def test_to_spherical_single_point(self): xyz = [1, 0, 0] np.testing.assert_allclose(cartesian_to_spherical(xyz), [1, np.pi / 2, 0], atol=np.finfo(float).eps) xyz = [0, 1, 0] np.testing.assert_allclose(cartesian_to_spherical(xyz), [1, np.pi / 2, np.pi / 2], atol=np.finfo(float).eps) xyz = [0, 0, 0] np.testing.assert_allclose(cartesian_to_spherical(xyz), [0, 0, 0], atol=np.finfo(float).eps)
def arc_between_two_points(coordinate_system, point1, point2, radius=1, right=True): global_point1 = coordinate_system.to_parent(point1) global_point2 = coordinate_system.to_parent(point2) direction = point2 - point1 distance = np.sqrt(np.dot(direction, direction)) arc_coordinate_system = Cartesian(basis=np.copy(coordinate_system.basis), origin=np.copy(global_point1), name='Arc coordinate_system') r_theta_phi = transforms.cartesian_to_spherical(direction) arc_coordinate_system.rotate_axis_angle([0, 0, 1], r_theta_phi[2]) arc_coordinate_system.rotate_axis_angle([0, 1, 0], r_theta_phi[1] + np.pi/2) x_offset = -distance / 2 y_offset = np.sqrt(radius**2 - x_offset**2) if right: y_offset *= -1 arc_coordinate_system.origin = arc_coordinate_system.to_parent([x_offset, y_offset, 0]) local_point1 = arc_coordinate_system.to_local(global_point1) local_point2 = arc_coordinate_system.to_local(global_point2) start = transforms.cartesian_to_spherical(local_point1)[2] stop = transforms.cartesian_to_spherical(local_point2)[2] if not right: start = 2 * np.pi - start stop = 2 * np.pi - stop path = Arc(coordinate_system=arc_coordinate_system, a=radius, b=radius, start=start, stop=stop, right=right) return path
def test_to_cylindrical_and_back_many_points(self): points_num = 100 xyz = ((np.random.random(points_num * 3) - 0.5) * 200).reshape((points_num, 3)) rpz = cartesian_to_cylindrical(xyz) np.testing.assert_allclose(cylindrical_to_cartesian(rpz), xyz) rtp = cylindrical_to_spherical(rpz) np.testing.assert_allclose(cartesian_to_spherical(xyz), rtp) np.testing.assert_allclose(spherical_to_cylindrical(rtp), rpz) np.testing.assert_allclose(spherical_to_cartesian(rtp), xyz)
def helix_between_two_points(coordinate_system, point1, point2, radius=1, loops=1, right=True): direction = point2 - point1 distance = np.sqrt(np.dot(direction, direction)) origin = coordinate_system.to_parent(point1) helix_coordinate_system = Cartesian(basis=np.copy(coordinate_system.basis), origin=np.copy(origin), name='Helix coordinate system') r_theta_phi = transforms.cartesian_to_spherical(direction) helix_coordinate_system.rotate_axis_angle([0, 0, 1], r_theta_phi[2]) helix_coordinate_system.rotate_axis_angle([0, 1, 0], r_theta_phi[1]) pitch = distance / int(loops) name = 'Right Helix' if right else 'Left Helix' path = Helix(name=name, coordinate_system=helix_coordinate_system, radius=radius, pitch=pitch, start=0, stop=np.pi * 2 * int(loops), right=right) return path
def vector_field(self, xyz): rtp = gt.cartesian_to_spherical(xyz) rtp[np.where(rtp[:, 0] < self.r), 0] = self.r r = rtp[:, 0] ** 2 r = np.array([r, r, r]).T return self.q * xyz / r
def scalar_field(self, xyz): rtp = gt.cartesian_to_spherical(xyz) rtp[np.where(rtp[:, 0] < self.r), 0] = self.r return self.q / rtp[:, 0]