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coordinates.py
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181 lines (151 loc) · 5.38 KB
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from __future__ import division
import numpy as np
from numpy import pi
from copy import copy
from scipy.spatial import ConvexHull
def cartesian_to_spherical(x, y, z, degrees=False):
"""
Converts Cartesian coordinates to spherical coordinates
cart = (x, y, z)
sph = (r, theta, phi) [Rad]
>>> cartesian_to_spherical(1.0, 0.0, 0.0)
(1.0, 1.5707963267948966, 0.0)
>>> cartesian_to_spherical(0.0, 1.0, 0.0)
(1.0, 1.5707963267948966, 1.5707963267948966)
>>> cartesian_to_spherical(0.0, 0.0, 1.0)
(1.0, 0.0, 0.0)
"""
xsq, ysq, zsq = x*x, y*y, z*z
r = (xsq + ysq + zsq)**0.5
t = np.arctan2((xsq + ysq)**0.5, z)
p = np.arctan2(y, x)
if degrees:
t, p = np.degrees(t), np.degrees(p)
return r, t, p
def spherical_to_cartesian(r, t, p, degrees=False):
if degrees:
t, p = np.radians(t), np.radians(p)
x = r * np.sin(t) * np.cos(p)
y = r * np.sin(t) * np.sin(p)
z = r * np.cos(t)
return x, y, z
class Coordinates:
"""
This class manages a list of coordinates.
"""
def cart2sph(self):
r, t, p = cartesian_to_spherical(self.x, self.y, self.z)
# use our conventions, phi from 0 to 2*pi
p = np.mod(p, 2*np.pi)
return r, t, p
def sph2cart(self, r, t, p):
x, y, z = spherical_to_cartesian(np.ravel(r), np.ravel(t), np.ravel(p))
self.cart = np.vstack((x, y, z)).T
def __init__(self, cart=np.ndarray((0,3))):
self._cart = np.array(cart)
self.simplices = None
def _get_cart(self):
return self._cart
def _set_cart(self, value):
# reshape if the input is a 1d numpy array
self._cart = value.reshape(-1,3)
cart = property(_get_cart, _set_cart)
def _get_x(self):
return self.cart[:, 0]
def _set_x(self, value):
self.cart[:, 0] = value
x = property(_get_x, _set_x)
def _get_y(self):
return self.cart[:,1]
def _set_y(self, value):
self.cart[:, 1] = value
y = property(_get_y, _set_y)
def _get_z(self):
return self.cart[:, 2]
def _set_z(self, value):
self.cart[:, 2] = value
z = property(_get_z, _set_z)
def _get_r(self):
r, t, p = self.cart2sph()
return r
def _set_r(self, value):
r, t, p = self.cart2sph()
r = np.array(value).ravel()
self.sph2cart(r, t, p)
r = property(_get_r, _set_r)
def _get_theta(self):
r, t, p = self.cart2sph()
return t
def _set_theta(self, value):
r, t, p = self.cart2sph()
t = np.array(value).ravel()
self.sph2cart(r, t, p)
theta = property(_get_theta, _set_theta)
def _get_theta_deg(self):
return self.theta * 180 / np.pi
def _set_theta_deg(self, value):
self.theta = value * np.pi / 180
theta_deg = property(_get_theta_deg, _set_theta_deg)
def _get_phi(self):
r, t, p = self.cart2sph()
return p
def _set_phi(self, value):
r, t, p = self.cart2sph()
p = np.array(value).ravel()
self.sph2cart(r, t, p)
phi = property(_get_phi, _set_phi)
def _get_phi_deg(self):
return self.phi * 180 / np.pi
def _set_phi_deg(self, value):
self.phi = value * np.pi / 180
phi_deg = property(_get_phi_deg, _set_phi_deg)
def _get_sph(self):
r, t, p = self.cart2sph()
return np.vstack((r, t, p)).T
def _set_sph(self, value):
# reshape if the input is a 1d numpy array
value = value.reshape(-1,3)
if value.shape[0] != self.cart.shape[0]:
# size does not match, initialize with zeros
self.cart = np.zeros_like(value)
try:
r = value[:, 0]
t = value[:, 1]
p = value[:, 2]
self.sph2cart(r, t, p)
except IndexError:
# still no data here, do nothing
print('do nothing, no data here')
sph = property(_get_sph, _set_sph)
def _get_nPoints(self):
return self.cart.shape[0]
def _set_nPoints(self, value):
self.cart = np.zeros((value,3))
nPoints = property(_get_nPoints, _set_nPoints)
def update_simplices(self):
#simplices = np.ndarray((0,3))
THETA_LIMIT = 10 / 180. * np.pi # in rad
DEVIATION_PERCENT = np.cos(THETA_LIMIT)
if self.cart.shape[1] == 3 and self.cart.size > 0:
# link: http://www.qhull.org/html/qh-optq.htm#QbB
simplices = ConvexHull(points=self.cart, qhull_options='QbB').simplices
grid = self.pull_on_unit_sphere()
max_z = np.max(grid.z)
min_z = np.min(grid.z)
# open only gaps which are large
if max_z > DEVIATION_PERCENT: max_z = 1.
if min_z < -DEVIATION_PERCENT: min_z = -1.
is_z_max = np.isclose(grid.z[simplices], max_z)
is_z_min = np.isclose(grid.z[simplices], min_z)
#is_z_min = self.z[simplices] == np.min(self.z)
is_valid_min = np.sum(is_z_min, axis=1) < 3
is_valid_max = np.sum(is_z_max, axis=1) < 3
is_valid = np.logical_and(is_valid_min, is_valid_max)
self.simplices = simplices[is_valid,:]
def pull_on_unit_sphere(self):
grid = copy(self)
grid.cart = grid.cart / self.r[:, None] # pull on unit sphere
return grid
if __name__=='__main__':
import doctest
doctest.testmod()