scipy.spatial.transform.Rotation.align_vectors测试脚本返回结果异常

我尝试将两个平面对齐中心后，用scipy.spatial.transform.Rotation.align_vectors获取旋转矩阵实现平面对齐，但测试失败。先设计了相对旋转90°的矩形简单案例，运行脚本后提示“给定向量集的最优旋转定义不明确或不佳”，返回单位四元数，结果不符合预期。后续用12个点的复杂案例（点集先沿一个方向旋转90°，再沿另一个方向旋转180°），结果仍无法正确对齐点集，旋转结果存在偏差，求问题原因及排查方向。

简单案例 #

FROM #

0.0 0.0 0.0
1.0 0.0 0.0
0.0 2.0 0.0
1.0 2.0 0.0

TO #

0.0 0.0 0.0
2.0 0.0 0.0
2.0 1.0 0.0
0.0 1.0 0.0

测试代码 #

import numpy as np
import files
from scipy.spatial.transform import Rotation

from_ = np.genfromtxt(files.FROM)
to = np.genfromtxt(files.TO)

mean_from = np.mean(from_, axis=0)
mean_to = np.mean(to, axis=0)

centered_from = from_ - mean_from
centered_to = to - mean_to

rot,res = Rotation.align_vectors(centered_from,centered_to)
print(res)
sol = rot.as_quat()
print("({}f, {}f, {}f, {}f)".format(sol[0],sol[1],sol[2],sol[3]))

运行输出 #

Optimal rotation is not uniquely or poorly defined for the given sets of vectors.
rot,res = Rotation.align_vectors(centered_from,centered_to)
2.449489742783178
(0.0f, 0.0f, 0.0f, 1.0f)

复杂案例 #

点集先沿一个方向旋转90°，再沿另一个方向旋转180°

FROM #

-1.061441 1.029105 0.3137982
-1.058325 0.6978046 0.3261206
-0.5160019 1.044142 0.5801408
-0.5128856 0.7128415 0.5924632
-0.5150666 1.089168 0.5781018
-0.5124189 0.733911 0.5916736
0.09491175 1.098186 0.6951484
0.09755945 0.7429286 0.7087202
-0.4337781 0.6063982 0.2094956
-0.3675401 0.5803195 0.08044138
-0.1081934 0.6057502 0.3767354
-0.04195532 0.5796715 0.2476811

TO #

0.6978049 -1.058325 -0.3261207
0.7128419 -0.5128859 -0.5924634
1.029105 -1.061442 -0.3137983
1.044142 -0.5160022 -0.580141
0.7339112 -0.512419 -0.5916737
0.7429286 0.09755942 -0.7087204
1.089168 -0.5150667 -0.5781019
1.098186 0.09491169 -0.6951486
0.5795034 -0.2047889 -0.1641395
0.5804876 -0.2047065 -0.1639829
0.6055822 -0.271027 -0.2931938
0.6065664 -0.2709446 -0.2930371

内容的提问来源于stack exchange，提问作者Jake_3