1. GRAFIKA
KOMPUTER
~ M. Ali Fauzi

2. Drawing
3D Graphics

3. 3D
TRANSFORMATION

4. Transformation Pipeline
Vertex
Modelview
Matrix
Projection
Perspective
Division
Viewport
Transformation
Object
Coordinates
Eye
Clip
Normalized
device
Window
GL_MODELVIEW mode
glTranslate()
glRotate()
glScale()
glLoadMatrix()
glMultMatrix()
gluLookAt()
GL_PROJECTION mode
glOrtho()
gluOrtho2D()
glFrustum()
gluPerspective()
glViewport()

5. Matrix Modes ~ ModelView Matrix (GL_MODELVIEW)
These concern model-related operations such as translation, rotation, and scaling, as well as viewing transformations.

6. THE
TRANSFORMATION

7. Translation
The path is represented by a vector, called the translation or shift vector.
P' = P T tx ty tz x’ y’ z’ x y z =
New Position
Current Position
Translation Vector

8. Translation Translasi 3D -> 4D Translasi 2D -> 3D Koordinat Asal
Koordinat Homogen

9. Scaling The transformation using Scale Matrix P' = S • P New Position
Current Position

10. Scaling In Homogeneous Coordinate : P' = S • P New Position
Scale Matrix
Current Position

11. Rotation For 2D : P' = R . P New Position Rotation Matrix
Current Position

12. Rotation
For 2D :

13. Rotation
2D Rotation about an arbitrary axis (Rotasi pada sembarang sumbu (Xr,Yr) dengan sudut Ө) :

14. Rotation
3D Rotation, Roll y z x

15. Rotation
3D Rotation, Yaw y z x

16. Rotation
3D Rotation, Pitch y z x

17. sumbu putar sembarang titik (Ax,Ay,Az)
Rotation
3D Rotation about an arbitrary axis (Rotasi pada sembarang sumbu (Ax,Ay,Az) dengan sudut Ө)
sumbu putar sembarang titik (Ax,Ay,Az) y x z

18. Shearing 3D
Shearing-x
Shearing-y

19. Shearing 3D
Shearing-z