pykv package¶

Submodules¶

pykv.geo module¶

Geo¶

Functions for general geometric problems

Created on Wed Oct 30 22:00:43 2019

@author: andmo55

pykv.geo.angleaxis_from_w(ws)¶

pykv.geo.exp_skew(so, out=None)¶

Exponential of a list of skew-symmetric matrices so(3), i.e., the result is a list of rotations SO(3). It applies Rodrigues’ formula.

\[e^{[\boldsymbol\omega]_\times} = \mathrm{I}_3 + \sin\theta[\boldsymbol\omega]_\times + (1-\cos\theta)[\boldsymbol\omega]_\times^2, \hspace{2em}\theta=\|\boldsymbol\omega\|\]

so: ndarray(…,3,3): The ndarray of skew-symmetric matrices
out: ndarray(…,3,3): The ndarray of rotation matrices (if None is supplied, a new array is created)

SO: ndarray(…,3,3): The ndarray of rotation matrices

>>> import pcdlib as pc
>>> import numpy as np
>>> aa = [1,2,3]
>>> so = pc.skew_from_angleaxis(aa)
>>> pc.exp_skew()

pykv.geo.exp_skew_from_w(ws, out=None, so=None, theta=None, sintheta=None, costheta=None, dtype=<class 'numpy.float32'>)¶

Exponential of skew-symmetric matrices directly from angle-axis vectors. Some intermediate steps (so, theta, sintheta, costheta) can be provided for efficiency (they are generated and returned if not provided).

ws: ndarray or list: list of angle-axis vectors
out: ndarray: list of 3x3 special orthogonal (SO) matrices (if None, then a new array is created)

so: ndarray

theta: ndarray

sintheta: ndarray costheta: ndarray

ndarray: list of 3x3 special orthogonal (SO) matrices
ndarray: list of skew-symmetric matrices
ndarray: list of angles
ndarray: list of sines of angles
ndarray: list of cosines of angles

pykv.geo.frustum(l, r, b, t, n, f, out=None, dtype=<class 'numpy.float32'>)¶

Creates a perspective matrix from parameters of its frustrum Node: numpy uses row-major order (OpenGL uses column-major), so you see the transpose of common OpenGL frustrum matrices in the literature

dtype l: float

left

r: float: right
b: float: bottom
t: float: top
n: float: near
f: float: far
out: ndarray (4x4) (default: None): perspective matrix (preallocated or fresh new)

ndarray(4x4): perspective matrix

pykv.geo.log_SO(SO, out=None)¶

Compute the logarithm of special orthogonal matrices (SO(3)), resulting in skew-symmetric matrices (so(3)) or angle-axis w

\[\log (R\in SO(3)) = \log e^{[\omega]_\times} = [\omega]_\times \in so(3)\]

SO: ndarray(…,3,3): The rotation matrices in SO(3)
angleaxis: bool (default: False): True to return just the angle-axis vectors instead of skew symmetric matrices.
out: ndarray(…,3,3) or ndarray(…,3) (default: None): Array of skew-symmetric matrices or angle-axis vectors (if None, a new array is generated and returned)

out: ndarray(…,3,3): Array of skew-symmetric matrices
what: ndarray(…,3): Array of directions
theta: ndarray(…,3): Array of angles

>>> 
>>> 
>>> 

pykv.geo.ortho(l, r, b, t, n, f, out=None, dtype=<class 'numpy.float32'>)¶

Ortographic projection matrix

dtype l r b t n f out

pykv.geo.perspective(fov=45, aspect=1.8, near=0.1, far=100, out=None, dtype=<class 'numpy.float32'>)¶

Symmetric perspective projection matrix. It uses the same

fov: float: define the vertical field of view (in degrees)
aspect: float: relation between horizontal and vertical sizes
near: float: positive (near > 0) number
far: float: positive (far > near > 0) number
out: ndarray: preallocated or new array
dtype: type of new array (if out is None)

ndarray: preallocated (if out != None) or fresh new array

pykv.geo.rigid(pcd, R, out=None)¶

pykv.geo.rotate(M, n, theta, out=None)¶

pykv.geo.scale(M, s, out=None)¶

pykv.geo.skew_from_angleaxis(n=None, theta=None, ws=None, out=None)¶: Convert angle-axis vectors to skew-symmetric matrices

pykv.geo.skew_from_w(ws, out=None)¶

Convert angle-axis vectors to skew-symmetric matrices. Opposite: angleaxis_from_skew.

\[\boldsymbol\omega\mapsto[\boldsymbol{\omega}]_\times, \hspace{2em} \boldsymbol{\omega} = \theta \hat{\boldsymbol{\omega}}\]

ws: ndarray(…,3): ND list/array of angle-axis vectors
out: ndarray(…,): Pre-allocated array for storing the skew-symmetric matrices (if None, a new fresh array is allocated and returned)

so: ndarray(…,3, 3): (N+1)D array of skew-symmetric matrices

>>> import pcdlib as pc
>>> import numpy as np
>>> pc.skew_from_angleaxis(np.random.rand(2,3))
array([[[ 0.        , -0.18267483,  0.66990937],
      [ 0.18267483,  0.        , -0.154273  ],
      [-0.66990937,  0.154273  ,  0.        ]],       
     [[ 0.        , -0.63770203,  0.70667849],
      [ 0.63770203,  0.        , -0.36215796],
      [-0.70667849,  0.36215796,  0.        ]]])

pykv.geo.translate(t, M=None, out=None, dtype=<class 'numpy.float32'>)¶

Translate a NxN matrix M by a (N-1)-D vector. If M is None, then a new translation matrix is created

t: list or ndarray: the translation vector of size N-1.
M:: the source matrix of size NxN (identity if not provided)
out: the destination matrix (None for new matrix, not None for existing one, or even M). Default: None.

out: the destination matrix (None for new matrix, not None for existing one, or even M). Default: None.

pykv.geo.w_from_skew(so, out=None)¶

Extract angle-axis vectors from skew-symmetric matrices. Opposite: skew_from_angleaxis.

\[f:so=[\boldsymbol{\omega}]_\times\mapsto{\boldsymbol{\omega}}, \hspace{2em} \theta = \|\boldsymbol{\omega}\| \hspace{1em} \hat{\boldsymbol{\omega}} = \frac{\boldsymbol{\omega}}{\theta}\]

so: ndarray(…,3,3): ND list/array of skew-symmetric matrices
out: ndarray(…,3): ND list of angle-axis vectors (if None is supplied, a new array is created).

out: ndarray(…,3): ND list of angle-axis vectors.

>>> import pcdlib as pc
>>> aa = [1,2,3]
>>> so = pc.skew_from_angleaxis(aa)
>>> aa2 = pc.angleaxis_from_skew(so)
>>> aa2
array([1., 2., 3.])

pykv.kitti module¶

pykv.ouster module¶

pykv.ouster.apply_px_offset(images, px_offset, im=None)¶: Apply offset Parameters ———- images px_offset

pykv.ouster.get_px_offset(W: int)¶

Get the offsets for each row of range images generated by Ouster lidar devices

W: width of the image

ndarray(64)

pykv.ouster.make_xyz_lut(W, H, azimuth_angles, altitude_angles)¶

Create the rays for the ouster lidar data, assuming constant device rotation speed.

W: width of the image (number of angles) H: height of the image (number of lasers) azimuth_angles (initial horizontal offset for each laser) altitude_angles (vertical angle for each laser)

ndarray(H, W, 3): the set of HW rays which represents

pykv.ouster_rosbag module¶

Created on Wed Oct 30 13:07:02 2019