Describe the Steps in Dda Algorithm for Circle Drawing

Line Drawing Algorithms-

In computer graphics, popular algorithms used to generate lines are-

1. Digital Differential Analyzer (DDA) Line Cartoon Algorithm
2. Bresenham Line Cartoon Algorithm
3. Mid Point Line Drawing Algorithm

In this article, we will discuss about DDA Algorithm.

DDA Algorithm-

DDA Algorithm is the simplest line drawing algorithm.

Given the starting and catastrophe coordinates of a line,

DDA Algorithm attempts to generate the points betwixt the starting and ending coordinates.

Procedure-

Given-

• Starting coordinates = (X₀, Y₀)
• Catastrophe coordinates = (X_{due north}, Y_n)

The points generation using DDA Algorithm involves the post-obit steps-

Pace-01:

Calculate ΔX, ΔY and M from the given input.

These parameters are calculated as-

• ΔX = X_n – 10₀
• ΔY =Y_n – Y₀
• M = ΔY / ΔX

Step-02:

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

if (absolute (ΔX) > absolute (ΔY))

Steps = accented (ΔX);

else

Steps = absolute (ΔY);

Step-03:

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

Find the next indicate by post-obit the beneath 3 cases-

Step-04:

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

PRACTICE PROBLEMS BASED ON DDA ALGORITHM-

Trouble-01:

Calculate the points between the starting point (5, vi) and ending point (8, 12).

Solution-

Given-

• Starting coordinates = (X₀, Y₀) = (5, half-dozen)
• Ending coordinates = (Ten_n, Y_north) = (8, 12)

Step-01:

Summate ΔX, ΔY and M from the given input.

• ΔX = X_northward – X₀ = 8 – 5 = 3
• ΔY =Y_{due north} – Y₀ = 12 – 6 = 6
• M = ΔY / ΔX = 6 / iii = 2

Step-02:

Calculate the number of steps.

Every bit |ΔX| < |ΔY| = iii < half dozen, then number of steps = ΔY = 6

Step-03:

Equally M > i, so case-03 is satisfied.

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

Xp	Yp	Tenp+one	Yp+one	Circular off (Xp+1, Yp+1)
5	6	5.5	seven	(vi, 7)
		6	8	(6, 8)
		6.5	9	(7, 9)
		7	10	(7, 10)
		7.5	xi	(8, 11)
		8	12	(eight, 12)

Trouble-02:

Calculate the points between the starting point (5, vi) and ending signal (13, x).

Solution-

Given-

• Starting coordinates = (10₀, Y₀) = (5, 6)
• Ending coordinates = (X_northward, Y_n) = (13, x)

Pace-01:

Calculate ΔX, ΔY and M from the given input.

• ΔX = Ten_n – X₀ = 13 – five = eight
• ΔY =Y_n – Y₀ = 10 – 6 = iv
• Yard = ΔY / ΔX = iv / 8 = 0.50

Footstep-02:

Calculate the number of steps.

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

Step-03:

Every bit One thousand < 1, so example-01 is satisfied.

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

Tenp	Yp	Xp+one	Yp+i	Round off (Xp+ane, Yp+1)
v	6	6	6.5	(6, 7)
		seven	seven	(7, 7)
		8	7.5	(eight, 8)
		9	8	(9, 8)
		ten	8.5	(x, 9)
		eleven	9	(eleven, 9)
		12	ix.5	(12, 10)
		thirteen	x	(13, 10)

Problem-03:

Calculate the points between the starting point (1, 7) and ending point (11, 17).

Solution-

Given-

• Starting coordinates = (Ten₀, Y₀) = (ane, 7)
• Catastrophe coordinates = (Ten_north, Y_n) = (11, 17)

Stride-01:

Calculate ΔX, ΔY and Chiliad from the given input.

• ΔX = Ten_n – 10₀ = 11 – i = 10
• ΔY =Y_{due north} – Y₀ = 17 – vii = 10
• M = ΔY / ΔX = 10 / 10 = ane

Step-02:

Calculate the number of steps.

Every bit |ΔX| = |ΔY| = ten = 10, so number of steps = ΔX = ΔY = 10

Step-03:

As M = 1, so case-02 is satisfied.

Now, Stride-03 is executed until Footstep-04 is satisfied.

Xp	Yp	Xp+1	Yp+1	Round off (10p+1, Yp+1)
1	7	2	eight	(2, 8)
		3	ix	(iii, nine)
		4	x	(iv, 10)
		v	11	(5, 11)
		vi	12	(6, 12)
		seven	13	(vii, 13)
		eight	fourteen	(8, 14)
		9	15	(9, 15)
		ten	xvi	(10, sixteen)
		11	17	(11, 17)

Advantages of DDA Algorithm-

The advantages of DDA Algorithm are-

• It is a simple algorithm.
• Information technology is like shooting fish in a barrel to implement.
• It avoids using the multiplication operation which is costly in terms of time complexity.

Disadvantages of DDA Algorithm-

The disadvantages of DDA Algorithm are-

• At that place is an extra overhead of using circular off( ) function.
• Using round off( ) function increases time complexity of the algorithm.
• Resulted lines are not shine because of round off( ) function.
• The points generated by this algorithm are non accurate.

To gain better agreement most DDA Algorithm,

Lookout man this Video Lecture

Next Article- Bresenham Line Drawing Algorithm

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Summary

Article Name

DDA Algorithm | Line Drawing Algorithms

Description

Line Drawing Algorithms- In computer graphics, DDA Line Drawing Algorithm is the simplest line drawing algorithm. DDA Line Drawing Algorithm attempts to generate the points betwixt the starting and ending coordinates.

Author

Akshay Singhal

Publisher Name

Gate Vidyalay

Publisher Logo

bardenalievespecon67.blogspot.com

Source: https://www.gatevidyalay.com/dda-algorithm-line-drawing-algorithms/

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