def field_cartesian(self, x, y, z):
potential_sign = -1 if self.attractive else 1
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = -potential_sign * self.a / r_grid**2
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
potential_sign = -1 if self.attractive else 1
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = -potential_sign * self.a / r_grid**2
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def potential_on_grid(self, r_grid, theta_grid, phi_grid):
if self.external_field[0] == 0:
return np.zeros_like(r_grid)
F_r = np.ones_like(r_grid) * self.external_field[0]
F_theta = np.ones_like(r_grid) * self.external_field[1]
F_phi = np.ones_like(r_grid) * self.external_field[2]
x, y, z = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
angles_grid = Vectors3D.angle_between_vectors((x, y, z), (F_x, F_y, F_z))
return F_r * r_grid * np.cos(angles_grid)
def potential_on_grid(self, r_grid, theta_grid, phi_grid):
if self.external_field[0] == 0:
return np.zeros_like(r_grid)
F_r = np.ones_like(r_grid) * self.external_field[0]
F_theta = np.ones_like(r_grid) * self.external_field[1]
F_phi = np.ones_like(r_grid) * self.external_field[2]
x, y, z = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
angles_grid = Vectors3D.angle_between_vectors((x, y, z), (F_x, F_y, F_z))
return F_r * r_grid * np.cos(angles_grid)
def field(self, r, theta, phi):
r_grid, theta_grid, phi_grid = np.meshgrid(r, theta, phi)
x_grid, y_grid, z_grid = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
super_x = np.zeros_like(x_grid)
super_y = np.zeros_like(y_grid)
super_z = np.zeros_like(z_grid)
for potential in self.potentials:
F_r, F_theta, F_phi = potential.field(r, theta, phi)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
super_x += F_x
super_y += F_y
super_z += F_z
super_r, super_theta, super_phi = Vectors3D.cartesian_to_spherical(super_x, super_y, super_z)
return super_r, super_theta, super_phi
def field(self, r, theta, phi):
r_grid, theta_grid, phi_grid = np.meshgrid(r, theta, phi)
x_grid, y_grid, z_grid = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
super_x = np.zeros_like(x_grid)
super_y = np.zeros_like(y_grid)
super_z = np.zeros_like(z_grid)
for potential in self.potentials:
F_r, F_theta, F_phi = potential.field(r, theta, phi)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
super_x += F_x
super_y += F_y
super_z += F_z
super_r, super_theta, super_phi = Vectors3D.cartesian_to_spherical(super_x, super_y, super_z)
return super_r, super_theta, super_phi
def plot_potential_cartesian(self, fig=None, x=None, y=None, z=None):
if not self.USE_MAYAVI:
return None
if fig is None:
fig = mlab.figure('Potential')#, bgcolor=(0, 0, 0))
#fig = mlab.figure('Potential', bgcolor=(0, 0, 0))
else:
mlab.figure(fig, bgcolor=fig.scene.background)
if x is None:
x = np.linspace(1e-9, 5e-8, num=100, endpoint=True)
if y is None:
y = np.linspace(1e-9, 5e-8, num=100, endpoint=True)
if z is None:
z = np.linspace(1e-9, 5e-8, num=100, endpoint=True)
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
volumetric_data = self.potential_on_grid(r_grid, theta_grid, phi_grid)
#volumetric_data = 1 / (x_grid**2 + y_grid**2 + z_grid**2)
#mlab.contour3d(x_grid, y_grid, z_grid, volumetric_data, colormap='jet')
#mlab.contour3d(volumetric_data, colormap='jet')
source = mlab.pipeline.scalar_field(volumetric_data)
min = volumetric_data.min()
max = volumetric_data.max()
vol = mlab.pipeline.volume(source)
#vol = mlab.pipeline.volume(source, vmin=min + 0.65 * (max - min),
# vmax=min + 0.9 * (max - min))
mlab.outline()
return fig
def plot_potential_cartesian(self, fig=None, x=None, y=None, z=None):
if not self.USE_MAYAVI:
return None
if fig is None:
fig = mlab.figure('Potential')#, bgcolor=(0, 0, 0))
#fig = mlab.figure('Potential', bgcolor=(0, 0, 0))
else:
mlab.figure(fig, bgcolor=fig.scene.background)
if x is None:
x = np.linspace(1e-9, 5e-8, num=100, endpoint=True)
if y is None:
y = np.linspace(1e-9, 5e-8, num=100, endpoint=True)
if z is None:
z = np.linspace(1e-9, 5e-8, num=100, endpoint=True)
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
volumetric_data = self.potential_on_grid(r_grid, theta_grid, phi_grid)
#volumetric_data = 1 / (x_grid**2 + y_grid**2 + z_grid**2)
#mlab.contour3d(x_grid, y_grid, z_grid, volumetric_data, colormap='jet')
#mlab.contour3d(volumetric_data, colormap='jet')
source = mlab.pipeline.scalar_field(volumetric_data)
min = volumetric_data.min()
max = volumetric_data.max()
vol = mlab.pipeline.volume(source)
#vol = mlab.pipeline.volume(source, vmin=min + 0.65 * (max - min),
# vmax=min + 0.9 * (max - min))
mlab.outline()
return fig
def field_cartesian(self, x, y, z):
grid = np.ones((np.array(x).size, np.array(y).size, np.array(z).size), dtype=np.float)
ex, ey, ez = Vectors3D.spherical_to_cartesian(self.external_field[0],
self.external_field[1],
self.external_field[2])
F_x = grid * ex
F_y = grid * ey
F_z = grid * ez
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
grid = np.ones((np.array(x).size, np.array(y).size, np.array(z).size), dtype=np.float)
ex, ey, ez = Vectors3D.spherical_to_cartesian(self.external_field[0],
self.external_field[1],
self.external_field[2])
F_x = grid * ex
F_y = grid * ey
F_z = grid * ez
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = self.a / r_grid
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def equation(r):
field = self.field(r, theta, 0)
field_x, field_y, field_z = Vectors3D.spherical_to_cartesian(field[0][0][0], field[1][0][0], field[2][0][0])
r_x, r_y, r_z = Vectors3D.spherical_to_cartesian(r, theta, 0)
F_r = field_x * r_x + field_y * r_y + field_z * r_z
return F_r
def field_cartesian(self, x, y, z):
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = self.a / r_grid
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def equation(r):
field = self.field(r, theta, 0)
field_x, field_y, field_z = Vectors3D.spherical_to_cartesian(field[0][0][0], field[1][0][0], field[2][0][0])
r_x, r_y, r_z = Vectors3D.spherical_to_cartesian(r, theta, 0)
F_r = field_x * r_x + field_y * r_y + field_z * r_z
return F_r
