1. Hidden Surfaces
Dr. Scott Schaefer

2. Hidden Surfaces

3. Hidden Surfaces

4. Hidden Surfaces

5. Backface Culling

6. Backface Culling
view direction

7. Backface Culling
view direction

8. Backface Culling
, draw polygon
view direction

9. Backface Culling
, cull polygon
view direction

10. Backface Culling

11. counter clock-wise orientation, draw polygon
Backface Culling
counter clock-wise orientation, draw polygon

12. clock-wise orientation, cull polygon
Backface Culling
clock-wise orientation, cull polygon

13. Backface Culling Advantages
Improves rendering speed by removing roughly half of polygons from scan conversion
Disadvantages
Assumes closed surface with consistently oriented polygons
NOT a true hidden surface algorithm!!!

14. Backface Culling
Is this all we have to do?

15. Backface Culling Is this all we have to do? No!
Can still have 2 (or more) front faces that map to the same screen pixel

16. Backface Culling Is this all we have to do? No!
Can still have 2 (or more) front faces that map to the same screen pixel
Which actually gets drawn?

17. Painter’s Algorithm Sort polygons according to distance from viewer
Draw from back to front
How do we sort polygons?

18. Painter’s Example Sort by depth: Green rect Red circle Blue tri
z = 0.7
z = 0.3
z = 0.1
Sort by depth:
Green rect
Red circle
Blue tri
z = 0

19. Painter’s Algorithm

20. Painter’s Algorithm
Sometimes there is NO ordering that produces correct results!!!

21. Painter’s Algorithm
Sort all objects’ zmin and zmax

22. Painter’s Algorithm Sort all objects’ zmin and zmax
If an object is uninterrupted (its zmin and zmax are adjacent in the sorted list), it is fine

23. Painter’s Algorithm Sort all objects’ zmin and zmax
If an object is uninterrupted (its zmin and zmax are adjacent in the sorted list), it is fine
If 2 objects DO overlap
3.1 Check if they overlap in x
- If not, they are fine
3.2 Check if they overlap in y
- If yes, need to split one

24. Painter’s Algorithm The splitting step is the tough one
- Need to find a plane to split one polygon by so that each new polygon is entirely in front of or entirely behind the other
- Polygons may actually intersect, so then need to split each polygon by the other

25. Painter’s Algorithm The splitting step is the tough one
- Need to find a plane to split one polygon by so that each new polygon is entirely in front of or entirely behind the other
- Polygons may actually intersect, so then need to split each polygon by the other
After splitting, you can resort the list and should be fine

26. Painter’s Algorithm-Summary
Advantages
Simple algorithm for ordering polygons
Disadvantages
Sorting criteria difficult to produce
Redraws same pixel many times
Sorting can also be expensive

27. Depth (“Z”) Buffer Simple modification to scan-conversion
Maintain a separate buffer storing the closest “z” value for each pixel
Only draw pixel if depth value is closer than stored “z” value
Update buffer with closest depth value

28. Depth (“Z”) Buffer Advantages Simple to implement
Allows for a streaming approach to polygon drawing
Disadvantages
Requires extra storage space
Still lots of overdraw

29. Binary Space Partitioning Trees
BSP tree: organize all of space (hence partition) into a binary tree
- Preprocess: overlay a binary tree on objects in the scene
- Runtime: correctly traversing this tree enumerates objects from back to front
- Idea: divide space recursively into half-spaces by choosing splitting planes
Splitting planes can be arbitrarily oriented

30. BSP Trees: Objects 9 8 6 7 5 4 1 2 3

31. BSP Trees: Objects 9 - 8 6 7 + 5 4 1 2 3

32. BSP Trees: Objects + - - + Put front objects in the left branch 9 8 67 + 1 2 3 4 5 6 7 8 9 5 4 1 2 3

33. BSP Trees: Objects + - + - + - Put front objects in the left branch 98 6 7 + - + - 5 4 1 2 3 4 5 6 7 8 9 1 2 3

34. BSP Trees: Objects + - + - + - + - + - + -
Put front objects in the left branch + - 9 8 6 7 + - + - 5 4 1 + - + - + - 1 2 3 2 4 3 5 6 7 9 8

35. BSP Trees: Objects + - + - + - + - + - + - + - + -
Put front objects in the left branch + - 9 8 6 7 + - + - 5 4 1 + - + - + - 1 2 3 3 5 6 8 + 2 - 6 + - 2 4 7 9

36. BSP Trees: Objects + - + - + - + - + - + - + - + -
Put front objects in the left branch + - 9 8 6 7 + - + - 5 4 1 + - + - + - 1 2 3 3 5 6 8 + 2 - 6 + - 2 4 7 9
When to stop the recursion?

37. Object Splitting No bunnies were harmed in my example
But what if a splitting plane passes through an object?
- Split the object; give half to each node:
- Worst case: can create up to O(n3) objects!
Ouch

38. Building a BSP Tree Choose a splitting polygon
Sort all other polygons as
Front
Behind
Crossing On
Add “front” polygons to front child, “behind” to back child
Split “crossing” polygons with infinite plane
Add “on” polygons to root
Recur

39. Building a BSP Tree 6 7 3 5 1 2 4

40. Building a BSP Tree 6 7 3 5 1 2 4 1 b
2,3,4,5,6,7

41. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2,6, 5-2f b
7-2,6, 5-2
2,4,5-1,7-1

42. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-1 7-2,6, 5-2 2f b
7-1
7-2,6, 5-2 f b 2
4, 5-1

43. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-1 7-2,6, 5-2 4 2f b
7-1
7-2,6, 5-2 f b 4 2 b
5-1

44. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-1 7-2,6, 5-2 4 2f b
7-1
7-2,6, 5-2 f b 4 2 b
5-1

45. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-1 7-2,6, 5-2 4 2f b
7-1
7-2,6, 5-2 f b 4 2 b
5-1

46. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 4 6, 5-2 2f b
7-2
7-1 b f b 4
6, 5-2 2 b
5-1

47. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4 2 5-2f b
7-2
7-1 b f b 6 4 b 2 b
5-2
5-1

48. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4 2 5-1f b
7-2
7-1 b f b 6 4 b 2 b
5-1
5-2

49. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4 2 5-1f b
7-2
7-1 b f b 6 4 b 2 b
5-1
5-2

50. Rendering with a BSP Tree
If eye is in front of plane
Draw “back” polygons
Draw “on” polygons
Draw “front” polygons
If eye is behind plane
Else eye is on plane

51. BSP Trees: Objects + - + - + - + - + - + - + - + -
Correctly traversing this tree enumerates objects from back to front + - 9 8 6 7 + - + - 5 4 1 + - + - + - 1 2 3 3 5 6 8 + 2 - 6 + - 2 4 7 9
Traversal order?

52. BSP Trees: Objects + - + - + - + - + - + - + - + -
Correctly traversing this tree enumerates objects from back to front + - 9 8 6 7 + - + - 5 4 1 + - + - + - 1 2 3 3 5 6 8 + 2 - 6 + - 2 4 7 9
Traversal order:
8->9->7->6->5->3->4->2->1

53. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4f b
7-2
7-1 b f b 6 4
Traversal order: b 2 b
5-1
5-2

54. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4f b
7-2
7-1 b f b 6 4
Traversal order:
6->(5-2)->(7-2)->3->(5-1)->4->(7-1)->2->1 b 2 b
5-1
5-2

55. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4f b
7-2
7-1 b f b 6 4
Traversal order: b 2 b
5-1
5-2

56. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4f b
7-2
7-1 b f b 6 4
Traversal order:
1->2->(7-1)->4->(5-1)->3->(7-2)->(5-2)->6 b 2 b
5-1
5-2

57. Building a BSP Tree 6 7-2 5-2 3 7-1 5-1 1 2 4 1 3 7-2 7-1 6 4f b
7-2
7-1 b f b 6 4
Traversal order? b 2 b
5-1
5-2

58. Rendering with a BSP Tree
Advantages
No depth comparisons needed
Polygons split and ordered automatically
Disadvantages
Computationally intense preprocess stage restricts algorithm to static scenes
Splitting increases polygon count
Redraws same pixel many times
Choosing splitting plane not an exact science

59. Improved BSP Rendering
Take advantage of view direction to cull away polygons behind viewer

60. Improved BSP Rendering
Take advantage of view direction to cull away polygons behind viewer
View frustum

61. Improved BSP Rendering
Take advantage of view direction to cull away polygons behind viewer

62. OpenGL and Hidden Surfaces
glEnable(GL_DEPTH_TEST);
glEnable(GL_CULL_FACE);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
glCullFace ( GL_BACK );

64. Scan Line Algorithm
Assume for each line of screen, we have scan-lines for all polygons intersecting that line
For each polygon, keep track of extents of scan line
Whenever the x-extents of two scan lines overlap, determine ordering of two polygons

65. Scan Line Algorithm

66. Scan Line Algorithm

67. Scan Line Algorithm

68. Scan Line Algorithm Advantages
Takes advantage of coherence resulting in fast algorithm
Does not require as much storage as depth buffer
Disadvantages
More complex algorithm
Requires all polygons sent to GPU before drawing