Great Circle - gc_aangle

[cyschneck]

gc_aangle NCL function as part of Great Circle functionality (see #131)

• ncl_entry for gc_aangle
• NCL receipt for gc_aangle

See math breakdown

def angle_between_arcs(start_gc1=None, end_gc1=None,
                       start_gc2=None, end_gc2=None):
    # get normal of planes containing great circles
    normal_one = np.cross([location_df.loc[start_gc1, "cart_x"],
                           location_df.loc[start_gc1, "cart_y"],
                           location_df.loc[start_gc1, "cart_z"]],
                          [location_df.loc[end_gc1, "cart_x"],
                           location_df.loc[end_gc1, "cart_y"],
                           location_df.loc[end_gc1,"cart_z"]])
    normal_two = np.cross([location_df.loc[start_gc2, "cart_x"],
                           location_df.loc[start_gc2, "cart_y"],
                           location_df.loc[start_gc2, "cart_z"]],
                          [location_df.loc[end_gc2, "cart_x"],
                           location_df.loc[end_gc2, "cart_y"],
                           location_df.loc[end_gc2,"cart_z"]])
    # dot product to obtain the angle between the normal planes
    angle_between_planes = np.dot(normal_one, normal_two)
    # divide by the magnitude of the vectors, inverse of cos to find angle
    angle = np.arccos(np.dot(normal_one, normal_two) / 
                    (np.linalg.norm(normal_one) * np.linalg.norm(normal_two)))
    obtuse_acute_angle = (np.rad2deg(angle), ((360-(2*np.rad2deg(angle)))/2))
    obtuse_angle = np.max(obtuse_acute_angle)
    print(f"Acute Angle  = {np.min(obtuse_acute_angle)} degrees")
    print(f"Obtuse Angle = {np.max(obtuse_acute_angle)} degrees")
    return obtuse_acute_angle