The relationship between three-dimensional coordinates and matrices

The relationship between three-dimensional coordinates and matrices
Three-dimensional coordinates of one or three-dimensional coordinates are points in space, commonly used (x, y, z) representations. But in the three-dimensional engine is commonly used in homogeneous coordinates to represent, to translate, rotate, zoom transformation.
The homogeneous coordinates of the second and homogeneous coordinates are represented by an n-dimensional vector with n+1 Bellavita, so that the points and vectors can be distinguished well. For example: (x,y,z,w), W equals 1, then the representation is a point, if w = 0, it is a vector. After we introduce three-dimensional coordinates to the four-bit homogeneous coordinates, we can simply translate, rotate, and scale the points in a three-dimensional coordinate by multiplying the 4-D matrix.
third, matrix multiplication Direct3D (Line vector): The order of matrix multiplication is from left to right, and the Order of transformation takes effect from left to right, V ' = v*t*r*s;
OpenGL (column vector): The order of matrix multiplication is right-to-left, V ' = s*r*t*v; (Left multiplication: transformation matrix at left) OSG (line vector): The order of matrix multiplication is from left to right, V ' = v*t*r*s;

Four, the reference matrix-directx and OpenGL different: row vector and column vector;