Scan Conversion of Polygons
Dr. Scott Schaefer
1
Drawing Rectangles
Which pixels should be filled?
2/70
Drawing Rectangles
Is this correct?
3/70
Drawing Rectangles
What if two rectangles overlap?
4/70
Drawing Rectangles
Is this correct?
5/70
Drawing Rectangles
Is this correct?
Overlap!!!
6/70
Drawing Rectangles
Solution: Exclude pixels on top and right
7/70
Drawing Rectangles
Artifacts are possible
8/70
General Polygons – Basic Idea
Intersect scan lines with edges
 Find ranges along x
 Fill interior of those
ranges

Don’t fill top/right
Edges may NOT match
with line drawing algo
9/70
General Polygons – Basic Idea
Intersect scan lines with edges
 Find ranges along x
 Fill interior of those
ranges

Use coherence to
speed up
Don’t fill top/right
Edges may NOT match
with line drawing algo
10/70
General Polygons – Basic Idea
Intersect scan lines with edges
 Find ranges along x
 Fill interior of those
ranges

Use coherence to
speed up
Edges intersection one scan
line are mostly same as those
intersecting previous scan line
11/70
General Polygons – Basic Idea
Intersect scan lines with edges
 Find ranges along x
 Fill interior of those
ranges

Use coherence to
speed up
The x-value of an intersection
with one scan line is close to
the intersection with the
previous one
12/70
General Polygons – Data Structures

Edge: ( x i , y i )  ( x i 1 , y i 1 )
Edge
maxY
currentX
xIncr
maxY:
max( y i , y i 1 )
y i  min( y i , y i  1 )
 xi ,
currentX: 
 x i  1 , otherwise
xIncr:
x i 1  x i
y i 1  y i
13/70
General Polygons – Data Structures

Edge: ( x i , y i )  ( x i 1 , y i 1 )
Edge
maxY
currentX
xIncr
maxY:
max( y i , y i 1 )
y i  min( y i , y i  1 )
 xi ,
currentX: 
 x i  1 , otherwise
xIncr:
x i 1  x i
y i 1  y i
Horizontal edges will not be used!!!
14/70
General Polygons – Data Structures
Scan Lines

Active Edge Table:
7
6
5
4
3
2
1
0
Store a linked-list per scanline.
Insert edges into table at
scan-line associated with
lowest end-point.
Edges
15/70
General Polygons – Data Structures

Active Edge List:
Edges
List of all edges intersecting
current scan-line sorted by
their x-values
16/70
General Polygons – Algorithm
line = 0
While (line < height )
Add edges to Active Edge List from Active Edge
Table starting at line
Remove edges that end at line
Fill pixels
Increment x-values on edges in Active Edge List
Increment line
17/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
Active Edge List
C
7
B
6
D
5
4
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
18/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
D
5
4
G
3
AB
Active Edge List
2
1
F
0
E
A
0
1
2
3
4
5
6
7
19/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
5
4
G
3
AB
Active Edge List
2
1
F
0
E
A
0
1
2
3
4
5
6
7
20/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
CD
D
5
4
G
3
AB
Active Edge List
2
1
F
0
E
A
0
1
2
3
4
5
6
7
21/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
CD
D
5
4
ED
AB
Active Edge List
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
22/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
CD
D
5
4
ED
AB
Active Edge List
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
23/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
Active Edge List
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
24/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
25/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
AG
maxY
6
3
currentX
0
0
xIncr
0
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
3
26/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
AG
FG
ED
maxY
6
3
3
5
currentX
0
2
3
5
xIncr
0
2
3
1
3
G
F
0
E
A
0
1
2
3
4
5
6
7
1
2
2
27/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
AG
FG
ED
maxY
6
3
3
5
currentX
0
2
3
5
xIncr
0
2
3
1
3
G
F
0
E
A
0
1
2
3
4
5
6
7
1
2
2
28/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
AG
FG
ED
maxY
6
3
currentX
0
4
3
2 12
5
5 12
xIncr
0
2
3
1
3
G
F
0
E
A
0
1
2
3
4
5
6
7
1
2
2
29/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
AG
FG
ED
maxY
6
3
currentX
0
4
3
2 12
5
5 12
xIncr
0
2
3
1
3
G
F
0
E
A
0
1
2
3
4
5
6
7
1
2
2
30/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
AG
FG
ED
maxY
6
3
3
5
currentX
0
2
2
6
xIncr
0
2
1
1
3
G
2
F
0
E
A
0
1
2
3
4
5
6
7
2
31/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
ED
maxY
6
5
currentX
0
6
xIncr
0
1
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
2
32/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
ED
maxY
6
5
currentX
0
6
xIncr
0
1
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
2
33/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
ED
maxY
6
currentX
0
5
6 12
xIncr
0
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
1
2
34/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
ED
maxY
6
currentX
0
5
6 12
xIncr
0
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
1
2
35/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
ED
CD
maxY
6
5
currentX
0
7
7
7
xIncr
0
1
2
G
F
0
E
A
0
1
2
3
4
5
6
7
2
36/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
3
2
1
Active Edge List
AB
ED
CD
maxY
6
7
currentX
0
5
6 12
xIncr
0
1
2
G
F
0
E
A
0
1
2
3
4
5
6
7
7
2
37/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
CD
maxY
6
7
currentX
0
7
xIncr
0
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
38/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
AB
CD
maxY
6
7
currentX
0
7
xIncr
0
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
39/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
G
3
2
1
Active Edge List
AB
BC
CD
maxY
6
7
7
currentX
0
0
5
xIncr
0
3
2
F
0
E
A
0
1
2
3
4
5
6
7
40/70
General Polygons – Example
C
Active Edge Table
7
6
5
4
3
2
1
0
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
G
3
2
1
Active Edge List
AB
BC
CD
maxY
6
7
7
currentX
0
0
5
xIncr
0
3
2
F
0
E
A
0
1
2
3
4
5
6
7
41/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
BC
CD
maxY
7
7
currentX
0
5
xIncr
3
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
42/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
BC
CD
maxY
7
7
currentX
0
5
xIncr
3
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
43/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
BC
CD
maxY
7
7
currentX
3
3
xIncr
3
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
44/70
General Polygons – Example
Active Edge Table
7
6
5
4
3
2
1
0
C
7
B
6
BC
D
CD
5
4
FG
ED
AB
AG
Active Edge List
BC
CD
maxY
7
7
currentX
3
3
xIncr
3
2
G
3
2
1
F
0
E
A
0
1
2
3
4
5
6
7
45/70
General Polygons – Problems

Sliver polygons may not be drawn correctly
No simple solution
 Long, thin triangles
cause problems
 Want triangles with
good aspect ratio
(close to equilateral)

46/70
Boundary Fill
Start with drawn outline of a polygon and an
interior point
 Recursively recolor outward from that point
• If neighbor different, then recolor and
recur


Everything within the boundary is changed to
that color
47/70
Boundary Fill

How to define a neighbor?
4-connected
8-connected
48/70
Boundary Fill – Example
49/70
Boundary Fill – Example
50/70
Boundary Fill – Example
51/70
Boundary Fill – Example
52/70
Boundary Fill – Example
53/70
Boundary Fill – Example
54/70
Flood Fill
Start with a point
 Define color under that point as the interior
color
 Recursively recolor outward from that point
• If neighbor is interior color, then recolor
and recur


Contiguous regions of the same color are
recolored
55/70
Flood Fill – Example
56/70
Flood Fill – Example
57/70
Flood Fill – Example
58/70
Flood Fill – Example
59/70
Flood Fill – Example
60/70
Flood Fill – Example
61/70
Flood Fill – Example
62/70
Flood Fill – Example
63/70
Flood Fill – Example
64/70
Flood Fill – Example
65/70
Flood Fill – Example
66/70
Flood Fill – Example
67/70
Flood Fill – Example
68/70
OpenGL: Drawing Polygons
Lots of different primitives supported
 GPU only draws triangles
• OpenGL triangulates all polygons
• Problems with concave polygons!
 How data is passed to GPU makes a
significant difference in speed

GL_TRIANGLES
GL_TRIANGLE_STRIP
GL_TRIANGLE_FAN
GL_QUADS
GL_QUAD_STRIP
GL_POLYGON
69/70
Performance
Nvidia 7300
GT1
Nvidia 8800
GTX1
ATI Radeon
HD 48502
ATI Radeon
HD 48502
New Drivers
Immediate Mode
15.5
15.5
21.0
33.0
Display Lists
28.3
22.0
463.5
497.5
Vertex Arrays
33.5
35.5
75.0
335.0
Vertex Buffer
Objects
50.0
200.0
476.3
506.0
1
2
Frames per second displaying a 413,236 triangle model. CPU was an Intel Core 2 6700 or Core i7 940 .
70/70