# BEGIN OF LICENSE NOTE
# This file is part of Pyoints.
# Copyright (c) 2018, Sebastian Lamprecht, Trier University,
# lamprecht@uni-trier.de
#
# Pyoints is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Pyoints is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Pyoints. If not, see <https://www.gnu.org/licenses/>.
# END OF LICENSE NOTE
"""Handling of polar coordinates.
"""
import numpy as np
from .import (
distance,
assertion,
)
from .misc import print_rounded
[docs]def coords_to_polar(coords):
"""Converts Cartesian coordinates to polar coordinates.
Parameters
----------
coords : array_like(Number, shape=(n, k))
Represents `n` data points of `k` dimensions in a Cartesian coordinate
system.
Returns
-------
pcoords : array_like(Number, shape=(n, k))
Represents `n` data points of `k` dimensions in a polar coordinate
system. First column represents the distance to the origin of the
coordinate system. All other columns represent the corresponding
axes angles.
See Also
--------
polar_to_coords
Examples
--------
2D coordinates.
>>> coords = [(0, 0), (0, 1), (1, 0), (1, 1), (-1, 1), (2, -5)]
>>> pcoords = coords_to_polar(coords)
>>> print_rounded(pcoords, 3)
[[ 0. 0. ]
[ 1. 1.571]
[ 1. 0. ]
[ 1.414 0.785]
[ 1.414 2.356]
[ 5.385 -1.19 ]]
3D coordinates.
>>> coords = [(0, 0, 0), (1, 1, 0), (-1, -1, -1), (2, -5, 9)]
>>> pcoords = coords_to_polar(coords)
>>> print_rounded(pcoords, 3)
[[ 0. 0. 0. ]
[ 1.414 0.785 1.571]
[ 1.732 -2.356 2.186]
[ 10.488 -1.19 0.539]]
"""
coords = assertion.ensure_coords(coords)
dim = coords.shape[1]
d = distance.norm(coords)
if dim == 2:
x = coords[:, 0]
y = coords[:, 1]
a = np.arctan2(y, x)
return assertion.ensure_polar([d, a], by_col=True)
elif dim == 3:
x = coords[:, 0]
y = coords[:, 1]
z = coords[:, 2]
# avoid nan
omega = np.zeros(len(d))
mask = d > 0
omega[mask] = np.arccos(z[mask] / d[mask])
phi = np.arctan2(y, x)
return assertion.ensure_polar([d, phi, omega], by_col=True)
else:
raise ValueError('%i dimensions are not supported yet.' % dim)
[docs]def polar_to_coords(pcoords):
"""Converts polar coordinates to Cartesian coordinates.
Parameters
----------
pcoords : array_like(Number, shape=(n, k))
Represents `n` data points of `k` dimensions in a polar coordinate
system. First column represents the distance to the origin of the
coordinate system. All other columns represent the corresponding
axes angles.
Returns
-------
coords : array_like(Number, shape=(n, k))
Represents `n` data points of `k` dimensions in a Cartesian coordinate
system.
See Also
--------
coords_to_polar
Examples
--------
2D coordinates.
>>> pcoords = [(0, 0), (3, 0), (3, np.pi), (4, -0.5*np.pi), (1, 0.5)]
>>> coords = polar_to_coords(pcoords)
>>> print_rounded(coords, 3)
[[ 0. 0. ]
[ 3. 0. ]
[-3. 0. ]
[ 0. -4. ]
[ 0.878 0.479]]
3D coordinates.
>>> pcoords = [(0, 0, 0), (2, 0, 0),(4, 0, np.pi), (4, 0.5*np.pi, 0.5)]
>>> coords = polar_to_coords(pcoords)
>>> print_rounded(coords, 3)
[[ 0. 0. 0. ]
[ 0. 0. 2. ]
[ 0. 0. -4. ]
[ 0. 1.918 3.51 ]]
"""
pcoords = assertion.ensure_polar(pcoords)
dim = pcoords.shape[1]
d = pcoords[:, 0]
if dim == 2:
a = pcoords[:, 1]
x = d * np.cos(a)
y = d * np.sin(a)
return assertion.ensure_coords([x, y], by_col=True)
elif dim == 3:
phi = pcoords[:, 1]
omega = pcoords[:, 2]
x = d * np.sin(omega) * np.cos(phi)
y = d * np.sin(omega) * np.sin(phi)
z = d * np.cos(omega)
return assertion.ensure_coords([x, y, z], by_col=True)
else:
raise ValueError('%i dimensions are not supported yet' % dim)
