def to_radius(r, v, c):
x,y,z = v
x0,y0,z0 = c
v = x-x0, y-y0, z-z0
rho, phi, theta = to_spherical(v, "radians")
x,y,z = from_spherical(r, phi, theta, "radians")
return x+x0, y+y0, z+z0
def evaluate(self, u, v):
rho = self.radius
phi = u
theta = v
x, y, z = from_spherical(rho, phi, theta, mode="radians")
point = np.array([x, y, z]) + self.center
return point
def evaluate(self, x, y, z):
v1 = self.sfield1.evaluate(x, y, z)
v2 = self.sfield2.evaluate(x, y, z)
v3 = self.sfield3.evaluate(x, y, z)
if self.coords == 'XYZ':
return np.array((v1, v2, v3))
elif self.coords == 'CYL':
return np.array(from_cylindrical(v1, v2, v3, mode='radians'))
else: # SPH:
return np.array(from_spherical(v1, v2, v3, mode='radians'))
def evaluate_grid(self, xs, ys, zs):
v1s = self.sfield1.evaluate_grid(xs, ys, zs)
v2s = self.sfield2.evaluate_grid(xs, ys, zs)
v3s = self.sfield3.evaluate_grid(xs, ys, zs)
if self.coords == 'XYZ':
return v1s, v2s, v3s
elif self.coords == 'CYL':
vectors = np.stack((v1s, v2s, v3s)).T
vectors = np.apply_along_axis(lambda v: np.array(from_cylindrical(*tuple(v), mode='radians')), 1, vectors).T
return vectors[0], vectors[1], vectors[2]
else: # SPH:
vectors = np.stack((v1s, v2s, v3s)).T
vectors = np.apply_along_axis(lambda v: np.array(from_spherical(*tuple(v), mode='radians')), 1, vectors).T
return vectors[0], vectors[1], vectors[2]
def out_coordinates(rho, phi, theta):
return from_spherical(rho, phi, theta, mode='radians')
def normal(self, u, v):
rho = self.radius
phi = u / (rho * np.cos(self.theta1))
theta = v / rho + self.theta1
x, y, z = from_spherical(rho, phi, theta, mode="radians")
return np.array([x, y, z])
def evaluate(self, u, v):
rho = self.radius
phi = u / (rho * cos(self.theta1))
theta = v / rho + self.theta1
x, y, z = from_spherical(rho, phi, theta, mode="radians")
return np.array([x, y, z]) + self.center
def normal(self, u, v):
rho = self.radius
phi = u
theta = v
x, y, z = from_spherical(rho, phi, theta, mode="radians")
return np.array([x, y, z])
def normal(self, u, v):
rho = self.radius
phi = u * sqrt(2) / rho
theta = 2 * atan(v / (rho * (1 + sqrt(2) / 2))) + pi / 2
x, y, z = from_spherical(rho, phi, theta, mode="radians")
return np.array([x, y, z])
def evaluate(self, u, v):
rho = self.radius
phi = u
theta = np.arcsin(v)
x, y, z = from_spherical(rho, phi, theta, mode="radians")
return np.array([x, y, z]) + self.center
def spherical(rho, phi, theta, mode):
return from_spherical(rho, phi, theta, mode)