# MidPoint Line Drawing Algorithm Solved Example

### MidPoint Line Drawing Algorithm Solved Example

We have three most popular line drawing algorithms in computer graphics.

1. DDA Line Drawing Algorithm

2. Bresenham Line Drawing Algorithm

3. Mid Point Line Drawing Algorithm

In this tutorial, we will discuss the Midpoint line algorithm and also, solve a numarical example using the Bresenham algorithm.

### Bresenham Algorithm

MidPoint Line Drawing Algorithm is one of the simplest and most powerful line drawing algorithm in computer graphics. This algorithm overcomes the disadvantages of DDA algorithm.

Given –

Starting coordinates = (X, Y)

Ending coordinates = (Xn, Yn)

A four-step approach is followed to generate the line.

Step 1:

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

These parameters are calculated as –

ΔX = Xn – X

ΔY =Yn – Y

Step 2:

Calculate the value of initial decision parameter and ΔD.

These parameters are calculated as –

Dinitial = 2ΔY – ΔX

ΔD = 2(ΔY – ΔX)

This Dinitial is used to decide, whether the X coordinate should be incremented or the Y coordinate should be incremented or both.

Step 3:

Suppose the current point is (Xk, Yk) and the next point is (Xk+1, Yk+1).

The decision whether to increment X or Y coordinate or both depends upon the values of Dinitial. Find the next point by following the below three cases –

Case 1: if (Dinitial<0)

Xk+1= Xk + 1

Yk+1= Yk

Dnew = Dinitial + 2ΔY

Case 2: if (Dinitial >= 0)

Xk+1= Xk + 1

Yk+1= Yk + 1

Dnew = Dinitial + ΔD

Step 4:

Dnew will become the decision parameter for the next iteration. (Xk+1, Yk+1) is the (Xk+1, Yk+1) in the next iteration. Keep repeating Step-03 until the endpoint is reached or the number of iterations equals to (ΔX-1) times.