Draw line segment - digital differential analyzer algorithm, Computer Graphics

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Example 1: Draw line segment from point (2, 4) to (9, 9) by using Digital Differential Analyzer algorithm.

Solution: We know usual equation of line is specified via

y = mx+c; here m =( y1 - y0/( x1 - x0)

Specified (x0, y0) → (2, 4) ; (x1, y1) → (9, 9)

⇒ m = ( y1 -y0)/( x1 - x0)

= (9 - 4) /(9 - 2)= 5/7..that is 0< m<1

C = y1- mx1 = 9 - ((5/7)* 9) = (63 - 45)/7 = 18/7

Conversely, by Equation of line (y = mx + c) we have

Y = (5/7)x + (18/7)

DDA Algorithm Two case:

Case 1: m < 1             xi + 1 = xi + 1 yi + 1 = yi + m

Case 2: m > 1             xi + 1 = xi + (1/m)

yi + 1 = yi + 1

Since 0 < m < 1  so as per to DDA algorithm case 1

xi + 1 = xi + 1                   yi + 1 = yi + m

Specified (x0, y0) = (2, 4)

1)      x1 = x0 + 1 = 3

Y1 = y0 + m= 4 +5/7= 4 (5/7)

Place pixel (x0, round y, colour)

That is put on (3, 5)

2) x2 = x1 + 1 = 3 + 1 = 4

y2 = y1 + m = (33/7) +(5/7)

Place on (4, 5)

Likewise go on till (9, 9) is reached.


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