Explanation of coordinate conversion examples

Topic content

The camera is known to be 0 The posture of the moment $T_0=(R_0,t_0)$, And the position and posture of the current moment $T=(R,t)$, Seek in order to 0 The camera coordinate system at the time is used as the reference system , The pose expression at the current time T ′.

solve

1. The concept of posture

** translation ：** A point at the origin in the world coordinate system p ( sit mark by 0 ) towards x The axis moves in the positive direction t Distance of , Then its coordinates in the world coordinate system become t, The coordinates in the current coordinate system are 0, The pose translation part of the coordinate system is t .
rotate ：

2. Topic calculation

3. summary

$R_0(R^{\prime }x+t\prime )+t_0=Rx+t$

• $x：$ Represents the coordinates of the current time coordinate system
• $R^{\prime }、t\prime ：$ The current time coordinate system is relative to 0 Pose transformation of time coordinate system
• $R^{\prime }x+t\prime ：$ Indicates that the coordinates of the current time coordinate system are converted to 0 Coordinates of time coordinate system
• $R_0、t_0：$ 0 Position and pose transformation of the time coordinate system relative to the world coordinate system
• $R_0(R^{\prime }x+t\prime )+t_0：$ 0 Time coordinate system coordinates are converted to world coordinate system coordinates
• $R、t$ The pose change of the current time coordinate relative to the world coordinate system
• $Rx+t：$ The coordinates of the current time coordinate system are converted to the coordinates of the world coordinate system