Four dimensional matrix, flip (including mirror image), rotation, world coordinates and local coordinates

Homogeneous coordinate understanding ： Homogeneous coordinates _mrdonghe The blog of -CSDN Blog _ Homogeneous coordinates

Usually matrix is used 4*4 Express

  among  

a11 a12 a13  Usually used to represent an object x Coordinate information axis

a21 a22 a23  Usually used to represent an object y Coordinate information axis

a31 a32 a33  Usually used to represent an object z Coordinate information axis

a41 a42 a43  Usually used to represent the origin coordinate position of an object

a14 a24 a34  Usually used to represent the translational part of an object

Specific principle of object rotation ：

1. Change matrix ： First, get the normal vector of the object , Then the normal vector is multiplied by the matrix coordinates of the world system of the object , Get the normal vector in the world coordinate system , And cross product with the desired normal effect in the final world coordinate system to get the desired transformation matrix .

 

The specific principle of object overturning mirror ：

Rotation matrix

Three dimensional geometric transformation space can be viewed in the article

： Three dimensional space geometric transformation matrix _ The city flocculant wind -CSDN Blog _ Three dimensional transformation matrix

The relationship between matrices , And the method of finding invertible matrix

Find invertible matrix ： How to use the elementary transformation method to find the inverse matrix ？ - You know (zhihu.com)