Example DDA algorithm

   Example / Algorithm DDA

Ex1:/ consider the line from (0,0) to (6,6). Use the simple DDA algorithm?

sol//

x1=0  , y1=0   ,  x2=6    ,   y2=6

Length = 𝑦2− 𝑦1 = 𝑥2 − 𝑥1 =6

Δ𝑥 = (𝑥2 − 𝑥1)/𝑙𝑒𝑛𝑔𝑡ℎ

= 6/6 = 1    and

Δ𝑦 = (𝑦2 − 𝑦1)/𝑙𝑒𝑛𝑔𝑡ℎ

=6/6 = 1

Initial value for

𝑥 = 0 + 0.5 (1) =0.5

𝑌 = 0 + 0.5 (1) = 0.5

i	Plot	x	y
		0.5	0.5
1	(0,0)
		1.5	1.5
2	(1,1)
		2.5	2.5
3	(2,2)
		3.5	3.5
4	(3,3)
		4.5	4.5
5	(4,4)
		5.5	5.5
6	(5,5)
		6.5	6.5

/Ex2 /consider the line from (23,33) to (29,40) Use the simple DDA algorithm

//sol

x1=23  , y1=33  ,  x2=29   ,   y2=40

Δ𝑥 = 𝑥2 − 𝑥1 =6

Length = 𝑦2− 𝑦1=7

Δ𝑥 = (𝑥2 − 𝑥1)/𝑙𝑒𝑛𝑔𝑡ℎ

= 6/7 = 0.85   and

Δ𝑦 = (𝑦2 − 𝑦1)/𝑙𝑒𝑛𝑔𝑡ℎ

=7/7 = 1

Initial value for

𝑥 = 23 + 0.5 (0.8) =23

𝑌 = 33 + 0.5 (1) = 33.5

 

i	x	y	Plot(x,y)
1.	23.5	33.5	(23,33)
2.	24.3	34.5	(24,34)
3.	25.1	35.5	(25,35)
4.	25.9	36.5	(25, 36)
5.	26.7	37.5	(26, 37)
6.	27.5	38.5	(27, 38)
7.	28.3	39.5	(28, 39)

/Ex3/consider the line from (0,0) to (4,6). Use the simple DDA algorithm

//sol

x1=0 , y1=0 , x2=4, y2=6

Length = y2− y1 =6

Δ𝑥 = (x2 − x1)/ length = 4/6 and

Δy = (y2 − y1)/ length =6/6 = 1

 

Initial value for

𝑥 = 0+ 0.5 (4.6)=0.5

𝑌 = 0 + 0.5 (1) = 0.5

 

Ex4:/ consider the line from (5,6) to (8,12). Use the simple DDA algorithm?

sol//

Solution:

 o Given:

 Starting coordinates: (X0, Y0) = (5, 6) 

Ending coordinates: (Xn, Yn) = (8, 12) 

STEP – 01:

 o Calculate ΔX, ΔY and m from the given input.

 ΔX = Xn – X0 = 8 – 5 = 3 

ΔY =Yn – Y0 = 12 – 6 = 6 

m = ΔY / ΔX = 6 / 3 = 2 

STEP – 02:

 o Calculate the number of steps.

 As |ΔX| < |ΔY| = 3 < 6, so number of steps = ΔY = 6

STEP – 03: 

o As m > 1, so case-03 is satisfied.

 Now, Step-03 is executed until Step-04 is satisfied.

Ex5//    Using DDA algorithm, Calculate the points between the starting point (5, 6) and ending point (13, 10).

Solution:

 o Given:

 Starting coordinates: (X0, Y0) = (5, 6) 

Ending coordinates: (Xn, Yn) = (13, 10)

STEP – 01:

 o Calculate ΔX, ΔY and m from the given input.

 ΔX = Xn – X0 = 13 – 5 = 8 

ΔY =Yn – Y0 = 10 – 6 = 4 

m = ΔY / ΔX = 4 / 8 = 0.50

STEP – 02:

 o Calculate the number of steps. 

As |ΔX| > |ΔY| = 8 > 4, so number of steps = ΔX = 8

STEP – 03:

 o As m < 1, so case-01 is satisfied. 

Now, Step-03 is executed until Step-04 is satisfied.

Ex6//Using DDA algorithm, calculate the points between the starting point (1, 7) and ending point (11, 17).

Solution: 

o Given: 

Starting coordinates: (X0, Y0) = (1, 7) 

Ending coordinates: (Xn, Yn) = (11, 17)

STEP – 01:

 o Calculate ΔX, ΔY and m from the given input. 

ΔX = Xn – X0 = 11 – 1 = 10 

ΔY =Yn – Y0 = 17 – 7 = 10 

m = ΔY / ΔX = 10 / 10 = 1

STEP – 02:

 o Calculate the number of steps.

 As |ΔX| = |ΔY| = 10 = 10, so number of steps = ΔX = ΔY = 10 

STEP – 03:

 o As m = 1, so case-01 is satisfied. 

Now, Step-03 is executed until Step-04 is satisfied.

تعديل المقال