1.Affine matrix
===============

x' = ax + dy + gz +tx
y' = bx + ey + hz +ty
z' = cx + fy + iz +tz

                           -            -
                          | a   b   c  0 |
[x' y' z' 1] = [x y z 1]  | d   e   f  0 |
                          | g   h   i  0 |
                          | tx  ty  tz 1 |
                           -            -
 | a b c |
 | d e f | != 0
 | g h i |

2.Scalings
===============
                           -       -
                          | a 0 0 0 |
[x' y' z' 1] = [x y z 1]  | 0 e 0 0 |
                          | 0 0 i 0 |
                          | 0 0 0 1 |
                           -       -
 
3.translation
===============

                           -          -
                          | 1  0  0  0 |
[x' y' z' 1] = [x y z 1]  | 0  1  0  0 |
                          | 0  0  1  0 |
                          | tx ty tz 1 |
                           -          -


4.Rotations
===============
Affine-transformation when only angle theta  is rotated by centering on X axis. In view of the 
starting point, the direction of the rotation is clockwise. 

 (1)x axis rotation 
                           -                    -
                          | 1   0        0     0 |
[x' y' z' 1] = [x y z 1]  | 0  cos(t)  sin(t)  0 |
                          | 0  -sin(t) cos(t)  0 |
                          | 0   0        0     1 |
                           -                     -

 (2)y axis rotation 
                           -                         -
                          | cos(t)   0   -sin(t)   0  |
[x' y' z' 1] = [x y z 1]  | 0        1      0      0  |
                          | sin(t)   0    cos(t)   0  |
                          | 0        0      0      1  |
                           -                         -

 (3)z axis rotation 
                           -                        -
                          | cos(t)   sin(t)   0   0  |
[x' y' z' 1] = [x y z 1]  | -sin(t)  sin(t)   0   0  |
                          | 0         0       1   0  |
                          | 0         0       0   1  |
                           -                        -

