空间直角坐标系旋转点的坐标变化（一）

空间直角坐标系旋转，空间中点的坐标变化如下，坐标系xyz旋转后到坐标系x'y'z'变换矩阵如下表

	x	y	z
x'	1	1	1
y'	2	2	2
z'	3	3	3

那么

1. 空间直角坐标系绕x轴顺时针旋转θ空间坐标的变化如下

   

   	x	y	z
   x'	0°	90°	90°
   y'	90°	θ°	θ+90°
   z'	90°	90°-θ	θ°

   那么变换后

2. python实现对3d点云数据进行坐标变换

   import open3d as o3d
   import numpy as np
   import math as m
   
   def exchange_coor(pcd,theta_yz):
       '''
       绕x轴顺时针旋转theta_yz度点云坐标转换
       :param pcd: 原始点云
       :param theta_yz: 旋转的角度
       :return: 变换坐标后的点云
       '''
       point_arr =np.asarray(pcd.points)
       color_arr =np.asarray(pcd.colors)
       ex_arr = np.array([[1,0,0],[0,m.cos(theta_yz),-m.sin(theta_yz)],[0,m.sin(theta_yz),m.cos(theta_yz)]])
       print(ex_arr)
       point_new =ex_arr.dot(np.transpose(point_arr))
       pcd_new = o3d.geometry.PointCloud()
       pcd_new.points = o3d.utility.Vector3dVector(np.transpose(point_new))
       pcd_new.colors = o3d.utility.Vector3dVector(color_arr)
       return pcd_new
   
   if __name__ == '__main__':
       ply_path =r'D:\data\fabricated_building\mech_mind_plysave\1600-13.ply'
       pcd = o3d.io.read_point_cloud(ply_path)
       theta_yz = -15*np.pi/180
       pcd_new = exchange_coor(pcd,theta_yz)
       o3d.io.write_point_cloud('ex_coor.pcd', pcd_new)