Consider the midpoint (or Bresenham) algorithm for rasterizing lines given below:

(1) Input (x₁, y₁) and (x₂, y₂)

(2) y = y₁

(3) d = f(x₁ + 1, y₁ + ½) / f is the implicit form of a line

(4) for x = x 1 to x 2

(5) do

(6) plot(x,y)

(7) if(d<0)

(8) then

(9) y = y + 1

(10) d = d + (y₁ - y₂) + (x₂ - x₁)

(11) else

(12) d = d + (y₁ - y₂)

(13) end

(14) end

Which statements are true?

P: For a line with slope m>1, we should change the outer loop in line (4) to be over y.

Q: Lines (10) and (12) update the decision variable d through an incremental evaluation of the line equation f.

R: The algorithm fails if d is ever 0.

Statement P: For a line with slope m>1, we should change the outer loop in line (4) to be over y.

Line 4) for x = x₁ to x₂ should be changed to be over y and slope m > 1

Slope of a line m = (y₂ – y₁)/ (x₂ – x₁). Because now it depends on x coordinates, to be over y it should depend on y coordinates.

Statement Q: Lines (10) and (12) update the decision variable d through an incremental evaluation of the line equation f.

It is clearly shown in the algorithm, that line (10) and line (12) are changing the values of d through incremental evaluation. i.e. adding d with itself.

d = d + (y₁​ - y₂) + (x₂​ - x₁)       ---- line (10)

d = d + (y₁ - y₂)                       ---- line (12)

R: The algorithm fails if d is ever 0