Hidden Surfaces - TAMU Computer Science Faculty Pages
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Transcript Hidden Surfaces - TAMU Computer Science Faculty Pages
Hidden Surfaces
Dr. Scott Schaefer
1
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
6/62
Backface Culling
n
view direction
v
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Backface Culling
n v 0, draw polygon
n
view direction
v
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Backface Culling
n v 0, cull polygon
n
view direction
v
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Backface Culling
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Backface Culling
1
3
2
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
Disadvantages
Assumes closed surface with consistently
oriented polygons
NOT 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 = 0.7
z = 0.3
z = 0.1
Sort by depth:
Green rect
Red circle
Blue tri
z=0
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Painter’s Algorithm
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Painter’s Algorithm
Sometimes there is NO ordering that
produces correct results!!!
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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
Advantages
Simple algorithm for ordering polygons
Disadvantages
Sorting criteria difficult to produce
Redraws same pixel many times
Sorting 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” value
Update buffer with closest depth value
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Depth (“Z”) Buffer
Advantages
Simple to implement
Allows for a streaming approach to
polygon drawing
Disadvantages
Requires extra storage space
Still 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
9
6
8
7
5
4
1
2
3
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BSP Trees: Objects
9
6
-
8
7
+
5
4
1
2
3
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BSP Trees: Objects
Put front objects in the left branch
+
9
6
-
8
7
-
+
1
2
3
4
5
6
7
8
9
5
4
1
2
3
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BSP Trees: Objects
Put front objects in the left branch
+
9
6
-
8
7
-
+
+
5
4
1
2
1
2
3
4
5
6
7
8
9
3
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BSP Trees: Objects
Put front objects in the left branch
+
9
6
-
8
7
-
+
+
5
4
1
2
-
1
+
3
2
4
-
+
3
5
6
-
+
7
9
8
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BSP Trees: Objects
Put front objects in the left branch
+
9
6
-
8
7
-
+
+
5
4
1
2
-
1
+
3
2
+
2
4
-
+
3
5
-
-
+
6
6
8
+ 7
9
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BSP Trees: Objects
Put front objects in the left branch
+
9
6
-
8
7
-
+
+
5
4
1
2
-
1
+
3
2
+
2
4
-
+
3
5
-
-
+
6
6
8
+ 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
6
7
3
1
2
5
4
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Building a BSP Tree
6
7
3
1
2
5
4
1
b
2,3,4,5,6,7
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
f
7-2,6, 5-2
3
b
2,4,5-1,7-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
f
7-2,6, 5-2
3
f
2
b
7-1
b
4, 5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
f
7-2,6, 5-2
3
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
f
7-2,6, 5-2
3
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
f
7-2,6, 5-2
3
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
f
7-2
b
3
f
6, 5-2 2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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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
Correctly traversing this tree enumerates objects from back to front
+
9
6
-
8
7
-
+
+
5
4
1
2
-
1
+
3
2
+
2
4
-
+
3
5
-
-
+
6
6
8
+ 7
9
Traversal order?
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BSP Trees: Objects
Correctly traversing this tree enumerates objects from back to front
+
9
6
-
8
7
-
+
+
5
4
1
2
-
1
+
3
2
+
2
4
-
+
3
5
-
-
+
6
6
8
+ 7
9
Traversal order:
8->9->7->6->5->3->4->2->1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
Traversal order:
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
Traversal order:
6->(5-2)->(7-2)->3->(5-1)->4->(7-1)->2->1
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
Traversal order:
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
Traversal order:
1->2->(7-1)->4->(5-1)->3->(7-2)->(5-2)->6
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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Building a BSP Tree
6
7-2
5-2
7-1
5-1
3
1
2
4
1
b
3
f
7-2
Traversal order?
b
6
b
5-2
f
2
b
7-1
b
4
b
5-1
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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
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
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