and axis sequence.

ai, aj, ak : Euler's roll, pitch and yaw angles
axes : One of 24 axis sequences as string or encoded tuple

>>> q = quaternion_from_euler(1, 2, 3, 'ryxz')
>>> numpy.allclose(q, [0.310622, -0.718287, 0.444435, 0.435953])
True

Definition at line 1100 of file transformations.py.

def tf_quaternion.transformations.quaternion_from_matrix (   matrix)
Return quaternion from rotation matrix.

>>> R = rotation_matrix(0.123, (1, 2, 3))
>>> q = quaternion_from_matrix(R)
>>> numpy.allclose(q, [0.0164262, 0.0328524, 0.0492786, 0.9981095])
True

Definition at line 1196 of file transformations.py.

def tf_quaternion.transformations.quaternion_inverse (   quaternion)
Return inverse of quaternion.

>>> q0 = random_quaternion()
>>> q1 = quaternion_inverse(q0)
>>> numpy.allclose(quaternion_multiply(q0, q1), [0, 0, 0, 1])
True

Definition at line 1258 of file transformations.py.

def tf_quaternion.transformations.quaternion_matrix (   quaternion)
Return homogeneous rotation matrix from quaternion.

>>> R = quaternion_matrix([0.06146124, 0, 0, 0.99810947])
>>> numpy.allclose(R, rotation_matrix(0.123, (1, 0, 0)))
True

Definition at line 1174 of file transformations.py.

def tf_quaternion.transformations.quaternion_multiply (   quaternion1,
  quaternion0 
)
Return multiplication of two quaternions.

>>> q = quaternion_multiply([1, -2, 3, 4], [-5, 6, 7, 8])
>>> numpy.allclose(q, [-44, -14, 48, 28])
True

Definition at line 1228 of file transformations.py.

def tf_quaternion.transformations.quaternion_slerp (   quat0,
  quat1,
  fraction,
  spin = 0,
  shortestpath = True 
)
Return spherical linear interpolation between two quaternions.

>>> q0 = random_quaternion()
>>> q1 = random_quaternion()
>>> q = quaternion_slerp(q0, q1, 0.0)
>>> numpy.allclose(q, q0)
True
>>> q = quaternion_slerp(q0, q1, 1.0, 1)
>>> numpy.allclose(q, q1)
True
>>> q = quaternion_slerp(q0, q1, 0.5)
>>> angle = math.acos(numpy.dot(q0, q))
>>> numpy.allclose(2.0, math.acos(numpy.dot(q0, q1)) / angle) or \
    numpy.allclose(2.0, math.acos(-numpy.dot(q0, q1)) / angle)
True

Definition at line 1270 of file transformations.py.

def tf_quaternion.transformations.random_quaternion (   rand = None)
Return uniform random unit quaternion.

rand: array like or None
    Three independent random variables that are uniformly distributed
    between 0 and 1.

>>> q = random_quaternion()
>>> numpy.allclose(1.0, vector_norm(q))
True
>>> q = random_quaternion(numpy.random.random(3))
>>> q.shape
(4,)

Definition at line 1311 of file transformations.py.

def tf_quaternion.transformations.random_rotation_matrix (   rand = None)
Return uniform random rotation matrix.

rnd: array like
    Three independent random variables that are uniformly distributed
    between 0 and 1 for each returned quaternion.

>>> R = random_rotation_matrix()
>>> numpy.allclose(numpy.dot(R.T, R), numpy.identity(4))
True

Definition at line 1341 of file transformations.py.

def tf_quaternion.transformations.random_vector (   size)
Return array of random doubles in the half-open interval [0.0, 1.0).

>>> v = random_vector(10000)
>>> numpy.all(v >= 0.0) and numpy.all(v < 1.0)
True
>>> v0 = random_vector(10)
>>> v1 = random_vector(10)
>>> numpy.any(v0 == v1)
False

Definition at line 1618 of file transformations.py.

def tf_quaternion.transformations.reflection_from_matrix (   matrix)
Return mirror plane point and normal vector from reflection matrix.

>>> v0 = numpy.random.random(3) - 0.5
>>> v1 = numpy.random.random(3) - 0.5
>>> M0 = reflection_matrix(v0, v1)
>>> point, normal = reflection_from_matrix(M0)
>>> M1 = reflection_matrix(point, normal)
>>> is_same_transform(M0, M1)
True

Definition at line 246 of file transformations.py.

def tf_quaternion.transformations.reflection_matrix (   point,
  normal 
)
Return matrix to mirror at plane defined by point and normal vector.

>>> v0 = numpy.random.random(4) - 0.5
>>> v0[3] = 1.0
>>> v1 = numpy.random.random(3) - 0.5
>>> R = reflection_matrix(v0, v1)
>>> numpy.allclose(2., numpy.trace(R))
True
>>> numpy.allclose(v0, numpy.dot(R, v0))
True
>>> v2 = v0.copy()
>>> v2[:3] += v1
>>> v3 = v0.copy()
>>> v2[:3] -= v1
>>> numpy.allclose(v2, numpy.dot(R, v3))
True

Definition at line 220 of file transformations.py.

def tf_quaternion.transformations.rotation_from_matrix (   matrix)
Return rotation angle and axis from rotation matrix.

>>> angle = (random.random() - 0.5) * (2*math.pi)
>>> direc = numpy.random.random(3) - 0.5
>>> point = numpy.random.random(3) - 0.5
>>> R0 = rotation_matrix(angle, direc, point)
>>> angle, direc, point = rotation_from_matrix(R0)
>>> R1 = rotation_matrix(angle, direc, point)
>>> is_same_transform(R0, R1)
True

Definition at line 319 of file transformations.py.

def tf_quaternion.transformations.rotation_matrix (   angle,
  direction,
  point = None 
)
Return matrix to rotate about axis defined by point and direction.

>>> angle = (random.random() - 0.5) * (2*math.pi)
>>> direc = numpy.random.random(3) - 0.5
>>> point = numpy.random.random(3) - 0.5
>>> R0 = rotation_matrix(angle, direc, point)
>>> R1 = rotation_matrix(angle-2*math.pi, direc, point)
>>> is_same_transform(R0, R1)
True
>>> R0 = rotation_matrix(angle, direc, point)
>>> R1 = rotation_matrix(-angle, -direc, point)
>>> is_same_transform(R0, R1)
True
>>> I = numpy.identity(4, numpy.float64)
>>> numpy.allclose(I, rotation_matrix(math.pi*2, direc))
True
>>> numpy.allclose(2., numpy.trace(rotation_matrix(math.pi/2,
...                                                direc, point)))
True

Definition at line 275 of file transformations.py.

def tf_quaternion.transformations.scale_from_matrix (   matrix)
Return scaling factor, origin and direction from scaling matrix.

>>> factor = random.random() * 10 - 5
>>> origin = numpy.random.random(3) - 0.5
>>> direct = numpy.random.random(3) - 0.5
>>> S0 = scale_matrix(factor, origin)
>>> factor, origin, direction = scale_from_matrix(S0)
>>> S1 = scale_matrix(factor, origin, direction)
>>> is_same_transform(S0, S1)
True
>>> S0 = scale_matrix(factor, origin, direct)
>>> factor, origin, direction = scale_from_matrix(S0)
>>> S1 = scale_matrix(factor, origin, direction)
>>> is_same_transform(S0, S1)
True

Definition at line 396 of file transformations.py.

def tf_quaternion.transformations.scale_matrix (   factor,
  origin = None,
  direction = None 
)
Return matrix to scale by factor around origin in direction.

Use factor -1 for point symmetry.

>>> v = (numpy.random.rand(4, 5) - 0.5) * 20.0
>>> v[3] = 1.0
>>> S = scale_matrix(-1.234)
>>> numpy.allclose(numpy.dot(S, v)[:3], -1.234*v[:3])
True
>>> factor = random.random() * 10 - 5
>>> origin = numpy.random.random(3) - 0.5
>>> direct = numpy.random.random(3) - 0.5
>>> S = scale_matrix(factor, origin)
>>> S = scale_matrix(factor, origin, direct)

Definition at line 359 of file transformations.py.

def tf_quaternion.transformations.shear_from_matrix (   matrix)
Return shear angle, direction and plane from shear matrix.

>>> angle = (random.random() - 0.5) * 4*math.pi
>>> direct = numpy.random.random(3) - 0.5
>>> point = numpy.random.random(3) - 0.5
>>> normal = numpy.cross(direct, numpy.random.random(3))
>>> S0 = shear_matrix(angle, direct, point, normal)
>>> angle, direct, point, normal = shear_from_matrix(S0)
>>> S1 = shear_matrix(angle, direct, point, normal)
>>> is_same_transform(S0, S1)
True

Definition at line 655 of file transformations.py.

def tf_quaternion.transformations.shear_matrix (   angle,
  direction,
  point,
  normal 
)
Return matrix to shear by angle along direction vector on shear plane.

The shear plane is defined by a point and normal vector. The direction
vector must be orthogonal to the plane's normal vector.

A point P is transformed by the shear matrix into P" such that
the vector P-P" is parallel to the direction vector and its extent is
given by the angle of P-P'-P", where P' is the orthogonal projection
of P onto the shear plane.

>>> angle = (random.random() - 0.5) * 4*math.pi
>>> direct = numpy.random.random(3) - 0.5
>>> point = numpy.random.random(3) - 0.5
>>> normal = numpy.cross(direct, numpy.random.random(3))
>>> S = shear_matrix(angle, direct, point, normal)
>>> numpy.allclose(1.0, numpy.linalg.det(S))
True

Definition at line 624 of file transformations.py.

def tf_quaternion.transformations.superimposition_matrix (   v0,
  v1,
  scaling = False,
  usesvd = True 
)
Return matrix to transform given vector set into second vector set.

v0 and v1 are shape (3, \*) or (4, \*) arrays of at least 3 vectors.

If usesvd is True, the weighted sum of squared deviations (RMSD) is
minimized according to the algorithm by W. Kabsch [8]. Otherwise the
quaternion based algorithm by B. Horn [9] is used (slower when using
this Python implementation).

The returned matrix performs rotation, translation and uniform scaling
(if specified).

>>> v0 = numpy.random.rand(3, 10)
>>> M = superimposition_matrix(v0, v0)
>>> numpy.allclose(M, numpy.identity(4))
True
>>> R = random_rotation_matrix(numpy.random.random(3))
>>> v0 = ((1,0,0), (0,1,0), (0,0,1), (1,1,1))
>>> v1 = numpy.dot(R, v0)
>>> M = superimposition_matrix(v0, v1)
>>> numpy.allclose(v1, numpy.dot(M, v0))
True
>>> v0 = (numpy.random.rand(4, 100) - 0.5) * 20.0
>>> v0[3] = 1.0
>>> v1 = numpy.dot(R, v0)
>>> M = superimposition_matrix(v0, v1)
>>> numpy.allclose(v1, numpy.dot(M, v0))
True
>>> S = scale_matrix(random.random())
>>> T = translation_matrix(numpy.random.random(3)-0.5)
>>> M = concatenate_matrices(T, R, S)
>>> v1 = numpy.dot(M, v0)
>>> v0[:3] += numpy.random.normal(0.0, 1e-9, 300).reshape(3, -1)
>>> M = superimposition_matrix(v0, v1, scaling=True)
>>> numpy.allclose(v1, numpy.dot(M, v0))
True
>>> M = superimposition_matrix(v0, v1, scaling=True, usesvd=False)
>>> numpy.allclose(v1, numpy.dot(M, v0))
True
>>> v = numpy.empty((4, 100, 3), dtype=numpy.float64)
>>> v[:, :, 0] = v0
>>> M = superimposition_matrix(v0, v1, scaling=True, usesvd=False)
>>> numpy.allclose(v1, numpy.dot(M, v[:, :, 0]))
True

Definition at line 866 of file transformations.py.

def tf_quaternion.transformations.translation_from_matrix (   matrix)
Return translation vector from translation matrix.

>>> v0 = numpy.random.random(3) - 0.5
>>> v1 = translation_from_matrix(translation_matrix(v0))
>>> numpy.allclose(v0, v1)
True

Definition at line 208 of file transformations.py.

def tf_quaternion.transformations.translation_matrix (   direction)
Return matrix to translate by direction vector.

>>> v = numpy.random.random(3) - 0.5
>>> numpy.allclose(v, translation_matrix(v)[:3, 3])
True

Definition at line 195 of file transformations.py.

def tf_quaternion.transformations.unit_vector (   data,
  axis = None,
  out = None 
)
Return ndarray normalized by length, i.e. eucledian norm, along axis.

>>> v0 = numpy.random.random(3)
>>> v1 = unit_vector(v0)
>>> numpy.allclose(v1, v0 / numpy.linalg.norm(v0))
True
>>> v0 = numpy.random.rand(5, 4, 3)
>>> v1 = unit_vector(v0, axis=-1)
>>> v2 = v0 / numpy.expand_dims(numpy.sqrt(numpy.sum(v0*v0, axis=2)), 2)
>>> numpy.allclose(v1, v2)
True
>>> v1 = unit_vector(v0, axis=1)
>>> v2 = v0 / numpy.expand_dims(numpy.sqrt(numpy.sum(v0*v0, axis=1)), 1)
>>> numpy.allclose(v1, v2)
True
>>> v1 = numpy.empty((5, 4, 3), dtype=numpy.float64)
>>> unit_vector(v0, axis=1, out=v1)
>>> numpy.allclose(v1, v2)
True
>>> list(unit_vector([]))
[]
>>> list(unit_vector([1.0]))
[1.0]

Definition at line 1574 of file transformations.py.

def tf_quaternion.transformations.vector_norm (   data,
  axis = None,
  out = None 
)
Return length, i.e. eucledian norm, of ndarray along axis.

>>> v = numpy.random.random(3)
>>> n = vector_norm(v)
>>> numpy.allclose(n, numpy.linalg.norm(v))
True
>>> v = numpy.random.rand(6, 5, 3)
>>> n = vector_norm(v, axis=-1)
>>> numpy.allclose(n, numpy.sqrt(numpy.sum(v*v, axis=2)))
True
>>> n = vector_norm(v, axis=1)
>>> numpy.allclose(n, numpy.sqrt(numpy.sum(v*v, axis=1)))
True
>>> v = numpy.random.rand(5, 4, 3)
>>> n = numpy.empty((5, 3), dtype=numpy.float64)
>>> vector_norm(v, axis=1, out=n)
>>> numpy.allclose(n, numpy.sqrt(numpy.sum(v*v, axis=1)))
True
>>> vector_norm([])
0.0
>>> vector_norm([1.0])
1.0

Definition at line 1535 of file transformations.py.

Variable Documentation

string tf_quaternion.transformations.__docformat__ = "restructuredtext en"
private

Definition at line 177 of file transformations.py.

dictionary tf_quaternion.transformations._AXES2TUPLE
private
Initial value:
1 = {
2  'sxyz': (0, 0, 0, 0), 'sxyx': (0, 0, 1, 0), 'sxzy': (0, 1, 0, 0),
3  'sxzx': (0, 1, 1, 0), 'syzx': (1, 0, 0, 0), 'syzy': (1, 0, 1, 0),
4  'syxz': (1, 1, 0, 0), 'syxy': (1, 1, 1, 0), 'szxy': (2, 0, 0, 0),
5  'szxz': (2, 0, 1, 0), 'szyx': (2, 1, 0, 0), 'szyz': (2, 1, 1, 0),
6  'rzyx': (0, 0, 0, 1), 'rxyx': (0, 0, 1, 1), 'ryzx': (0, 1, 0, 1),
7  'rxzx': (0, 1, 1, 1), 'rxzy': (1, 0, 0, 1), 'ryzy': (1, 0, 1, 1),
8  'rzxy': (1, 1, 0, 1), 'ryxy': (1, 1, 1, 1), 'ryxz': (2, 0, 0, 1),
9  'rzxz': (2, 0, 1, 1), 'rxyz': (2, 1, 0, 1), 'rzyz': (2, 1, 1, 1)}

Definition at line 1521 of file transformations.py.

float tf_quaternion.transformations._EPS = numpy.finfo(float).eps*4.0
private

Definition at line 1515 of file transformations.py.

list tf_quaternion.transformations._NEXT_AXIS = [1, 2, 0, 1]
private

Definition at line 1518 of file transformations.py.

tf_quaternion.transformations._TUPLE2AXES = dict((v, k) for k, v in _AXES2TUPLE.items())
private

Definition at line 1531 of file transformations.py.



uuv_assistants
Author(s): Musa Morena Marcusso Manhaes , Sebastian Scherer , Luiz Ricardo Douat
autogenerated on Mon Jul 1 2019 19:39:08