IGNOU MMTE 4 2026 - Using the Midpoint method and taking symmetry into account develop an

Question

Using the Midpoint method and taking symmetry into account develop an efficient method for scan converting the curve y = x³/12 in [-10, 10].

06 Mar 2026

Answer :

Word Count : 488

To scan convert the curve (y = \frac{x^3}{12}) using the Midpoint method, we exploit symmetry about the origin because the curve is odd. We consider only (x \ge 0) and reflect points for (x < 0). The Midpoint method is based on choosing the next pixel based on the value of the decision parameter (d) at the midpoint between candidate pixels. Let the pixel grid spacing be 1 unit in both (x) and (y). The function is (f(x) = \frac{x^3}{12}). Start at the origin ((0,0)). For each step, we have two candidate pixels: 1. East (E): ((x+1, y)) 2. North-East (NE): ((x+1, y+1)) Decision parameter at midpoint (M = (x+1, y+\frac{1}{2})) is [ d = f(x+1) - \left(y + \frac{1}{2}\right) ] * If (d \ge 0), choose NE and increment (y) by

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