Assimp
v3.1.1 (June 2014)
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Classes | |
class | Arcball |
Functions | |
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) |
def transformations.arcball_constrain_to_axis | ( | point, | |
axis | |||
) |
Return sphere point perpendicular to axis.
def transformations.arcball_map_to_sphere | ( | point, | |
center, | |||
radius | |||
) |
Return unit sphere coordinates from window coordinates.
def transformations.arcball_nearest_axis | ( | point, | |
axes | |||
) |
Return axis, which arc is nearest to point.
def transformations.clip_matrix | ( | left, | |
right, | |||
bottom, | |||
top, | |||
near, | |||
far, | |||
perspective = False |
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) |
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.])
def transformations.compose_matrix | ( | scale = None , |
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shear = None , |
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angles = None , |
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translate = None , |
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perspective = None |
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) |
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
def 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
def 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
def transformations.euler_from_matrix | ( | matrix, | |
axes = 'sxyz' |
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) |
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"
def transformations.euler_from_quaternion | ( | quaternion, | |
axes = 'sxyz' |
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) |
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
def transformations.euler_matrix | ( | ai, | |
aj, | |||
ak, | |||
axes = 'sxyz' |
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) |
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)
def 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
def 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
def 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
def 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
def transformations.projection_from_matrix | ( | matrix, | |
pseudo = False |
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) |
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
def transformations.projection_matrix | ( | point, | |
normal, | |||
direction = None , |
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perspective = None , |
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pseudo = False |
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) |
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
def 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
def 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
def transformations.quaternion_from_euler | ( | ai, | |
aj, | |||
ak, | |||
axes = 'sxyz' |
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) |
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
def 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
def 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
def 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
def 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
def transformations.quaternion_slerp | ( | quat0, | |
quat1, | |||
fraction, | |||
spin = 0 , |
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shortestpath = True |
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) |
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
def 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,)
def 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
def 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
def 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
def 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
def 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
def transformations.rotation_matrix | ( | angle, | |
direction, | |||
point = None |
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) |
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
def 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
def transformations.scale_matrix | ( | factor, | |
origin = None , |
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direction = None |
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) |
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)
def 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
def 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
def transformations.superimposition_matrix | ( | v0, | |
v1, | |||
scaling = False , |
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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
def 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
def 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
def transformations.unit_vector | ( | data, | |
axis = None , |
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out = None |
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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]
def transformations.vector_norm | ( | data, | |
axis = None , |
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out = None |
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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