Examples Mid Point Line Drawing Algorithm
Ex1//Using Mid Point Algorithm calculate the points between the starting coordinates (20, 10) and ending coordinates (30, 18).
Solution:
o Given:
Starting coordinates: (X0, Y0) = (20, 10)
Ending coordinates: (Xn, Yn) = (30, 18)
STEP – 01:
o Calculate ΔX, ΔY from the given input.
ΔX = Xn – X0 = 30– 20 = 10
ΔY =Yn – Y0 = 18 – 10 = 8
STEP – 02:
o Calculate Dinitial and ΔD as:
Dinitial = 2ΔY – ΔX = 2×8 – 10 = 6
ΔD = 2(ΔY – ΔX) = 2×(8 – 10) = -4
STEP – 03:
o As Dinitial >= 0, so case-02 is satisfied. Thus,
Xk+1 = Xk + 1 = 20 + 1 = 21
Yk+1 = Yk + 1 = 10 + 1 = 11
Dnew = Dinitial + ΔD = 6 + (-4) = 2
o Similarly, Step-03 is executed until the end point is reached.
Ex2//Using Mid Point Algorithm calculate the points between the starting coordinates (5, 9) and ending coordinates (12, 16).
Solution:
o Given:
Starting coordinates: (X0, Y0) = (5, 9)
Ending coordinates: (Xn, Yn) = (12, 16)
STEP – 01:
o Calculate ΔX, ΔY from the given input.
ΔX = Xn – X0 = 12– 5= 7
ΔY =Yn – Y0 = 16– 9= 7
STEP – 02:
o Calculate Dinitial and ΔD as:
Dinitial = 2ΔY – ΔX = 2 ×7 – 7 = 7
ΔD = 2(ΔY – ΔX) = 2 × (7 – 7) = 0
STEP – 03:
o As Dinitial >= 0, so case-02 is satisfied. Thus,
Xk+1 = Xk + 1 = 5+ 1 = 6
Yk+1 = Yk + 1 = 9+ 1 = 10
Dnew = Dinitial + ΔD = 7+ 0 = 7
o Similarly, Step-03 is executed until the end point is reached.
STEP – 04:
o As Pk >= 0, so case-02 is satisfied. Thus,
Pk+1 = Pk + 2ΔY – 2ΔX = 6 + (2 x 8) – (2 x 10) = 2
Xk+1 = Xk + 1 = 20 + 1 = 21
Yk+1 = Yk + 1 = 10 + 1 = 11
Similarly, Step-03 is executed until the end point is reached or number of iterations equals to 9 times. (Number of iterations = ΔX – 1 = 10 – 1 = 9)
