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Dr. Scott Schaefer

Hidden Surfaces

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Hidden Surfaces

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Hidden Surfaces

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Hidden Surfaces

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Backface Culling

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Backface Culling

view direction

v

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Backface Culling

view direction

n

v

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Backface Culling

view direction

n

v

0vn , draw polygon

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Backface Culling

view direction

n

v

0vn , cull polygon

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Backface Culling

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Backface Culling

1

2

3

counter clock-wise orientation, draw polygon

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Backface Culling

1

2

3

clock-wise orientation, cull polygon

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Backface Culling

Advantages Improves rendering speed by removing

roughly half of polygons from scan conversion

DisadvantagesAssumes closed surface with consistently

oriented polygonsNOT a true hidden surface algorithm!!!

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Backface Culling

Is this all we have to do?

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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

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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?

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Painter’s Algorithm

Sort polygons according to distance from viewer

Draw from back to front

How do we sort polygons?

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Painter’s Example

z = 0.7z = 0.3

z = 0.1

Sort by depth:Green rectRed circle

Blue triz = 0

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Painter’s Algorithm

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

Painter’s Algorithm

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Painter’s Algorithm

1. Sort all objects’ zmin and zmax

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Painter’s Algorithm

1. Sort all objects’ zmin and zmax

2. If an object is uninterrupted (its zmin and zmax are adjacent in the sorted list), it is fine

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Painter’s Algorithm

1. Sort all objects’ zmin and zmax

2. If an object is uninterrupted (its zmin and zmax are adjacent in the sorted list), it is fine

3. 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

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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

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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

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Painter’s Algorithm-Summary

AdvantagesSimple algorithm for ordering polygons

DisadvantagesSorting criteria difficult to produceRedraws same pixel many timesSorting can also be expensive

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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” valueUpdate buffer with closest depth value

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Depth (“Z”) Buffer

AdvantagesSimple to implementAllows for a streaming approach to

polygon drawing Disadvantages

Requires extra storage spaceStill lots of overdraw

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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

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BSP Trees: Objects

1 2 3

45

6 78

9

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BSP Trees: Objects

1 2 3

45

6 78

9

+

-

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BSP Trees: Objects

1 2 3

45

6 78

9

985 61 42 3

Put front objects in the left branch

7

+

--+

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BSP Trees: Objects

1 2 3

45

6 78

9

985 61 42 3

Put front objects in the left branch

7

-+

-+ -+

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BSP Trees: Objects

1 2 3

45

6 78

9

895 6

1

32 4

Put front objects in the left branch

7

-+

-+ -+

-+ -+ -+

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BSP Trees: Objects

1 2 3

45

6 78

9

865 6

1

32

2 4

Put front objects in the left branch

7 9

-+

-+ -+

+ + -+- -

+ - + -

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BSP Trees: Objects

1 2 3

45

6 78

9

865 6

1

32

2 4

Put front objects in the left branch

7 9

-+

-+ -+

+ + -+- -

+ - + -

When to stop the recursion?

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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

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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

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Building a BSP Tree

1 2

3

4

5

6

7

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Building a BSP Tree

1 2

3

4

5

6

7

2,3,4,5,6,7

1

b

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

3

7-2,6, 5-2

1

b

bf

2,4,5-1,7-1

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2 4, 5-1

3

7-17-2,6, 5-2

1

b

b

b

f

f

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2

5-1

3

7-1

47-2,6, 5-2

1

b

b

b

b

f

f

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2

5-1

3

7-1

47-2,6, 5-2

1

b

b

b

b

f

f

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2

5-1

3

7-1

47-2,6, 5-2

1

b

b

b

b

f

f

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2

7-2

5-1

3

7-1

46, 5-2

1

b b

b

b

b

f

f

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

5-2

2

7-2

5-1

3

7-1

46

1

b b

bb

b

b

f

f

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2

7-2

5-1

3

7-1

46

1

b b

b

b

b

f

f

5-2

b

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2

7-2

Building a BSP Tree

1 2

3

4

6

5-1

3

7-1

46

1

7-2

7-1

5-2

5-1

b b

b

b

b

f

f

5-2

b

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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

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BSP Trees: Objects

1 2 3

45

6 78

9

865 6

1

32

2 4

Correctly traversing this tree enumerates objects from back to front

7 9

-+

-+ -+

+ + -+- -

+ - + -

Traversal order?

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BSP Trees: Objects

1 2 3

45

6 78

9

865 6

1

32

2 4

Correctly traversing this tree enumerates objects from back to front

7 9

-+

-+ -+

+ + -+- -

+ - + -

Traversal order:8->9->7->6->5->3->4->2->1

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

Traversal order: 2

7-2

5-1

3

7-1

46

1

b b

b

b

b

f

f

5-2

b

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

Traversal order:6->(5-2)->(7-2)->3->(5-1)->4->(7-1)->2->1

2

7-2

5-1

3

7-1

46

1

b b

b

b

b

f

f

5-2

b

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

Traversal order: 2

7-2

5-1

3

7-1

46

1

b b

b

b

b

f

f

5-2

b

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

2

7-2

5-1

3

7-1

46

1

b b

b

b

b

f

f

5-2

bTraversal order:1->2->(7-1)->4->(5-1)->3->(7-2)->(5-2)->6

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Building a BSP Tree

1 2

3

4

6

7-2

7-1

5-2

5-1

Traversal order? 2

7-2

5-1

3

7-1

46

1

b b

b

b

b

f

f

5-2

b

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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

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Improved BSP Rendering

Take advantage of view direction to cull away polygons behind viewer

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Improved BSP Rendering

Take advantage of view direction to cull away polygons behind viewer

View frustum

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Improved BSP Rendering

Take advantage of view direction to cull away polygons behind viewer

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OpenGL and Hidden Surfaces

glEnable(GL_DEPTH_TEST);

glEnable(GL_CULL_FACE);

glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );

glCullFace ( GL_BACK );

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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

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Scan Line Algorithm

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Scan Line Algorithm

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Scan Line Algorithm

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Scan Line Algorithm

AdvantagesTakes advantage of coherence resulting in

fast algorithmDoes not require as much storage as depth

buffer Disadvantages

More complex algorithmRequires all polygons sent to GPU before

drawing