Understanding Transformation Matrix

1. Every matrix m is associated with a coordinate system. This Coordinate System has origin (T_{0, T1, t2) and vectors (00, A110,20), (01,11,21), and (02,12,22) as axes. matrix M maps the standard coordinate system to the coordinate system with the origin (0, 0, 0) and axes (1, 0, 0), (0, 1, 0 ), and (0, 0, 1 ).
Directly paste an explanation of acgematrix3d:}

 

Class acgematrix3d represents an affine transformation of 3D space, including translation. Each matrix m has the form:

a00 a01 a02 t0
 a10 a11 a12 t1
 a20 a21 a22 t2

Where the matrix:

a00 a01 a02
 a10 a11 a12
a20 a21 a22

Is called the linear part of M.

Column T:

t0
 t1
 t2

Is called a translational part of M.

To get acgepoint3dpnt transformed by corresponding transformation one has to take the product m x P of the matrix m and point-column P = (PNT. x, PNT. y, PNT. z, 1.0) to the power of T. to get acgevector3dvec transformed by corresponding transformation one has to take the product m x V of the matrix m and vector-Column V = (VEC. x, VEC. y, VEC. z, 0.0) to the power of T.

Every matrix m is associated with a coordinate system. this Coordinate System has origin (T0, T1, T2) and vectors (a00, a110, A20), (A01, A11, A21), and (A02, A12, A22) as axes. matrix M maps the standard coordinate system to the coordinate system with the origin (0, 0, 0) and axes (1, 0, 0), (0, 1, 0 ), and (0, 0, 1 ).
2. Notes about 3D mathematical basics: graphics and Game Development

1) Translate> Rotation> Object coordinate system. There is also the camera coordinate system.
2) matrix: matrix is an important foundation of 3D mathematics. It is mainly used to describe the relationship between two coordinate systems. by defining an operation, the vector of one coordinate system is converted to another coordinate system.
3) use the base vector (, 0), (, 0), (, 1) to multiply any matrix m, and get: each row of matrix m can be considered as the base vector after conversion.
4) The rotating coordinate system is equivalent to rotating an object with the opposite amount.
5) One reason for using the 4*4 matrix is that it can contain translation ).
6) include the translation of the affine transformation, the basic idea: the transformation of the center point to the origin, linear transformation, and then the center point to the original position. TRT-1