Many people have written articles to describe the rotation of the point in the coordinate system. As long as Baidu searches for "rotation matrix", there will be a lot of them. However, some netizens have seen the term "transformation matrix" and may be a little confused. Here, I will use "human words" to explain what is "rotation matrix" and "transformation matrix".
There is a point p in space.
Define a coordinate system xyz, then the vector corresponding to the point p in the coordinate system xyz is v .
In the coordinate system xyz, the point p rotates an angle around a certain axis of rotation to reach another position, which corresponds to The vector of is represented by v' . Then:
v' = M * v
M is called the rotation matrix. It
can be considered that the rotation matrix is the matrix used to calculate the point rotation.
The point p in space does not move. The
coordinate system xyz rotates a certain angle around a certain axis of rotation to reach another position, the new coordinate system is set to XYZ, and the vector of the point p in the new coordinate system XYZ is set to V. Then:
V = R * v
R is the transformation matrix. It
can be considered that the transformation matrix is used to calculate the rotation of the coordinate system.
The difference and connection between "rotation matrix" and "transformation matrix".
Similarities: Both matrices are used to calculate the coordinates of
points . Differences: rotation matrix, which emphasizes "the coordinate system does not move, the point moves" and the point rotates Well, the coordinates must change, so it is called the rotation matrix. The "transformation matrix" emphasizes "the coordinate system moves, the point does not move". The point does not move, but the coordinates still change (because the coordinate system moves), so it is called " Transformation matrix".