Post on 19-Dec-2015
1
CSCE 441: Computer GraphicsScan Conversion of Polygons
Jinxiang Chai
2/95
OpenGL Geometric Primitives
All geometric primitives are specified by vertices
GL_QUAD_STRIPGL_QUAD_STRIP
GL_POLYGONGL_POLYGON
GL_TRIANGLE_STRIPGL_TRIANGLE_STRIP
GL_TRIANGLE_FANGL_TRIANGLE_FAN
GL_POINTSGL_POINTSGL_LINESGL_LINES
GL_LINE_LOOPGL_LINE_LOOPGL_LINE_STRIPGL_LINE_STRIP
GL_TRIANGLESGL_TRIANGLES
GL_QUADSGL_QUADS
3/95
OpenGL Geometric Primitives
All geometric primitives are specified by vertices
GL_QUAD_STRIPGL_QUAD_STRIP
GL_POLYGONGL_POLYGON
GL_TRIANGLE_STRIPGL_TRIANGLE_STRIP
GL_TRIANGLE_FANGL_TRIANGLE_FAN
GL_POINTSGL_POINTSGL_LINESGL_LINES
GL_LINE_LOOPGL_LINE_LOOPGL_LINE_STRIPGL_LINE_STRIP
GL_TRIANGLESGL_TRIANGLES
GL_QUADSGL_QUADS
4/95
OpenGL Geometric Primitives
All geometric primitives are specified by vertices
GL_QUAD_STRIPGL_QUAD_STRIP
GL_POLYGONGL_POLYGON
GL_TRIANGLE_STRIPGL_TRIANGLE_STRIP
GL_TRIANGLE_FANGL_TRIANGLE_FAN
GL_POINTSGL_POINTSGL_LINESGL_LINES
GL_LINE_LOOPGL_LINE_LOOPGL_LINE_STRIPGL_LINE_STRIP
GL_TRIANGLESGL_TRIANGLES
GL_QUADSGL_QUADS
5/95
Drawing General Polygons
How to draw every interior pixels?
?
6/95
Drawing Curved Objects
How to draw every interior pixels?
?
7/95
Outline
Methods for drawing polygons or curved objects
- Scanline conversion of polygons
- Boundary-fill
- Flood-fill
Required readings:
- HB 4-9 to 4-14
8/95
Drawing Rectangles
Which pixels should be filled?
9/95
Drawing Rectangles
Is this correct?
10/95
Drawing Rectangles
What if two rectangles overlap?
11/95
Drawing Rectangles
Is this correct?
12/95
Drawing Rectangles
Is this correct? Overlap!!!
13/95
Drawing Rectangles
Solution: Exclude pixels on top and right
14/95
Drawing Rectangles
Artifacts are possible
15/95
General Polygons – Basic Idea
How to draw every interior pixels?
16/95
General Polygons – Basic Idea
How to draw every interior pixels for a scan line?
17/95
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
18/95
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
Use coherence to
speed up
19/95
General Polygons – Basic Idea
Intersect scan lines with edges Find ranges along x Fill interior of those
ranges
Use coherence to
speed up
Edges intersecting one scan line are
mostly same as those intersecting
previous scan line
20/95
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
21/95
How to store polygon edges?
22/95
General Polygons – Data Structures
Sorted Edge Table:
01234567
Sca
n L
ines
Edges
Store a linked-list per scan-line.
Insert edges into table at scan-
line associated with lowest end-
point.
23/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
Sorted Edge Table
24/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
Sorted Edge Table
25/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
Sorted Edge Table
26/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
Sorted Edge Table
Exclude horizontal edges!
27/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
Sorted Edge Table
28/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
Sorted Edge Table
29/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
30/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Which edges are intersecting with the current scan
line?
31/95
General Polygons – Data Structures
Active Edge List:
Edges
List of all edges intersecting
current scan-line sorted by their
x-values
32/95
General Polygons – Data Structures
Active Edge List:
Edges
List of all edges intersecting
current scan-line sorted by their
x-values
Implement active edge list with linked list
33/95
General Polygons – Data Structures
Active Edge List:
Edges
List of all edges intersecting
current scan-line sorted by their
x-values
Implement active edge list with linked list
So what kind of information should be stored in the linked list for our polygon drawing algorithm?
34/95
General Polygons – Data Structures
Edge:
maxY: highest y-value
currentX: x-value of end-point
with lowest y-value
xIncr: 1 / slope
mazY
currentX
xIncr
Edge
35/95
Scan line intersection
kk
kk
xx
yym
1
1
Scan line yk+1Scan line yk
mxx kk
11
),( 00 yx
m
kxxk 0
),( endend yx
),( 11 kk yx
),( kk yx
36/95
Scan line intersection
),( 11 kk yx
),( kk yx
kk
kk
xx
yym
1
1
Scan line yk+1Scan line yk
mxx kk
11
),( 00 yx
m
kxxk 0
),( endend yx
37/95
General Polygons – Data Structures
Edge:
maxY: highest y-value
currentX: x-value of end-point
with lowest y-value
xIncr: 1 / slope
mazY
currentX
xIncr
Edge
Horizontal edges will not be used!!!
38/95
General Polygons – Algorithm
line = 0
While (line < height )
Add edges to Active Edge List from Sorted Edge Table starting at line
Remove edges that end at line
Fill pixels
Increment x-values on edges in Active Edge List
Increment line
39/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Active Edge List
40/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Active Edge List
maxY
currentX
xIncr
AG
30
32
600
AB
41/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Active Edge List?
42/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Active Edge List
maxY
currentX
xIncr
ED
55
21
33
21
FG
43/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Active Edge List
maxY
currentX
xIncr
ED
55
21
33
21
FG
Is it correct?
44/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Sorted Edge Table
Active Edge List
AG
33
2
32
600
AB
maxY
currentX
xIncr
ED
55
21
33
21
FG
45/95
General Polygons – Algorithm
line = 0
While (line < height )
Add edges to Active Edge List from Sorted Edge Table starting at line
Remove edges that end at line
Fill pixels
Increment x-values on edges in Active Edge List
Increment line
46/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
AG
33
2
32
600
AB
maxY
currentX
xIncr
ED
55
21
33
21
FG
47/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
AG
33
2
32
600
AB
maxY
currentX
xIncr
ED
55
21
33
21
FG
? ? ? ?
48/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
AG
33
4
32
600
AB
maxY
currentX
xIncr
ED
52
15
21
32
12
21
FG
49/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
AG
33
4
32
600
AB
maxY
currentX
xIncr
ED
52
15
21
32
12
21
FG
50/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
AG
32
32
600
AB
maxY
currentX
xIncr
ED
56
21
32
21
FG
51/95
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 scan line
52/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
AG
32
32
600
AB
maxY
currentX
xIncr
ED
56
21
32
21
FG
53/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
ED
56
21
54/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
ED
56
21
55/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
ED
52
16
21
56/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
ED
52
16
21
57/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
ED
57
21
CD
77
2
58/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
ED
52
16
21
CD
772
59/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
CD
772
60/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
600
AB
maxY
currentX
xIncr
CD
772
61/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
703
BC
maxY
currentX
xIncr
CD
752
600
AB
62/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
703
BC
maxY
currentX
xIncr
CD
752
600
AB
63/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
703
BC
maxY
currentX
xIncr
CD
752
64/95
General Polygons – Example
0 1 2 3 4 5 6 70
1
2
3
4
5
6
7
A
B
C
D
EF
G
01234567
AB AG
FG ED
CD
BC
Active Edge Table
Active Edge List
733
BC
maxY
currentX
xIncr
CD
732
65/95
General Polygons – Algorithm
line = 0
While (line < height )
Add edges to Active Edge List from Sorted Edge Table starting at line
Remove edges that end at line
Fill pixels
Increment x-values on edges in Active Edge List
Increment scan line
66/95
Pixel Fill-in
Which intervals should we draw?
67/95
Pixel Fill-in
Which intervals should we draw? - Odd intervals. But need to pay attention to scan lines
passing through vertices.
68/95
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)
69/95
Curved Boundaries
How to deal with curved boundaries?
70/95
Boundary Fill
Start with drawn boundaries 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
71/95
Boundary Fill
Start with drawn boundaries 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
72/95
Boundary Fill
Work for inner and outer boundaries
73/95
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
74/95
Boundary Fill
How to define a neigbhbor?
4-connected 8-connected
75/95
Boundary Fill – Example
Black pixels indicate boundary pixels
76/95
Boundary Fill – Example
77/95
Boundary Fill – Example
Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!
78/95
Boundary Fill – Example
Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!
79/95
Boundary Fill – Example
Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!
80/95
Boundary Fill – Example
Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!
81/95
Boundary Fill – Example
Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!
82/95
Boundary Fill
83/95
How to deal with this?
Multiple color boundaries?
How to paint this region to yellow?
84/95
How to deal with this?
Multiple color boundaries?
How to paint this region to yellow?
Three keys:- a start pixel
- a target color
- a paint color
85/95
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 are recolored
86/95
Flood Fill – Example
87/95
Flood Fill – Example
88/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
89/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
90/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
91/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
92/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
93/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
94/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
95/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
96/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
97/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!
98/95
Flood Fill – Example
Continue setting the colors for neighboring pixels if it is interior pixels!