CPSC 441: Computer Graphics Hidden Surface Removal

1
CPSC 441 Computer Graphics Hidden Surface Removal

• Jinxiang Chai

2
3D Rendering pipeline
Modeling transformation
lighting
Viewing transformation
Project transformation
Clipping
Scan conversion
Image
3
3D Rendering pipeline
Modeling transformation
Transform into 3D world system
Illuminate according to lighting and reflectance
lighting
Transform into 3D camera coordinate system
Viewing transformation
Transform into 2D camera system
Project transformation
Clip primitives outside cameras view
Clipping
Draw pixels (includes texturing, hidden surface,
etc.)
Scan conversion
Image
4
3D Geometry Pipeline
View space
World space
Object space
Normalized project space
Image space
4
5
Hidden Surfaces
6
Hidden Surfaces
7
Hidden Surfaces
8
Outline

• Backface Culling
• Painters algorithm
• BSP
• Scanline
• Z-buffer
• Ray casting
• Required reading section 9-1 to 9-11

9
Backface Culling
10
Backface Culling
view direction
11
Backface Culling
view direction
12
Backface Culling
view direction
13
Backface Culling
, draw polygon
view direction
14
Backface Culling
, cull polygon
view direction
15
Backface Culling

• Is this all we have to do?

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

17
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?

18
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!!!

19
Painters Algorithm

• Basic idea similar to oil painting
• - draw background first
• - then most distant object
• - then nearer object
• - and so forth

20
Painters Algorithm

• Sort polygons according to distance from viewer
• Draw from back (farthest) to front (nearest)
• - the entire object
• Near objects will overwrite farther ones

21
Painters Example
Sort by depth Green rect Red circle Blue tri
22
Painters Algorithm

• Does anyone see a problem with this?

23
Painters Algorithm

• Does anyone see a problem with this?
• - Objects can have a range of depth, not just a
  single value
• - Need to make sure they dont overlap for this
  algorithm to work

24
Painters Algorithm

• Does anyone see a problem with this?
• - Objects can have a range of depth, not just a
  single value
• - Need to make sure they dont overlap for this
  algorithm to work

25
Painters Algorithm

• Sort all objects zmin and zmax

26
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

27
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

28
Painters Algorithm

• The splitting step is the tough one
• - Need to find a plane to split one polygon 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

29
Painters Algorithm

• The splitting step is the tough one
• - Need to find a plane to split one polygon 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

30
Painters Algorithm-Summary

• Advantages
• - Simple algorithm for ordering polygons
• Disadvantages
• - Splitting is not an easy task
• - Sorting can also be expensive
• - Redraws same pixel many times

31
Binary Space Partitioning Trees

• Basic principle Objects in the half space
  opposite of the viewpoint do not obscure objects
  in the half space containing the viewpoint thus,
  one can safely render them without covering
  foreground objects

6
4
5
7
1
3
2
32
Binary Space Partitioning Trees

• Basic principle Objects in the half space
  opposite of the viewpoint do not obscure objects
  in the half space containing the viewpoint thus,
  one can safely render them without covering
  foreground objects

-
6

4
5
7
1
3
2
33
Binary Space Partitioning Trees

• Basic principle Objects in the half space
  opposite of the viewpoint do not obscure objects
  in the half space containing the viewpoint thus,
  one can safely render them without covering
  foreground objects

-
6

4
5
7
If we want to draw 5 correctly - we need draw
6 and 7 first, - then draw 5, - then draw
1,2,3,4
1
3
2
34
Binary Space Partitioning Trees

• Basic principle Objects in the half space
  opposite of the viewpoint do not obscure objects
  in the half space containing the viewpoint thus,
  one can safely render them without covering
  foreground objects

-
6

4
5
7
If we want to draw 5 correctly - we need draw
6 and 7 first, - then draw 5, - then draw
1,2,3,4
1
3
2
We need to do this for every polygon Can we do
this more efficiently?
35
Binary Space Partitioning Trees

• Basic principle Objects in the half space
  opposite of the viewpoint do not obscure objects
  in the half space containing the viewpoint thus,
  one can safely render them without covering
  foreground objects

-
6

4
5
7
If we want to draw 5 correctly - we need draw
6 and 7 first, - then draw 5, - then draw
1,2,3,4
1
3
2
We need to do this for every polygon Can we do
this more efficiently? BSP tree
36
Binary Space Partition 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

37
Binary Space Partition Trees (1979)

• 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

38
BSP Trees Objects
9
8
7
6
5
4
1
2
3
39
BSP Trees Objects
9
-
8
7

6
5
4
1
2
3
40
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
41
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
42
BSP Trees Objects
Put front objects in the left branch
-

9
-
8
7

6
9
8
5
6
7
-

5
4
1
4
2
3
1
2
3
43
BSP Trees Objects
Put front objects in the left branch
-

9
-
8
7

6
9
8
5
6
7
-

-

5
4
1
4
2
3
9
?
?
4
1
2
3
44
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
45
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
46
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
47
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?
48
Object Splitting

• No bunnies were harmed in my example
• But what if a splitting plane passes through an
  object?

49
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!

50
Polygons BSP Tree Construction

• Split along the plane containing any polygon
• Classify all polygons into positive or negative
  half-space of the plane
• If a polygon intersects plane, split it into two
• Recurse down the negative half-space
• Recurse down the positive half-space

51
Binary Space Partition Trees (1979)

• 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

52
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?
53
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
54
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
55
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
56
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
57
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
58
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
59
Building a BSP Tree for Polygons

• 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/current node
• Recur

60
Building a BSP Tree
6
7
3
5
1
2
4
61
Building a BSP Tree
6
7
3
5
1
2
4
1
b
2,34,5,6,7
62
Building a BSP Tree
6
7
3
5
1
2
4
1
b
2,34,5,6,7
How to divide 2,3,4,5,6,7?
63
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-2, 6,5-2
2,4,5-1,7-1
64
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-2, 6,5-2
2,4,5-1,7-1
65
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
66
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
7-1
b
f
4
2
b
5-1
67
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2, 6,5-2
b
f
4
2
b
5-1
68
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2, 6,5-2
b
f
4
2
b
5-1
69
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6,5-2
2
b
5-1
70
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
b
f
5-1
5-2
71
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
b
f
5-2
5-1
72
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
b
f
5-2
5-1
73
Rendering with a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
How to traverse the tree?
b
b
f
4
6
2
b
f
5-2
5-1
74
Rendering with a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
How to traverse the tree? - draw back
polygons - draw on polygons - draw front
polygons
b
b
f
4
6
2
b
f
5-2
5-1
75
Rendering with a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
b
f
Traversal order
5-2
5-1
76
Rendering with a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 6
5-2
5-1
77
Rendering a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 6-gt(5-2)
5-2
5-1
78
Rendering a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 6-gt(5-2)-gt(7-2)
5-2
5-1
79
Rendering 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
b
b
f
4
6
2
f
b
Traversal order 6-gt(5-2)-gt(7-2)-gt3
5-2
5-1
80
Rendering 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
b
b
f
4
6
2
f
b
Traversal order 6-gt(5-2)-gt(7-2)-gt3-gt(5-1)
5-2
5-1
81
Rendering 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
b
b
f
4
6
2
f
b
Traversal order 6-gt(5-2)-gt(7-2)-gt3-gt(5-1)-gt4-gt(7-
1)-gt2-gt1
5-2
5-1
82
Rendering a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
1
b
3
b
f
7-1
7-2
b
b
f
4
6
2
b
f
Traversal order 6-gt(5-2)-gt(7-2)-gt3-gt(5-1)-gt4-gt(7-
1)-gt2-gt1
5-2
5-1
83
Rendering with a BSP Tree

• How to traverse the tree
• Draw back polygons
• Draw on polygons
• Draw front polygons

1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
5-2
5-1
84
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
1
b
3
b
f
7-1
7-2
Do we need to build a new tree?
b
b
f
4
6
2
b
f
5-2
5-1
85
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
1
b
3
b
f
7-1
7-2
Do we need to build a new tree? - No, we use
the same tree if objects are static
b
b
f
4
6
2
b
f
5-2
5-1
86
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
1
b
3
b
f
7-1
7-2
Do we need to build a new tree? - No, we use
the same tree if objects are static How can we
traverse the tree?
b
b
f
4
6
2
b
f
5-2
5-1
87
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

88
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
-
1
b
3

f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order
5-2
5-1
89
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1
5-2
5-1
90
Different View Point?
6
-
7-2
5-2
3
7-1
5-1

1
2
4
1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1
5-2
5-1
91
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
-

b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1
5-2
5-1
92
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
-

b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1-gt2
5-2
5-1
93
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
-

b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1-gt2-gt(7-1)
5-2
5-1
94
Different View Point?
6
7-2
5-2
3
-
7-1
5-1
1
2
4

1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1-gt2-gt(7-1)-gt4
5-2
5-1
95
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
-

1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1-gt2-gt(7-1)-gt4-gt(5-1)
5-2
5-1
96
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1-gt2-gt(7-1)-gt4-gt(5-1)-gt3
5-2
5-1
97
Different View Point?
6
7-2
5-2
3
7-1
5-1
1
2
4
1
b
3
f
b
7-1
7-2
b
b
f
4
6
2
f
b
Traversal order 1-gt2-gt(7-1)-gt4-gt(5-1)-gt3-gt(7-2)-gt
(5-2)-gt6
5-2
5-1
98
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
1
b
3
f
b
7-1
7-2
f
b
b
4
6
2
b
f
Traversal order?
5-2
5-1
99
Building a BSP Tree
6
7-2
5-2
3
7-1
5-1
1
2
4
1
1
b
3
f
b
7-1
7-2
f
b
b
4
6
2
b
f
Traversal order? 1-gt6-gt(5-2)-gt(7-2)-gt3-gt4-gt(5-1)-gt
(7-1)-gt2
5-2
5-1
100
Summary BSP Trees

• Pros
• Simple, elegant scheme
• No depth comparisons needed
• Polygons split and ordered automatically
• Only writes to framebuffer (i.e., painters
  algorithm)

101
Summary BSP Trees

• Cons
• Computationally intense preprocess stage
  restricts algorithm to static scenes
• Worst-case time to construct tree O(n3)
• Splitting increases polygon count
• Again, O(n3) worst case
• Redraws same pixel many times
• Choosing splitting plane not an exact science

102
Improved BSP Rendering

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

103
Improved BSP Rendering

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

View frustum
104
Improved BSP Rendering

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

105
Outline

• Backface Culling
• Painters algorithm
• BSP
• Scan line
• Z-buffer
• Ray casting
• Reading section 9-1 to 9-11