1. THREE-DIMENSIONAL VIEWING12
고려대학교 컴퓨터 학과
김 창 헌

2. Contents Viewing Pipeline Viewing Coordinates Projections
View Volumes and Projection Transformations
Clipping
Hardware Implementations
3D Viewing Functions
Summary

3. Viewing Pipeline General 3D Transformation Pipeline Clipping against
Modeling
Coordinates
Modeling
Transformation
World
Coordinates
Viewing
Transformation
Viewing
Coordinates
Clipping against
Viewing volume
Projection
Transformation
Projection
Coordinates
Workstation
Transformation
Device
Coordinates
Project onto
Projection plane

4. Viewing Coordinates Specifying the View Plane
Viewing-coordinate system
View-plane normal vector (N)
(1, 0, 0)
(1, 0, 1)

5. Viewing Coordinates (con’t)
Specifying the View Plane (con’t)
View-up vector (V)
uvn system

6. Viewing Coordinates (con’t)
Specifying the View Plane (con’t)
View-plane distance
Series of views of a scene

7. Viewing Coordinates (con’t)
Transformation from WC to VC
Transformation sequences
1. Translate the view reference point to the origin of the WC system
2. Apply rotations to align the xv, yv, and zv axes with the world axes
Translation
view reference point(x0, y0, z0)

8. Viewing Coordinates (con’t)
Transformation from WC to VC (con’t)
General sequence of translate-rotate transformation
Rotation
rotate around the world xw axis to bring zv into the xwzw plane
rotate around the world yw axis to align the zw and zv axis
final rotation is about the zw axis to align the yw and yv axis

9. Viewing Coordinates (con’t)
Transformation from WC to VC (con’t)
Direct generating the rotation-transformation matrix

10. Projections
Parallel Projection
Perspective Projection

11. Projections Parallel Projections Orthographic parallel projection
the projection is perpendicular to the view plane
Oblique parallel projection

12. Projections (con’t) Parallel Projections (con’t)
Orthographic projection
Isometric projection

13. 12.3 Projections (con’t) Parallel Projections (con’t)
Orthographic projection coordinates

14. 12.3 Projections (con’t) Parallel Projections (con’t)
Oblique projection

15. 12.3 Projections (con’t) Parallel Projections (con’t)
Oblique projection

16. 12.3 Projections (con’t) Parallel Projections (con’t)
Oblique projection
cavalier projection ( )

17. 12.3 Projections (con’t) Perspective Projections P=(x, y, z)
(xp,yp,zp)
zvp
zprp
view plane

18. 12.3 Projections (con’t)
Perspective Projections (con’t)

19. 12.3 Projections (con’t) Perspective Projections (con’t) zvp = 0
zprp = 0

20. 12.3 Projections (con’t) Perspective Projections (con’t)
Principal vanishing point

21. View Volumes and Projection Transformation
View Window

22. View Volumes … (con’t)
Parallel projection

23. View Volumes … (con’t)
Perspective projection

24. View Volumes … (con’t)
View volume boundary

25. View Volumes … (con’t)
Changing the shape of the oblique-projection view volume

26. View Volumes … (con’t)
Moving the projection reference point

27. View Volumes … (con’t)
Projected object size

28. View Volumes … (con’t)
Animation

29. 12.4 View Volumes … (con’t)
General Parallel-Projection Transformations
Oblique projection view volume
Regular parallelepiped view volume

30. 12.4 View Volumes … (con’t)
General Parallel-Projection Transformations (con’t)
Projection vector
Transformation

31. 12.4 View Volumes … (con’t)
General Parallel-Projection Transformations (con’t)
General parallel-projection matrix

32. 12.4 View Volumes … (con’t)
General Parallel-Projection Transformations (con’t)
Element Relationship

33. 12.4 View Volumes … (con’t)
General Perspective-Projection Transformation
Perspective view volume

34. View Volumes … (con’t)
General Perspective-Projection Transformation

35. View Volumes … (con’t)
General Perspective-Projection Transformation (con’t)

36. Clipping
Clipping
Identify and save all surface segments within the view volum
View-volume clipping boundary : planes

37. Clipping (con’t)
Normalized View Volumes  Why?
View Volume

38. Clipping (con’t)
Normalized View Volumes (con’t)
Pipeline

39. Clipping (con’t) Normalized View Volumes (con’t) Advantages
provides a standard shape for representing any sized view volume
clipping procedures are simplified and standardized with unit cube
depth cueing and visible-surface determination are simplified
Mapping position
within a rectangular view volume to a 3D rectangular viewport

40. Clipping (con’t) Normalized View Volumes (con’t)
Ratios of the dimensions of the viewport and view volume
Translation factors

41. Clipping (con’t) Viewport Clipping 1. Parametric line equation
2. Calculation of parameter value
3. Intersection point

42. Clipping (con’t)
Viewport Clipping (con’t)

43. Clipping (con’t)
Clipping in Homogeneous Coordinates

44. Hardware Implementations

45. 3D Viewing Functions
Multiple Views Using Difference Camera Orientations

46. 3D Viewing Functions (con’t)
A Wide-Angle Perspective Display
Same viewing position, but with slight shifts in the viewing direction

47. Summary Modeling Coordinates Modeling Transformation World Coordinates
Viewing
Transformation
Viewing
Coordinates
Projection
Transformation
Projection
Coordinates
Workstation
Transformation
Device
Coordinates