Source Code for Module geometry.rotations_embedding

 1  from . import (map_hat_2d, contract, np, angle_from_rot2d, 
 2      rotation_from_axis_angle, hat_map, rot2d) 
 3   
 4   
 5  @contract(returns='SO3', a='SO2') 
 6 -def SO3_from_SO2(a): 
 7      theta = angle_from_rot2d(a) 
 8      return rotation_from_axis_angle(np.array([0, 0, 1]), theta) 
 9   
10   
11  @contract(returns='SO2', b='SO3') 
12 -def SO2_project_from_SO3(b): 
13      direction = np.array([1, 0, 0]) 
14      vector = np.dot(b, direction) 
15      n = np.linalg.norm(vector) 
16      atol = 1e-8 # XXX: make common 
17      if n < atol: 
18          return rot2d(0) 
19      else: 
20          theta = np.arctan2(vector[1], vector[0]) 
21          return rot2d(theta) 
22   
23   
24  @contract(returns='so3', a='so2') 
25 -def so3_from_so2(a): 
26      omega = map_hat_2d(a) 
27      return hat_map(np.array([0, 0, omega])) 
28   
29   
30  @contract(returns='so2', b='so3') 
31 -def so2_project_from_so3(b): 
32      return b[0:2, 0:2] 
33