pcg_gazebo

pcg_gazebo¶

Procedural generation package

This module implements the client for the procedural generation plugins in Gazebo. This interface allows using Python to control the simulation state in runtime with the help of the specific plugins write in the pcg_gazebo_ros_plugins.

Example:

Attributes: module_level_variable1 (int):

Todo: * For module TODOs

pcg_gazebo.log¶

pcg_gazebo.transformations¶

Homogeneous Transformation Matrices and Quaternions.

A library for calculating 4x4 matrices for translating, rotating, reflecting, scaling, shearing, projecting, orthogonalizing, and superimposing arrays of 3D homogeneous coordinates as well as for converting between rotation matrices, Euler angles, and quaternions. Also includes an Arcball control object and functions to decompose transformation matrices.

:Authors: Christoph Gohlke <http://www.lfd.uci.edu/~gohlke/>__, Laboratory for Fluorescence Dynamics, University of California, Irvine

:Version: 20090418

Requirements¶

Python 2.6 <http://www.python.org>__
Numpy 1.3 <http://numpy.scipy.org>__
transformations.c 20090418 <http://www.lfd.uci.edu/~gohlke/>__ (optional implementation of some functions in C)

Notes¶

Matrices (M) can be inverted using numpy.linalg.inv(M), concatenated using numpy.dot(M0, M1), or used to transform homogeneous coordinates (v) using numpy.dot(M, v) for shape (4, *) "point of arrays", respectively numpy.dot(v, M.T) for shape (*, 4) "array of points".

Calculations are carried out with numpy.float64 precision.

This Python implementation is not optimized for speed.

Vector, point, quaternion, and matrix function arguments are expected to be "array like", i.e. tuple, list, or numpy arrays.

Return types are numpy arrays unless specified otherwise.

Angles are in radians unless specified otherwise.

Quaternions ix+jy+kz+w are represented as [x, y, z, w].

Use the transpose of transformation matrices for OpenGL glMultMatrixd().

A triple of Euler angles can be applied/interpreted in 24 ways, which can be specified using a 4 character string or encoded 4-tuple:

Axes 4-string: e.g. 'sxyz' or 'ryxy'

first character : rotations are applied to 's'tatic or 'r'otating frame
remaining characters : successive rotation axis 'x', 'y', or 'z'

Axes 4-tuple: e.g. (0, 0, 0, 0) or (1, 1, 1, 1)

inner axis: code of axis ('x':0, 'y':1, 'z':2) of rightmost matrix.
parity : even (0) if inner axis 'x' is followed by 'y', 'y' is followed by 'z', or 'z' is followed by 'x'. Otherwise odd (1).
repetition : first and last axis are same (1) or different (0).
frame : rotations are applied to static (0) or rotating (1) frame.

References¶

(1) Matrices and transformations. Ronald Goldman. In "Graphics Gems I", pp 472-475. Morgan Kaufmann, 1990. (2) More matrices and transformations: shear and pseudo-perspective. Ronald Goldman. In "Graphics Gems II", pp 320-323. Morgan Kaufmann, 1991. (3) Decomposing a matrix into simple transformations. Spencer Thomas. In "Graphics Gems II", pp 320-323. Morgan Kaufmann, 1991. (4) Recovering the data from the transformation matrix. Ronald Goldman. In "Graphics Gems II", pp 324-331. Morgan Kaufmann, 1991. (5) Euler angle conversion. Ken Shoemake. In "Graphics Gems IV", pp 222-229. Morgan Kaufmann, 1994. (6) Arcball rotation control. Ken Shoemake. In "Graphics Gems IV", pp 175-192. Morgan Kaufmann, 1994. (7) Representing attitude: Euler angles, unit quaternions, and rotation vectors. James Diebel. 2006. (8) A discussion of the solution for the best rotation to relate two sets of vectors. W Kabsch. Acta Cryst. 1978. A34, 827-828. (9) Closed-form solution of absolute orientation using unit quaternions. BKP Horn. J Opt Soc Am A. 1987. 4(4), 629-642. (10) Quaternions. Ken Shoemake. http://www.sfu.ca/~jwa3/cmpt461/files/quatut.pdf (11) From quaternion to matrix and back. JMP van Waveren. 2005. http://www.intel.com/cd/ids/developer/asmo-na/eng/293748.htm (12) Uniform random rotations. Ken Shoemake. In "Graphics Gems III", pp 124-132. Morgan Kaufmann, 1992.

Examples¶

alpha, beta, gamma = 0.123, -1.234, 2.345 origin, xaxis, yaxis, zaxis = (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1) I = identity_matrix() Rx = rotation_matrix(alpha, xaxis) Ry = rotation_matrix(beta, yaxis) Rz = rotation_matrix(gamma, zaxis) R = concatenate_matrices(Rx, Ry, Rz) euler = euler_from_matrix(R, 'rxyz') numpy.allclose([alpha, beta, gamma], euler) True Re = euler_matrix(alpha, beta, gamma, 'rxyz') is_same_transform(R, Re) True al, be, ga = euler_from_matrix(Re, 'rxyz') is_same_transform(Re, euler_matrix(al, be, ga, 'rxyz')) True qx = quaternion_about_axis(alpha, xaxis) qy = quaternion_about_axis(beta, yaxis) qz = quaternion_about_axis(gamma, zaxis) q = quaternion_multiply(qx, qy) q = quaternion_multiply(q, qz) Rq = quaternion_matrix(q) is_same_transform(R, Rq) True S = scale_matrix(1.23, origin) T = translation_matrix((1, 2, 3)) Z = shear_matrix(beta, xaxis, origin, zaxis) R = random_rotation_matrix(numpy.random.rand(3)) M = concatenate_matrices(T, R, Z, S) scale, shear, angles, trans, persp = decompose_matrix(M) numpy.allclose(scale, 1.23) True numpy.allclose(trans, (1, 2, 3)) True numpy.allclose(shear, (0, math.tan(beta), 0)) True is_same_transform(R, euler_matrix(axes='sxyz', *angles)) True M1 = compose_matrix(scale, shear, angles, trans, persp) is_same_transform(M, M1) True

identity_matrix¶

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

translation_matrix¶

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

translation_from_matrix¶

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

reflection_matrix¶

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

reflection_from_matrix¶

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

rotation_matrix¶

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

rotation_from_matrix¶

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

scale_matrix¶

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)

scale_from_matrix¶

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

projection_matrix¶

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

projection_from_matrix¶

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

clip_matrix¶

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.])

shear_matrix¶

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

shear_from_matrix¶

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

decompose_matrix¶

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

compose_matrix¶

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

orthogonalization_matrix¶

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

superimposition_matrix¶

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

euler_matrix¶

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)

euler_from_matrix¶

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"

euler_from_quaternion¶

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

quaternion_from_euler¶

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

quaternion_about_axis¶

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

quaternion_matrix¶

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

quaternion_from_matrix¶

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

quaternion_multiply¶

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

quaternion_conjugate¶

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

quaternion_inverse¶

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

quaternion_slerp¶

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

random_quaternion¶

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,)

random_rotation_matrix¶

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

Arcball¶

Arcball()

Virtual Trackball Control.

ball = Arcball() ball = Arcball(initial=numpy.identity(4)) ball.place([320, 320], 320) ball.down([500, 250]) ball.drag([475, 275]) R = ball.matrix() numpy.allclose(numpy.sum(R), 3.90583455) True ball = Arcball(initial=[0, 0, 0, 1]) ball.place([320, 320], 320) ball.setaxes([1,1,0], [-1, 1, 0]) ball.setconstrain(True) ball.down([400, 200]) ball.drag([200, 400]) R = ball.matrix() numpy.allclose(numpy.sum(R), 0.2055924) True ball.next()

place¶

Arcball.place(center, radius)

Place Arcball, e.g. when window size changes.

center : sequence[2] Window coordinates of trackball center. radius : float Radius of trackball in window coordinates.

setaxes¶

Arcball.setaxes(*axes)

Set axes to constrain rotations.

setconstrain¶

Arcball.setconstrain(constrain)

Set state of constrain to axis mode.

getconstrain¶

Arcball.getconstrain()

Return state of constrain to axis mode.

down¶

Arcball.down(point)

Set initial cursor window coordinates and pick constrain-axis.

drag¶

Arcball.drag(point)

Update current cursor window coordinates.

next¶

Arcball.next(acceleration=0.0)

Continue rotation in direction of last drag.

matrix¶

Arcball.matrix()

Return homogeneous rotation matrix.

arcball_map_to_sphere¶

arcball_map_to_sphere(point, center, radius)

Return unit sphere coordinates from window coordinates.

arcball_constrain_to_axis¶

arcball_constrain_to_axis(point, axis)

Return sphere point perpendicular to axis.

arcball_nearest_axis¶

arcball_nearest_axis(point, axes)

Return axis, which arc is nearest to point.

vector_norm¶

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

unit_vector¶

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]

random_vector¶

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

inverse_matrix¶

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

concatenate_matrices¶

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

is_same_transform¶

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

pcg_gazebo.visualization¶

Path¶

Path()