import numpy as np
[docs]def update_spherical(eptm):
"""Computes the spherical coordinates (rho, theta, phi)
of an epithelium.
rho is the distance to the coordinate system's origin, theta
is the co-latitude (0 ≤ θ < π) and phi is the longitude (0 ≤ ϕ < 2π).
"""
for element in ["vert", "face", "cell"]:
if eptm.datasets.get(element) is None:
continue
eptm.datasets[element]["rho"] = np.linalg.norm(
eptm.datasets[element][["x", "y", "z"]], axis=1
)
eptm.datasets[element]["theta"] = np.arccos(
eptm.datasets[element].eval("z / rho")
)
eptm.datasets[element]["phi"] = np.arctan2(
eptm.datasets[element].eval("y / (rho * sin(theta))"),
eptm.datasets[element].eval("x / (rho * sin(theta))"),
)
[docs]def rotation_matrix(angle, direction):
# Copyright (c) 2006-2015, Christoph Gohlke
# Copyright (c) 2006-2015, The Regents of the University of California
# Produced at the Laboratory for Fluorescence Dynamics
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# * Neither the name of the copyright holders nor the names of any
# contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
# IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
# OF THE POSSIBILITY OF SUCH DAMAGE.
"""
Returns the 3X3 rotation matrix around `direction` by `angle`
adapted from http://www.lfd.uci.edu/~gohlke/code/transformations.py.html
"""
sina = np.sin(angle)
cosa = np.cos(angle)
direction = direction / np.linalg.norm(direction)
# rotation matrix around unit vector
R = np.diag([cosa, cosa, cosa])
R += np.outer(direction, direction) * (1.0 - cosa)
direction *= sina
R += np.array(
[
[0.0, -direction[2], direction[1]],
[direction[2], 0.0, -direction[0]],
[-direction[1], direction[0], 0.0],
]
)
return R
[docs]def rotation_matrices(angle, direction):
"""Return an (N, 3, 3) array of rotation matrices
along N angles and N directions
Parameters
----------
angle : np.ndarray of shape (N,)
array of rotation angles
directions : np.ndarray of shape (N, 3)
array of rotation vectors
Returns
-------
rots : np.ndarray of shape (N, 3, 3)
the array of rotation matrices
"""
sint, cost = np.sin(angle), np.cos(angle)
rots = np.zeros((cost.size, 3, 3))
for i in range(3):
rots[:, i, i] = cost
rots += np.einsum("ij, ik -> ijk", direction, direction) * (1 - cost[:, None, None])
direction *= sint[:, None]
rots[:, 0, 1] -= direction[:, 2]
rots[:, 0, 2] += direction[:, 1]
rots[:, 1, 0] += direction[:, 2]
rots[:, 1, 2] -= direction[:, 0]
rots[:, 2, 0] -= direction[:, 1]
rots[:, 2, 1] += direction[:, 0]
return rots
