On the Number of Digital Straight Line Segments.
Berenstein, Carlos A.
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Let L_N be the number of digital line segments of length N that correspond to lines of the form y = ax + BETA, 0 <= a, BETA <=1. In a previous paper , a closed form expression for the quantity L_N was obtained. We prove an asymptotic estimate for L_N that might prove useful for many applications. Namely,