1. Projection and Clipping
網媒所林宏祥
Self introduction
Why I am here in lecture
The lecture will cover projection and clipping, the remaining time is any open question about homework 1

2. Overview
Overview of the content: orthogonal projection, perspective projection, and viewing volume

3. Orthogonal ProjectionX
xviewport
xcamera -Z
Ask whether the student know viewport coordinates?
Orthogonal projection: the focal point is at infinity

4. Perspective ProjectionX
xcamera
xviewport -Z d z
The distance between focal point and image plane is d

5. View Volume—orthogonal projectiony -z x
Far Clipping Plane
Left Clipping Plane
Right Clipping Plane
Bottom Clipping Plane
Top Clipping Plane
Finite visual field
Orthogonal projection+finite visual field = cuboid
Near Clipping Plane

6. View Volume—Perspective projection modely -z x
Left Clipping Plane
Far Clipping Plane
Top Clipping Plane
Near Clipping Plane
Bottom Clipping Plane
Right Clipping Plane

7. Y x z Clipping Cuboid: transformed volume after projection
viewport coordinates x
This is cuboid on viewport coordinates z

8. Implementation behind OpenGL Functions….

9. In OpenGL, the clipping cuboid is fixed.
(Since the screen size is fixed)

10. Y x z Clipping Cuboid: enclosed by:
xviewport = 1,xviewport=-1,yviewport=1,yviewport=-1,zviewport =1,zviewport=-1 Y x z

11. The openGL functions ensure the view volume fits clipping cuboid.

12. glOrtho(left, right, bottom, top, nearVal, farVal)

13. glOrtho(left, right, bottom, top, nearVal, farVal)

14. Orthogonal ProjectionX
xviewport
xcamera -Z
some scaling

15. A linear mapping for orthogonal projection

16. A canonical view.. Clipping cuboid Viewing Volume 1 -1 left right
xviewport
xcamera

17. Same mapping ways in y direction and z direction..

18. gluPerspective(fovy, aspect, zNear, zFar)
Left Clipping Plane
Far Clipping Plane
Top Clipping Plane
Near Clipping Plane
Bottom Clipping Plane
Right Clipping Plane

19. gluPerspective(fovy, aspect, zNear, zFar)

20. Perspective ProjectionX X
xcamera
xcamera
xviewport
xviewport -Z -Z d d
= 1 z z
some scaling

21. A canonical view.. Y
-zFar
-zNear
ycamera
fovy
zcamera -Z

22. Y
-zFar
-zNear
ycamera
fovy
zcamera -Z

23. Y
-zFar
-zNear
ycamera
fovy
zcamera -Z
After projection, the boundaries should map to 1, -1

24. Similarly in x, but consider the aspect.

25. Mapping on z: To present more details in closer objects, the viewport coordinate is inverse proportional to camera coordinates.

26. -zFar is mapping to 1, -zNear is mapping to -1, then

28. Remember perspective projection?
(xcamera, ycamera coordinates will be divided by zcamera)

29. Perspective projection <--> maintaining homogeneous coordinates

30. In the clipping part of your homework..

31. You need to adjust the coordinates in glVertex3f()
You need to create your own clipping cuboid which is different from openGL clipping cuboid. NOT modify the viewing volume.
(eg: xviewport: [-0.5,0.5], yviewport:[-0.5,0.5], zviewport:[-0.5, 0.5])
You need to adjust the coordinates in glVertex3f()

32. You need to calculate intersection
In 2D example,
screen
One capable way to handle it: Cohen-Sutherland Algorithm

33. Any Question?

34. From normalized device coordinates to screen coordinates
glViewport(x, y, w,h)