recursive process
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step 0
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from k to k+1 : choice (xk + 1, yk) or (xk + 1, yk + 1)
y = m (xk + 1) + b
d1 = y - yk = m (xk + 1) + b - yk
d2 = (yk + 1) - y = yk + 1 - m (xk + 1) -b
what we want to know : which of d1 and d2 is smaller, what we'll study : the sign of d1 - d2
d1 - d2 = 2 m (xk + 1) - 2 yk + 2b -1
