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The Best-Fit DDA Algorithm

The Best-Fit DDA is an algorithm for converting a segment into a nice-looking sequence of pixels. The conversion of a segment from to with involves a sequence of steps. At each step the segment is approximated by the concatenation of copies of a path with copies of a path . Initially, , , (a single horizontal increment), and (a diagonal increment). Update: if then , , else , The algorithm terminates when .

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This is a fast algorithm used in raster-scan systems. It is based on the subtractive version of Euclid's algorithm for the computation of the GCD of two positive integers and . The classical algorithm of Bresenham for drawing line segments is strictly related to the optimal placement of leap years in a cycle of years, and both are related to the Best-Fit DDA via Euclid's algorithm for the GCD of and and the continued fraction expansion of .
The Best-Fit DDA is described in Sect. 2.5 of D. Salomon, Computer Graphics and Geometric Modeling, New York: Springer-Verlag, 1999.
The Best-Fit DDA is due to C. M. A. Castle and M. L. V. Pitteway, "An Application of Euclid's Algorithm to Drawing Straight Lines," in Fundamental Algorithms for Computer Graphics, (R. A. Earnshaw, ed.), New York: Springer-Verlag, 1985 pp. 135-139.
The striking connections among Bresenham's algorithm, leap years, and Euclid's algorithm are discussed in M. A. Harris and E. M. Reingold, "Line Drawing, Leap Years, and Euclid," ACM Computing Surveys, 36(1), 2004 pp. 68–80.
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