1. Projection v VP u
VPN n

2. Projection v
VRP u
VRP n
Eye Point

3. Camera & World
Up Vector
Look At
Vector

4. Orthographic Projection
View
Plane
Back Clipping
Plane
VPN
Front Clipping
Plane

5. In OpenGL glOrtho(GLdouble left, GLdouble right, GLdouble bottom,
GLdouble top, GLdouble near, GLdouble far)
far
The direction of projection
is parallel to Z-axis. Looking
at the negative direction
near
top
left
Back Clipping
Plane
VPN
right
bottom
Front Clipping
Plane

6. Perspective Projection
View
Plane
Back Clipping
Plane
VPN
Front Clipping
Plane

7. In OpenGL glFrustum(GLdouble left, GLdouble right, GLdouble bottom,
GLdouble top, GLdouble near, GLdouble far)
far
The direction of projection
is parallel to Z-axis. Looking
at the negative direction
near
top
left
VPN
right
Back Clipping
Plane
bottom
Front Clipping
Plane

8. In OpenGL gluPerspective(GLdouble fovy, GLdouble aspect,
GLdouble near, GLdouble far)
far
The direction of projection
is parallel to Z-axis. Looking
at the negative direction.
Aspect = w/h
near w
VPN h
Back Clipping
Plane
fovy
Front Clipping
Plane

9. gluLookAt gluLookAt(GLdouble eyex, GLdouble eyey, GLdouble eyez,
GLdouble latx, GLdouble laty, GLdouble latz,
GLdouble upx, GLdouble upy, GLdouble upz)
The direction of projection
is parallel to Z-axis. Looking
at the negative direction.
Aspect = w/h
far
near up w
VPN h
Back Clipping
Plane
fovy
lat
Front Clipping
Plane

10. Parallel Projection

11. Parallel Projection
(x,y,d) x z y
(x,y,z) d
(x,y,z)
(x,y,d)

12. Perspective Projection

13. Perspective Projection
xp=x(zprp – zvp)/ (zprp – z)
View
Plane
yp=y(zprp – zvp)/ (zprp – z)
(x,y,z)
dp=(zprp – zvp)
(xp,yp,zvp)
zprp dp

14. Perspective Projection
xp=x(zprp – zvp)/ (zprp – z)
yp=y(zprp – zvp)/ (zprp – z)
dp=(zprp – zvp) x y z 1 xh yh zh h
zvp/dp zvp(zprp/dp)
/dp zprp/dp =
h = (zprp-z/dp)
xp=xh/h
yp=yh/h

15. Graphics Pipeline Modeling Coordinates World Coordinates Viewing
Transformation
Viewing
Transformation
Viewing
Coordinates
Projection
Coordinates
Projection
Transformation
Normalization
Transformation
Normalized
Projection
Coordinates
Device
Coordinates
Workstation
Transformation