python 欧拉角，旋转矩阵，四元数之间转换

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import numpy as np
import math
from scipy.spatial.transform import Rotation as R


Rq=[-0.71934025092983234, 1.876085535681999e-06, 3.274841213980097e-08, 0.69465790385533299]

# 四元数到旋转矩阵
r = R.from_quat(Rq)
Rm = r.as_matrix()
# 0:array([ 1.00000000e+00, -2.74458557e-06,  2.55936079e-06])
# 1:array([-2.65358979e-06, -3.49007932e-02,  9.99390782e-01])
# 2:array([-2.65358979e-06, -9.99390782e-01, -3.49007932e-02])

# 符号相反的四元数, 仍表示同一个旋转
Rq1= [0.71934025092983234, -1.876085535681999e-06, -3.274841213980097e-08, -0.69465790385533299]
# 四元数到旋转矩阵
r1 = R.from_quat(Rq1)
Rm1 = r1.as_matrix()
# 0:array([ 1.00000000e+00, -2.74458557e-06,  2.55936079e-06])
# 1:array([-2.65358979e-06, -3.49007932e-02,  9.99390782e-01])
# 2:array([-2.65358979e-06, -9.99390782e-01, -3.49007932e-02])

# 四元数到欧拉角
euler0 = r.as_euler('xyz', degrees=True)
# ([-9.20000743e+01,  1.52039496e-04, -1.52039496e-04])
euler3 = r.as_euler('xzy', degrees=True)
#([-9.20000743e+01, -1.52039496e-04,  1.52039496e-04])
euler1 = r.as_euler('zxy', degrees=True)
#([-179.99564367,  -87.99992566,  179.99579836])
euler2 = r.as_euler('zyx', degrees=True)
#([ 1.57253169e-04,  1.46640571e-04, -9.20000743e+01])

euler4 = r.as_euler('yxz', degrees=True)
#([179.99564367, -87.99992566, 179.99549428])

euler5 = r.as_euler('yzx', degrees=True)
#([ 1.46640571e-04,  1.57253169e-04, -9.20000743e+01])


# 旋转矩阵到四元数
r3 = R.from_matrix(Rm)
qua = r3.as_quat()
#[0.7193402509298323, -1.8760855356819988e-06, -3.2748412139801076e-08, -0.694657903855333] #与原始相反,但等价

# 旋转矩阵到欧拉角
euler_1 = r3.as_euler('zxy', degrees=True)
#([-179.99564367,  -87.99992566,  179.99579836])

# 欧拉角到旋转矩阵
r4 = R.from_euler('zxy', [-179.99564367,  -87.99992566,  179.99579836], degrees=True)
rm = r4.as_matrix()
# 0:array([ 1.00000000e+00, -2.74452529e-06,  2.55936075e-06])
# 1:array([-2.65358765e-06, -3.49007933e-02,  9.99390782e-01])
# 2:array([-2.65352955e-06, -9.99390782e-01, -3.49007933e-02])

# 欧拉角到四元数
qua1 = r4.as_quat()
#([-7.19340251e-01,  1.87606384e-06,  3.27274889e-08,  6.94657904e-01])


#----测试--------------------------------------------------------------------
theta=[-116,    0. , -105]
r6 = R.from_euler('xyz', theta, degrees=True)
rm = r6.as_matrix()
# 0:array([-0.25881905, -0.42343401,  0.86816838])
# 1:array([-0.96592583,  0.1134588 , -0.23262502])
# 2:array([ 0.        , -0.89879405, -0.43837115])

qua3 = r6.as_quat()
#array([-0.52720286,  0.68706415, -0.39667667,  0.30438071])

print(qua3)

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