translation, rotation, scaling

1. translation

    
   xxxxxxxxxx
   x' = x + dx;
   y' = y + dy;
   z' = z + dz;

   $$\begin{bmatrix} x' \\ y' \\ z' \\ 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & dx \\ 0 & 1 & 0 & dy \\ 0 & 0 & 1 & dz \\ 0 & 0 & 0 & 1 \end{bmatrix} \times \begin{bmatrix} x \\ y \\ z \\ 1 \end{bmatrix} \tag{1}$$

2. rotation

    
   xxxxxxxxxx
   x' = x * cosB - y * sinB;
   y' = y * cosB + x * sinB;
   z' = z;

   $$\begin{bmatrix} x' \\ y' \\ z' \\ 1 \end{bmatrix} = \begin{bmatrix} cosB & -sinB & 0 & 0 \\ sinB & cosB & 0 & 0 \\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{bmatrix} \times \begin{bmatrix} x \\ y \\ z \\ 1 \end{bmatrix} \tag{2}$$

3. scaling

    
   xxxxxxxxxx
   x' = x * sx;
   y' = y * sy;
   z' = z * sz;

   $$\begin{bmatrix} x' \\ y' \\ z' \\ 1 \end{bmatrix} = \begin{bmatrix} sx & 0 & 0 & 0 \\ 0 & sy & 0 & 0 \\ 0 & 0 & sz & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \times \begin{bmatrix} x \\ y \\ z \\ 1 \end{bmatrix} \tag{3}$$