Midpoint line decision ($d=2f(x+1,y+1/2)$)

For the implicit equation $f(X,Y)=\Delta y(X-x_0)-\Delta x(Y-y_0)$, the sign of $d$ compares the exact line with the midpoint between candidate pixel centres $(x+1,y)$ and $(x+1,y+1)$. Multiplication by two makes the test integral. A consistent equality rule specifies which tied pixel is selected.