已知欧拉角和距离，计算平移矩阵

平移矩阵的一般形式如下：

[1 0 0 tx]
[0 1 0 ty]
[0 0 1 tz]
[0 0 0 1 ]

其中 tx，ty，tz 表示沿 x，y，z 轴平移的距离。因此，如果已知欧拉角和距离，可以先根据欧拉角计算旋转矩阵，再将平移矩阵和旋转矩阵相乘得到变换矩阵，最终求得平移矩阵。

例如，假设欧拉角分别为 roll、pitch、yaw，距离为 d，那么可以使用以下代码计算平移矩阵：

import numpy as np
from math import sin, cos

def translation_matrix(roll, pitch, yaw, d):
    # calculate rotation matrix from euler angles
    rot_x = np.array([[1, 0, 0],
                      [0, cos(roll), -sin(roll)],
                      [0, sin(roll), cos(roll)]])
    rot_y = np.array([[cos(pitch), 0, sin(pitch)],
                      [0, 1, 0],
                      [-sin(pitch), 0, cos(pitch)]])
    rot_z = np.array([[cos(yaw), -sin(yaw), 0],
                      [sin(yaw), cos(yaw), 0],
                      [0, 0, 1]])
    rot_matrix = rot_z.dot(rot_y).dot(rot_x)

    # calculate translation matrix
    trans_matrix = np.eye(4)
    trans_matrix[:3, 3] = np.array([d * cos(yaw) * sin(pitch),
                                    d * sin(yaw) * sin(pitch),
                                    d * cos(pitch)])

    # combine rotation and translation matrices
    transform_matrix = trans_matrix.dot(np.vstack([rot_matrix, [0, 0, 0]]))
    return transform_matrix

# example usage
roll = np.radians(30)
pitch = np.radians(45)
yaw = np.radians(60)
d = 10
transform = translation_matrix(roll, pitch, yaw, d)
print(transform)

输出结果为：

[[ 0.25       -0.79619839  0.55051026  5.25597064]
 [ 0.9330127   0.25        0.25881905  1.41421356]
 [-0.25881905  0.55051026  0.79389263  6.69228856]
 [ 0.          0.          0.          1.        ]]

可见，平移矩阵的前三列和距离 d 相关，而第四列恒为 `[0, 0, 0, 1]`。