Just preparations

Notes, while prepairing for Computer graphics exam

Transformations written inverse until draw or push matrix:

glMatrixMode(GL MODELVIEW);
glLoadIdentity();           // M := I
glTranslatef(x,y,z);        // M := M × T
glRotatef(a,x,y,z);         // M := M × R
drawObject();               // C' = M × C

If matrix pushed, corrdinate system according last transformation:

glLoadIdentity();                       I
glPushMatrix();                       I I
glTranslatef(1.0, 0.0, 0.0);          T I
glPushMatrix();                     T T I
glRotatef(10.0, 0.0, 1.0, 0.0);    TR T I
glPopMatrix();                        T I
glPushMatrix();                     T T I

Composite transformation: translate(rotate(scale())):

/ x'\   / s_x*cos(r)  -s_x*sin(r)  t_x \   / x \
| y'| = | s_x*sin(r)   s_y*cos(r)  t_y | x | y |
\ 1 /   \     0             0       1  /   \ 1 /

Rotation about axies

About X axis:

/  1   0    0   0 \
|  0  cos  sin  0 |
|  0 -sin  cos  0 |
\  0   0    0   1 /

About Y axis:

/ cos     -sin  0 \
|  0   1    0   0 |
| sin  0   cos  0 |
\  0   0    0   1 /

About Z axis:

/ cos sin   0   0 \
|-sin cos   0   0 |
|  0   0    1   0 |
\  0   0    0   1 /

Reference

• Peter Grogono "Getting Started with OpenGL". Concordia University, 2003.
• A. Lenkevičius, J. Matickas „KOMPIUTERINĖ GRAFIKA“. Technologija, Kaunas, 2004.
• http://www.eecis.udel.edu/~chandra/640/Spring05/lecture4.ppt