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()) | |
|
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 |
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| ) |
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, | |
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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, | |
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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.
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Definition at line 177 of file transformations.py.
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Definition at line 1521 of file transformations.py.
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Definition at line 1515 of file transformations.py.
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Definition at line 1518 of file transformations.py.
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Definition at line 1531 of file transformations.py.