1. Three Dimensional Viewing

2. Figure 10-1 Coordinate reference for obtaining a selected view of a three-dimensional scene.

3. Figure Three parallel-projection views of an object, showing relative proportions from different viewing positions.

4. Figure The wire-frame representation of the pyramid in (a) contains no depth information to indicate whether the viewing direction is (b) downward from a position above the apex or (c) upward from a position below the base.

5. Figure A wire-frame object displayed with depth cueing, so that the brightness of lines decreases from the front of the object to the back.

6. Figure 10-5 Photographing a scene involves selection of the camera position and orientation.

7. Figure General three-dimensional transformation pipeline, from modeling coordinates (MC) to world coordinates (WC) to viewing coordinates (VC) to projection coordinates (PC) to normalized coordinates (NC) and, ultimately, to device coordinates (DC).

8. Figure A right-handed viewing-coordinate system, with axes x view, y view, and z view, relative to a right-handed world-coordinate frame.

9. Figure 10-8 Orientation of the view plane and view-plane normal vector N.

10. Figure 10-9 Three possible positions for the view plane along the z view axis.

11. Figure Specifying the view-plane normal vector N as the direction from a selected reference point Pref to the viewing-coordinate origin P0.

12. Figure Adjusting the input direction of the view-up vector V to an orientation perpendicular to the view-plane normal vector N.

13. Figure 10-12 A right-handed viewing system defined with unit vectors u, v, and n.

14. Figure 10-13 Panning across a scene by changing the viewing position, with a fixed direction for N.

15. Figure 10-14 Viewing an object from different directions using a fixed reference point.

16. Figure 10-15 Parallel projection of a line segment onto a view plane.

17. Figure 10-16 Perspective projection of a line segment onto a view plane.

18. Figure 10-17 Orthogonal projections of an object, displaying plan and elevation views.

19. Figure 10-18 An isometric projection of a cube.

20. Figure 10-19 An orthogonal projection of a spatial position onto a view plane.

21. Figure A clipping window on the view plane, with minimum and maximum coordinates given in the viewing reference system.

22. Figure 10-21 Infinite orthogonal-projection view volume.

23. Figure 10-22 A finite orthogonal view volume with the view plane “in front” of the near plane.

24. Figure 10-23 A left-handed screen-coordinate reference frame.

25. Figure Normalization transformation from an orthogonal-projection view volume to the symmetric normalization cube within a left-handed reference frame.

26. Figure An oblique parallel projection of a cube, shown in a top view (a), produces a view (b) containing multiple surfaces of the cube.

27. Figure An oblique parallel projection of coordinate position (x, y, z) to position (xp, yp, zvp) on a projection plane at position zvp along the z view axis.

28. Figure An oblique parallel projection (a) of a cube (top view) onto a view plane that is coincident with the front face of the cube produces the combination front, side, and top view shown in (b).

29. Figure Cavalier projections of a cube onto a view plane for two values of angle Φ. The depth of the cube is projected with a length equal to that of the width and height.

30. Figure Cabinet projections of a cube onto a view plane for two values of angle Φ. The depth is projected with a length that is one half that of the width and height of the cube.

31. Figure Oblique parallel projection of position (x, y, z) to a view plane along a projection line defined with vector VP .

32. Figure Top view of a finite view volume for an oblique parallel projection in the direction of vector VP.

33. Figure 10-32 Top view of an oblique parallel-projection transformation
Figure Top view of an oblique parallel-projection transformation. The oblique view volume is converted into a rectangular parallelepiped, and objects in the view volume, such as the green block, are mapped to orthogonal-projection coordinates.

34. Figure A perspective projection of two equal-length line segments at different distances from the view plane.

35. Figure A perspective projection of a point P with coordinates (x, y, z) to a selected projection reference point. The intersection position on the view plane is (xp, yp, zvp ).

36. Figure A perspective-projection view of an object is upside down when the projection reference point is between the object and the view plane.

37. Figure Changing perspective effects by moving the projection reference point away from the view plane.

38. Figure Principal vanishing points for perspective-projection views of a cube. When the cube in (a) is projected to a view plane that intersects only the z axis, a single vanishing point in the z direction (b) is generated. When the cube is projected to a view plane that intersects both the z and x axes, two vanishing points (c) are produced.

39. Figure 10-38 An infinite, pyramid view volume for a perspective projection.

40. Figure A perspective-projection frustum view volume with the view plane “in front” of the near clipping plane.

41. Figure A symmetric perspective-projection frustum view volume, with the view plane between the projection reference point and the near clipping plane. This frustum is symmetric about its centerline when viewed from above, below, or either side.

42. Figure Field-of-view angle θ for a symmetric perspective-projection view volume, with the clipping window between the near clipping plane and the projection reference point.

43. Figure Relationship between the field-of-view angle θ, the height of the clipping window, and the distance between the projection reference point and the view plane.

44. Figure Increasing the size of the field-of-view angle increases the height of the clipping window and increases the perspective-projection foreshortening.

45. Figure A symmetric frustum view volume is mapped to an orthogonal parallelepiped by a perspective-projection transformation.

46. Figure An oblique frustum, as viewed from at least one side or a top view, with the view plane positioned between the projection reference point and the near clipping plane.

47. Figure Normalization transformation from a transformed perspective-projection view volume (rectangular parallelepiped) to the symmetric normalization cube within a left-handed reference frame, with the near clipping plane as the view plane and the projection reference point at the viewing-coordinate origin.

48. Figure 10-47 Default orthogonal-projection view volume
Figure Default orthogonal-projection view volume. Coordinate extents for this symmetric cube are from −1 to +1 in each direction. The near clipping plane is at z near = 1, and the far clipping plane is at z far = −1.

49. Figure 10-48 Output display generated by the three-dimensional viewing example program.

50. Figure A possible ordering for the view-volume clipping boundaries corresponding to the region-code bit positions.

51. Figure Values for the three-dimensional, six-bit region code that identifies spatial positions relative to the boundaries of a view volume.

52. __
Figure Three-dimensional region codes for two line segments. Line P1P2 intersects the right and top clipping boundaries of the view volume, while line P3P4 is completely below the bottom clipping plane. __

53. Figure 10-52 Three-dimensional object clipping
Figure Three-dimensional object clipping. Surface sections that are outside the view-volume clipping planes are eliminated from the object description, and new surface facets may need to be constructed.

54. Figure 10-53 Clipping a line segment against a plane with normal vector N.

55. Figure Clipping the surfaces of a pyramid against a plane with normal vector N. The surfaces in front of the plane are saved, and the surfaces of the pyramid behind the plane are eliminated.

56. Table 10-1 Summary of OpenGL Three-Dimensional Viewing Functions