Source Code for Module geometry.manifolds.embedding_relations

  1  from . import (DifferentiableManifold, SO3, SO2, R1, R2, R3, SE2, SE3, S2, S1, 
  2      T1, T2, T3, so2, so3, se2, se3, np, Tran2, tran2, tran3, Tran3, tran1) 
  3  from .. import (S1_project_from_S2, S2_from_S1, S1_project_from_R2, 
  4      S2_project_from_R3, se2_from_so2, so2_project_from_se2, se3_from_so3, 
  5      so3_project_from_se3, SE3_from_SO3, SE2_from_SO2, SO2_project_from_SE2, 
  6      SO3_project_from_SE3, R2_project_from_SE2, SE2_from_R2, SE3_from_R3, 
  7      R3_project_from_SE3, SO2_project_from_SO3, SO3_from_SO2, 
  8      so2_project_from_so3, 
  9      so3_from_so2, SE2_project_from_SE3, se2_project_from_se3, se3_from_se2, 
 10      SE3_from_SE2, SO2_from_angle, angle_from_SO2) 
 11  from geometry.spheres import normalize_pi 
 12   
 13   
 14 -def embedding(small, big, embed_in, project_from, desc=None): 
 15      DifferentiableManifold.embedding(small, big, embed_in, project_from, 
 16                                       itype='user', desc=desc) 
 17   
 18   
 19 -def isomorphism(A, B, a_to_b, b_to_a, desc=None): 
 20      DifferentiableManifold.isomorphism(A, B, a_to_b, b_to_a, 
 21                                         itype='user', desc=desc) 
 22   
 23  embedding(R1, R2, lambda a: np.array([a[0], 0]), 
 24                lambda b: np.array([b[0]])) 
 25  embedding(R2, R3, lambda a: np.array([a[0], a[1], 0]), 
 26                lambda b: b[0:2]) 
 27   
 28  embedding(SO2, SO3, SO3_from_SO2, SO2_project_from_SO3) 
 29  embedding(so2, so3, so3_from_so2, so2_project_from_so3) 
 30   
 31  embedding(SO2, SE2, SE2_from_SO2, SO2_project_from_SE2) 
 32  embedding(SO3, SE3, SE3_from_SO3, SO3_project_from_SE3) 
 33   
 34  embedding(so3, se3, se3_from_so3, so3_project_from_se3) 
 35  embedding(so2, se2, se2_from_so2, so2_project_from_se2) 
 36   
 37  embedding(se2, se3, se3_from_se2, se2_project_from_se3) 
 38  embedding(SE2, SE3, SE3_from_SE2, SE2_project_from_SE3) 
 39   
 40  embedding(S1, S2, S2_from_S1, S1_project_from_S2) 
 41   
 42  embedding(S1, R2, lambda x: x, S1_project_from_R2) 
 43  embedding(S2, R3, lambda x: x, S2_project_from_R3) 
 44   
 45  embedding(R2, SE2, SE2_from_R2, R2_project_from_SE2) 
 46  embedding(R3, SE3, SE3_from_R3, R3_project_from_SE3) 
 47   
 48  isomorphism(T1, S1, lambda a: np.array([np.cos(float(a)), np.sin(float(a))]), 
 49                  lambda b: normalize_pi(np.array([np.arctan2(b[1], b[0])]))) 
 50  isomorphism(T1, SO2, lambda x: SO2_from_angle(x[0]), 
 51                      lambda y: np.array([angle_from_SO2(y)])) 
 52   
 53   
 54  embedding(T1, T2, lambda a: np.array([a[0], 0]), 
 55                lambda b: np.array([b[0]])) 
 56  embedding(T2, T3, lambda a: np.array([a[0], a[1], 0]), 
 57                lambda b: b[0:2]) 
 58   
 59  # TODO: more tori? 
 60  embedding(T1, R1, lambda x: x, lambda x: T1.normalize(x)) 
 61  embedding(T2, R2, lambda x: x, lambda x: T2.normalize(x)) 
 62  embedding(T3, R3, lambda x: x, lambda x: T3.normalize(x)) 
 63   
 64  embedding(tran1, tran2, lambda b: np.array([[0, 0, b[0, -1]], 
 65                                           [0, 0, 0], 
 66                                           [0, 0, 0]]), 
 67                      lambda b: np.array([[0, b[0, -1]], 
 68                                          [0, 0]])) 
 69   
 70   
 71  embedding(tran2, tran3, lambda b: np.array([[0, 0, 0, b[0, -1]], 
 72                                           [0, 0, 0, b[1, -1]], 
 73                                           [0, 0, 0, 0], 
 74                                           [0, 0, 0, 0]]), 
 75                      lambda b: np.array([[0, 0, b[0, -1]], 
 76                                           [0, 0, b[1, -1]], 
 77                                           [0, 0, 0]])) 
 78   
 79   
 80  embedding(tran2, se2, lambda x: x, 
 81                   lambda b: np.array([[0, 0, b[0, 2]], 
 82                                       [0, 0, b[1, 2]], 
 83                                       [0, 0, 0]])) 
 84   
 85  embedding(tran3, se3, lambda x: x, 
 86                      lambda b: np.array([[0, 0, 0, b[0, -1]], 
 87                                          [0, 0, 0, b[1, -1]], 
 88                                          [0, 0, 0, b[2, -1]], 
 89                                          [0, 0, 0, 0]])) 
 90   
 91   
 92  embedding(Tran2, SE2, lambda x: x, 
 93                   lambda b: np.array([[1, 0, b[0, 2]], 
 94                                       [0, 1, b[1, 2]], 
 95                                       [0, 0, 1]])) 
 96   
 97  embedding(Tran3, SE3, lambda x: x, 
 98                      lambda b: np.array([[1, 0, 0, b[0, -1]], 
 99                                          [0, 1, 0, b[1, -1]], 
100                                          [0, 0, 1, b[2, -1]], 
101                                          [0, 0, 0, 1]])) 
102