sketch line segment that joining by using

Question

Sketch Line Segment That Joining By Using Bresenham Line Algorithm

Example: Sketch line segment that joining (20, 10) and (25, 14) by using Bresenham line generation algorithm.

Solution: (x₀, y₀) → (20, 10)   ;   (x₁, y₁) → (25, 14)

m = (y₁- y₀)/(x₁ - x₀)

= (14- 10)/(25 - 20)

= 4/5 < 1

Like, m = (Δy)/ (Δx)

= 4/5 =› Δy = 4

→ plot point (20, 10)

p_i = 2Δy - Δx

i = 1:                 p_i = 2 * 4 - 5 = 3

Here p₁ > 0 consequently x₀ ← 21; y₀ ← 11 now plot (21, 11)

i = 2 as p₁ > 0

∴p₂ = p₁ + 2(Δy - Δx)

= 3 + 2 (4 - 5) = 3 - 2 = 1

p₂ > 0; hence x₀ ← 22; y₀ ← 12 plot (22,12)

i = 3 as p₂ > 0

∴p₃ = p₂ + 2 (Δy - Δx) = 1 + 2 (4 - 5) = - 1

p₃ < 0  ∴x₀ ← 23

y₀ ← 12

plot (23, 12)

i = 4 as p₃ < 0

∴p₄ = p₃ + 2Δy

= -1 + 2 * 4 = 7

∴ x₀ ← 24; y₀ ← 13

plot (24, 13)

i = 5 as p₄ > 0

∴p₅ = p₄ + 2 (Δy - Δx)

= 7 + 2 (4 - 5) = 5

x₀ ← 25; y₀ ← 14

Plot (25, 14)

{for i = 6, x0 will be > x_i so algorithm terminates