Transformation Matrix in 3D world

Matrix is a very important element in the 3D world.
The movement, scaling, and rotation of all objects, as well as the control of the camera, are reflected in the transformation matrix.

The transformation matrix is essentially the Conversion Relationship of a coordinate system.
In addition to generating a transformation matrix, we should pay more attention to the object meaning of the transformation matrix.

What is the physical meaning of the transformation matrix mAb from A to B in the two coordinate systems A and B.
The vectors that actually constitute the transformation matrix are the coordinate axes and the vectors and points of the origins in the coordinate system A in the coordinate system B.
This is easy to understand. Use the monoclonal antibody transform (0, 0), (, 0) (, 0) (0, 0) these special points are actually the component vectors of the transformation array.
What are these points? They are actually the correspondence between the new coordinate system and the old coordinate system vector and the origin.
This physical significance is very important. A typical application is the billbard technology.

Knowing the physical meaning, we can also directly construct the transformation matrix between two coordinate systems.

It is not explained here whether it is a row vector or a column vector. This is different in d3d and OpenGL. It is more related to the multiplication sequence between vectors and points, whether it is left multiplication or right multiplication, which determines whether the coordinate system vector corresponds to the row or column vector of the transformation matrix.

The physical meaning of the transformation matrix is directly used for collision detection and video cone cropping.Algorithm.