Dr' Scott Schaefer

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
Backface Culling
counter clock-wise orientation, draw polygon
12
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
Painters Algorithm

• Sort polygons according to distance from viewer
• Draw from back to front
• How do we sort polygons?

18
Painters Example
Sort by depth Green rect Red circle Blue tri
19
Painters Algorithm
20
Painters Algorithm

• Sometimes there is NO ordering that produces
  correct results!!!

21
Painters Algorithm

• Sort all objects zmin and zmax

22
Painters 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
Painters 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 not, they are fine
• - If yes, need to split one

24
Painters 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
Painters 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
Painters 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
7
6
5
4
1
2
3
31
BSP Trees Objects
9
-
8
7

6
5
4
1
2
3
32
BSP Trees Objects
Put front objects in the left branch
-

9
-
8
7

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

9
8
7
6
-

-

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

9
8
7
6
-

-

5
4
1
-
-
-



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

9
8
7
6
-

-

5
4
1
-
-
-



1
2
3
3
8
5
6
6
2
-
-


2
4
7
9
36
BSP Trees Objects
Put front objects in the left branch
-

9
8
7
6
-

-

5
4
1
-
-
-



1
2
3
3
8
5
6
6
2
-
-


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!

38
BSP Trees Objects
Correctly traversing this tree enumerates objects
from back to front
-

9
8
7
6
-

-

5
4
1
-
-
-



1
2
3
3
8
5
6
6
2
-
-


2
4
7
9
Traversal order?
39
BSP Trees Objects
Correctly traversing this tree enumerates objects
from back to front
-

9
8
7
6
-

-

5
4
1
-
-
-



1
2
3
3
8
5
6
6
2
-
-


2
4
7
9
Traversal order 8-gt9-gt7-gt6-gt5-gt3-gt4-gt2-gt1
40
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

41
Building a BSP Tree
6
7
3
5
1
2
4
42
Building a BSP Tree
6
7
3
5
1
2
4
1
b
2,3,4,5,6,7
43
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2,6, 5-2
2,4,5-1,7-1
44
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2,6, 5-2
b
f
4, 5-1
2
45
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2,6, 5-2
b
f
4
2
b
5-1
46
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2,6, 5-2
b
f
4
2
b
5-1
47
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2,6, 5-2
b
f
4
2
b
5-1
48
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6, 5-2
2
b
5-1
49
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
2
b
b
5-2
5-1
50
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
2
b
b
5-1
5-2
51
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
2
b
b
5-1
5-2
52
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
• Draw front polygons
• Draw on polygons
• Draw back polygons
• Else eye is on plane
• Draw front polygons
• Draw back polygons

53
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
Traversal order
2
b
b
5-1
5-2
54
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
Traversal order 6-gt(5-2)-gt(7-2)-gt3-gt(5-1)-gt4-gt(7-
1)-gt2-gt1
2
b
b
5-1
5-2
55
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
Traversal order
2
b
b
5-1
5-2
56
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
Traversal order 1-gt2-gt(7-1)-gt4-gt(5-1)-gt3-gt(7-2)-gt
(5-2)-gt6
2
b
b
5-1
5-2
57
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-2
7-1
b
b
f
4
6
Traversal order?
2
b
b
5-1
5-2
58
Rendering with a BSP Tree
59
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

60
Improved BSP Rendering

• Take advantage of view direction to cull away
  polygons behind viewer

61
Improved BSP Rendering

• Take advantage of view direction to cull away
  polygons behind viewer

View frustum
62
Improved BSP Rendering

• Take advantage of view direction to cull away
  polygons behind viewer

63
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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