university of missouri at columbia 2d scan-line conversion university of missouri at columbia
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![Page 1: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/1.jpg)
University of Missouri at Columbia
2D Scan-line Conversion
University of Missouri at Columbia
![Page 2: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/2.jpg)
University of Missouri at Columbia
2D Scan-line Conversion• DDA algorithm
• Bresenham’s algorithm
• DDA algorithm
• Bresenham’s algorithm
![Page 3: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/3.jpg)
University of Missouri at Columbia
DDA algorithm• The simplest algorithm.
• Named after Digital Differential Analyzer.
• The simplest algorithm.
• Named after Digital Differential Analyzer.
(x1, y1)
(x0, y0)
dy
dxmySo
xxmy
m
dx
dy
xx
yym
,
1,
1001
01
![Page 4: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/4.jpg)
University of Missouri at Columbia
DDA Algorithm
![Page 5: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/5.jpg)
University of Missouri at Columbia
DDA Algorithm
![Page 6: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/6.jpg)
University of Missouri at Columbia
DDA Algorithm
![Page 7: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/7.jpg)
University of Missouri at Columbia
DDA Algorithm
![Page 8: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/8.jpg)
University of Missouri at Columbia
DDA Algorithm
![Page 9: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/9.jpg)
University of Missouri at Columbia
DDA Algorithm
![Page 10: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/10.jpg)
University of Missouri at Columbia
2D Scan-line Conversion• DDA algorithm
• Bresenham’s algorithm
• DDA algorithm
• Bresenham’s algorithm
![Page 11: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/11.jpg)
University of Missouri at Columbia
Bresenham’s Midpoint Algorithm• DDA is simple, efficient, but needs floating points.• Bresenham’s use integer addition only.
• DDA is simple, efficient, but needs floating points.• Bresenham’s use integer addition only.
(x1, y1)
(x0, y0)
dy
dx
![Page 12: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/12.jpg)
University of Missouri at Columbia
Bresenham’s Midpoint Algorithm• To choose from the two pixels NE or E depending on the relative
position of the midpoint M and the line.
• Choose E if M is above the line,
• Choose NE if M is below the line.
• To choose from the two pixels NE or E depending on the relative position of the midpoint M and the line.
• Choose E if M is above the line,
• Choose NE if M is below the line.
M
E
NE
(x0, y0)
![Page 13: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/13.jpg)
University of Missouri at Columbia
Bresenham’s Midpoint Algorithm
M
E
NE
(x0, y0)0),(
so line, theon is ),(point Since
0),(
:formImplicit
:equation Line
0000
00
dxbydxxdyyxF
yx
dxbydxxdyyxF
bxdx
dybmxy
• Choose NE if d is positive,
• Choose E if d is negative.
• Choose NE if d is positive,
• Choose E if d is negative.
![Page 14: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/14.jpg)
University of Missouri at Columbia
Bresenham’s Midpoint Algorithm
M
E
NE
(x0, y0)
dxdyd
dxdyyxF
dxdyyxF
d
2
2),1(2
),1(
: variabledecision the
of value theon depends choice The
1
21
00
21
21
00
• Choose NE if d is positive,
• Choose E if d is negative.
• Choose NE if d is positive,
• Choose E if d is negative.
![Page 15: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/15.jpg)
University of Missouri at Columbia
Incremental Calculation of the decision variable dnew
dxdyd
dxbydxxdy
yxFd
NEif
dyd
dxbydxxdy
yxFd
Eif
dxbydxxdyyxFdSince
old
new
old
new
22
2)(2)2(2
),2(2
, choose
2
2)(2)2(2
),2(2
, choose
222),(2
23
00
23
00
21
00
21
00
M
E
NE
(x0, y0)
![Page 16: University of Missouri at Columbia 2D Scan-line Conversion University of Missouri at Columbia](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d5f5503460f94a3ed23/html5/thumbnails/16.jpg)
University of Missouri at Columbia
Bresenham’s Midpoint Algorithm
M
E
NE
(x0, y0)
NEfxyd
Eifydd
old
oldnew choose ,22
choose ,2