Digital Differential Analyzer (DDA) Algorithm in Computer Graphics

 
Dr. Snehlata Barde
 Profesor  & HoD, MSIT
MATS University,Raipur
 
In 
Computer Graphics 
the 
first basic line drawing
algorithm is Digital 
Differential 
Analyzer (DDA)
Algorithm.
A 
line 
connects 
two 
points. 
It 
is a basic element in
graphics. 
To 
draw a line, you need 
two 
points
between which you can draw a
 
line.
In 
computer graphics, a digital 
differential 
analyzer
(DDA) is hardware or software used 
for
interpolation 
of 
variables over an interval between
start 
and end point. DDAs are used 
for 
rasterization
of 
lines, triangles and polygons
.
 
DIGITAL 
DIFFERENTIAL 
ANALYZER 
(DDA)  ALGORITHM.
 
COMPUTER HAS 
TO 
TAKE 
CARE 
OF 
2
 
THINGS
:
 
Pixels
- Which 
pixels 
to
 
plot.
 
Computations
- 
Computations required 
to 
calculate pixel
 
positions
 
SLOPE INTERCEPT LINE
 
EQ:
 
y = mx +
 
b
m =
 
slope
b = 
is 
the y 
intercept, is 
called 
as 
“slope 
intercept
 
line
equation.”
Therefore
 
Slope(m) =
 
dy/dx
 
(
D
D
A
)
 
A
L
G
O
R
I
T
H
M
 
Step 1 Input the coordinates of the Two end
points A(x1, y1) and B(x2, y2) for the line AB
respectively. Note that points A and B are not
equal. (If they are equal, then it is a point. Plot
the point and return.)
Step 2: [Calculate dx and dy]
  
dx = (x2 — x1) and dy = (y2— y1)
Step 3: [Calculate the length L]
  
If (abs (x2 — x1) >abs (y2 — yl)) then
               L = abs(x2 — x1)
     
 
Else L = abs (y2 — y1)
 
 
(
D
D
A
)
 
A
L
G
O
R
I
T
H
M
 
(
D
D
A
)
 
A
L
G
O
R
I
T
H
M
 
A
D
V
A
N
T
AGES
 
1. It 
is 
the 
simplest algorithm and 
it 
does 
not 
require
special skills 
for
 
implementation.
 
2. It 
is a 
faster 
method 
for 
calculating 
pixel 
positions
than the direct use 
of 
equation 
y=mx + b. It
eliminates the multiplication in 
the 
equation by
making use 
of raster characteristics, 
so 
that
appropriate increments are applied in 
the x 
or 
y
direction 
to 
find 
the 
pixel 
positions along 
the 
line
path.
 
DISVANTANGES
 
1. 
Floating point arithmetic in DDA algorithm is still
time-consuming.
2. The 
algorithm is orientation dependent. Hence
end point accuracy is
 
poor.
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In computer graphics, the Digital Differential Analyzer (DDA) Algorithm is utilized as the basic line drawing algorithm. This method involves interpolation of variables between two endpoints to rasterize lines, triangles, and polygons efficiently. The algorithm requires inputting coordinates of two endpoints, calculating increments, and plotting pixels along the line. With advantages such as simplicity and speed, it serves as a fundamental tool for graphics rendering.


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  1. DDA Line Algorithm Dr. Snehlata Barde Profesor & HoD, MSIT MATS University,Raipur

  2. DIGITAL DIFFERENTIAL ANALYZER (DDA) ALGORITHM. In Computer Graphics the first basic line drawing algorithm is Digital Differential Analyzer (DDA) Algorithm. A line connects two points. It is a basic element in graphics. To draw a line, you need two points between which you can draw a line. In computer graphics, a digital differential analyzer (DDA) is hardware or software used for interpolation of variables over an interval between start and end point. DDAs are used for rasterization of lines, triangles and polygons.

  3. COMPUTER HAS TO TAKE CARE OF 2 THINGS: Pixels - Which pixels to plot. Computations - Computations required to calculate pixel positions

  4. SLOPE INTERCEPT LINEEQ: y = mx + b m = slope b = is the y intercept, is called as slope interceptline equation. Therefore Slope(m) = dy/dx Slope(m) = ??+1-?? /??+1-??

  5. (DDA)ALGORITHM Step 1 Input the coordinates of the Two end points A(x1, y1) and B(x2, y2) for the line AB respectively. Note that points A and B are not equal. (If they are equal, then it is a point. Plot the point and return.) Step 2: [Calculate dx and dy] dx = (x2 x1) and dy = (y2 y1) Step 3: [Calculate the length L] If (abs (x2 x1) >abs (y2 yl)) then L = abs(x2 x1) Else L = abs (y2 y1)

  6. (DDA) ALGORITHM Step 4: [Calculate the increment factor] x = (x2 x1)/L and y = (y2 y1)/L This step makes either x or y equal to 1, because L is either |x2 - x1| or |y2 y1| Therefore, a step increment in x or y direction is equal to 1. Step 5: [Initialize the initial point on the line and plot] xnew=x1 + 0.5 and ynew= ?1+ 0.5 Plot (Integer (????), Integer (????)) The values are rounded using the factor of 0.5 rather than truncating, so that the central pixel addressing is handled correctly. Moreover, the sign function given makes the algorithm work in all the quadrants.

  7. (DDA) ALGORITHM step 6: [Obtain the new pixel on the line and plot the same] Initialize i to 1 While (i<= L){ xnew = xnew+ x ????= ????+ y Plot (Integer(????), Integer(????)) i = i + 1} Step 7: Finish

  8. ADVANTAGES 1. It is the simplest algorithm and it does not require special skills for implementation. 2. It is a faster method for calculating pixel positions than the direct use of equation y=mx + b. It eliminates the multiplication in the equation by making use of raster characteristics, so that appropriate increments are applied in the x or y direction to find the pixel positions along the line path.

  9. DISVANTANGES 1. Floating point arithmetic in DDA algorithm is still time-consuming. 2. The algorithm is orientation dependent. Hence end point accuracy is poor.

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