Question

Using DDA algorithm, find the pixels for the line drawn from (8, 8) to (16, 14)..

Answer 1

Procedure-

Given-

• Starting coordinates = (X₀, Y₀)
• Ending coordinates = (X_n, Y_n)

The points generation using DDA Algorithm involves the following steps-

Step-01:

Calculate ΔX, ΔY and M from the given input.

These parameters are calculated as-

• ΔX = X_n – X₀
• ΔY =Y_n – Y₀
• M = ΔY / ΔX

Step-02:

Find the number of steps or points in between the starting and ending coordinates.

if (absolute (ΔX) > absolute (ΔY))

Steps = absolute (ΔX);

else

Steps = absolute (ΔY);

Step-03:

Suppose the current point is (X_p, Y_p) and the next point is (X_p+1, Y_p+1).

Find the next point by following the below three cases-

Step-04:

Keep repeating Step-03 until the end point is reached or the number of generated new points (including the starting and ending points) equals to the steps count.

solution

Given-

• Starting coordinates = (X₀, Y₀) = (8,8)
• Ending coordinates = (X_n, Y_n) = (16,14)

step 1

• Calculate ΔX, ΔY and M from the given input.

• ΔX = X_n – X₀ = 16-8 = 8
• ΔY =Y_n – Y₀ = 14-8 = 6
• M = ΔY / ΔX = 6 / 8 = 3/4=0.75=M

Step-02:

Calculate the number of steps.

As |ΔX| > |ΔY| = 8 > 6, so number of steps = ΔX = 8

Step-03:

As M < 1, so case-01 is satisfied.

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

Xp	Yp	Xp+1	Yp+1	Round off (Xp+1, Yp+1)
8	8	9	8.75	(9, 9)
		10	9.5	(10, 10)
		11	10.25	(11,10 )
		12	11	(12, 11)
		13	11.75	(13, 12)
		14	12.5	(14,13)

		15	13.25	(15, 13)
		16	14	(16, 14)