The original equation of the ellipse:

f(x, y) = b²x² + a²y² - a²b² = 0

• Initial point: (0, b)
• Decision parameter: p_1k = b² - a² b + 1/4 a²
• Next point:
• If f(x, y) < 0:
• The next point will be (X_k+1, y_k)
• p_1k+1 = p_1k + 2 b² X_k+1 + b²
• Else:
• The next point will be (X_k+1, y_k-1)
• p_1k+1 = p_1k + 2 b² X_k+1 + b² - 2 a² y_k+1
• Continue until 2b² X_k >= 2 a² y_k

• Initial point: (Ending point of Region 1)
• Decision parameter: p_2k = (x_k + 1/2)² b² + (y_k - 1)² a² - a²b²
• Next point:
• If f(x, y) > 0:
• The next point will be (x_k, y_k-1)
• p_2k+1 = p_2k + a² - 2 a² y_k-1
• Else:
• The next point will be (x_k+1, y_k-1)
• p_2k+1 = p_2k + a² - 2 a² y_k-1+ 2 b² x_k+1