在 Python 中连接矩阵和向量

Question

我是 MATLAB 用户，并尝试将旋转/平移代码转换为 Python：

from functools import reduce
import numpy as np
import matplotlib as plt
from math import pi as PI 
from math import sin as sin 
from math import cos as cos 

# plt.close('all')

#   coordinate in old system
x0 = np.array([ [10], 
                [5], 
                [0],])

x = x0


# translation
# origin of old coordinate system in relative to the new coordinate system 
T = np.array([  [10],
                [0],
                [0]])


## rotation
# rotate alpha, beta, and gamme about x-axis, y-axis, and z- axis,
# respectively, in relative to the new coordinate system

alpha = 0
beta  = 0
gamma = PI/2

# rotation matrices
Rx = np.array([ [1,           0,              0],
                [0,   cos(alpha),   -sin(alpha)], 
                [0,   sin(alpha),    cos(alpha)] ])

Ry = np.array([ [cos(beta),     0,       sin(beta)], 
                [0,             1,               0],
                [-sin(beta),    0,       cos(beta)]])

Rz = np.array([ [cos(gamma),   -sin(gamma),   0],
                [sin(gamma),    cos(gamma),   0], 
                [0,                      0,   1] ])

# R = Rz*Ry*Rx
R = reduce(np.dot, [Rz, Ry, Rx])

RT = np.array([ [R,       T],
                [0, 0, 0, 1]])

最后一行尝试通过堆叠 3X3 旋转矩阵

RT

和 3X1 平移向量

R

来创建齐次 4X4 矩阵

T

。矩阵底部的[0,0,0,1]只是将变换矩阵

RT

变成齐次格式。

代码将

R

、

T

和

[0,0,0,1]

堆叠在一起时存在问题。我想了解什么是正确的方法？谢谢！！

Answer 1

尝试

intermediate = np.concatenate((R, T.T), axis=1)
RT = np.concatenate((intermediate, np.array([0, 0, 0, 1])), axis=0)