The plot of the final rotated sphere, which was an upright sphere, rotated 45 degrees down, and 45 degrees to the left (the viewer's left).

1. 1
Final rotated sphere (45 degrees down, and 45 degrees to the left), and the closer
steps leading up to it.
xz view of rotated 45 degrees down sphere. With a view of the whole sphere, the upper (up 45
degrees) and lower (down 45 degrees) haloes.
Sharon Liu.
2023/10/17.

2. 2

3. 3

4. 4
Final rotated sphere.
l_horizontal_from_y_axis: sqrt(d_x_45_down^2+d_z_45_down^2).
theta_horizontal_with_y_axis_in_radians: atan(d_x_rotated_45_down/d_z_rotated_45_down).
Expressed theta in degrees, and cleaned this value, according to the xz plots.
theta_4_in_degrees: theta_horizontal_with_y_axis_in_degrees + 45.
Cleaned theta_4, to keep values between 0 and 360 degrees.
d_x_final_sphere: -sin(theta_4_in_degrees)*l_horizontal_from_y_axis.
d_y_final_sphere: same as d_y_rotated_45_degrees_down.
d_z_final_sphere: -cos(theta_4_in_degrees)*l_horizontal_from_y_axis.