example 1 draw line segment from point 2 4 to 9 9

Question

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             x_i + 1 = x_i + 1 y_i + 1 = y_i + m

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

y_i + 1 = y_i + 1

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

x_i + 1 = x_i + 1                   y_i + 1 = y_i + 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.