1. Normalizing Transformation (I)
3D Viewing
normalizing transform (3D WC  VRC) 
clipping (VRC)
projection (VRC  2D VC), mapping into a viewport
Virtual Reality & Computer Graphics lab.

2. Virtual Reality & Computer Graphics lab.
Model
(1,1,0)
(11,21,30) z x y
(10,20,30)
Virtual Reality & Computer Graphics lab.

3. Virtual Reality & Computer Graphics lab.
VRP(15,20,35) z x y
EYE
Virtual Reality & Computer Graphics lab.

4. Virtual Reality & Computer Graphics lab.
VUP(0,1,0)
VPN(-1,0,-1)
VRP(15,20,35) y z x y z
Virtual Reality & Computer Graphics lab.

5. Virtual Reality & Computer Graphics lab.z x y
Virtual Reality & Computer Graphics lab.

6. Virtual Reality & Computer Graphics lab.
Window(-3,2(,0))
Window(3,2(,0)) z x y
PRP(5,0,0)
Window(3,-2(,0))
Virtual Reality & Computer Graphics lab.

7. Virtual Reality & Computer Graphics lab.
Window(-3,2(,-5))
Window(3,2(,-5)) z x y
Z=-5
Window(3,-2(,-5))
Virtual Reality & Computer Graphics lab.

8. Virtual Reality & Computer Graphics lab.
Width=6
Height=4 z x y
F=4
Z=-7
Z=-5
Z=-1
Virtual Reality & Computer Graphics lab.

9. Virtual Reality & Computer Graphics lab.
(1,1,-1)
(-1/7,1/7,-1/7)
x or y -z 1 -1 B F
Z=-1 z x y
Z=-5/7
(1,-1,-1)
Z=-1/7
Virtual Reality & Computer Graphics lab.

10. Normalizing Transformation (I)
3D Viewing
normalizing transform (3D WC  VRC) 
3D clipping (VRC)
projection (VRC  2D VC), mapping into a viewport
Virtual Reality & Computer Graphics lab.

11. Virtual Reality & Computer Graphics lab.
(-1,1,-1)
(1,1,-1)
(x’, y’, z’)
(x, y, z)
If (-X+Z>0) clip;
If (X+Z>0) clip; z x y
(1,-1,-1)
If (Z>-1/7) clip;
(0,0,0)
Perspective clipping?
Virtual Reality & Computer Graphics lab.

12. Virtual Reality & Computer Graphics lab.
(-1,1,-1)
(1,1,-1)
(x’, y’, z’)
(-1,1,0)
(1,1,0)
(x, y, z)
If (X>1) clip;
If (X<-1) clip;
(1,-1,-1)
(-1,-1,0)
(1,-1,0)
Parallel clipping!
Virtual Reality & Computer Graphics lab.

13. Virtual Reality & Computer Graphics lab.
x or y -z
x or y -1 1 B F 1 B F -z -1
-1/7 -1
Virtual Reality & Computer Graphics lab.

14. Normalizing Transformation (I)
3D Viewing
normalizing transform (3D WC  VRC) 
3D clipping (VRC)
projection (VRC  2D VC), mapping into a viewport
Virtual Reality & Computer Graphics lab.

15. Virtual Reality & Computer Graphics lab.
1024*768
(x’, y’, z’)
(x, y, z)
Virtual Reality & Computer Graphics lab.