Equations of Digital Straight Lines
Digitization of a real straight line is defined as the set of closest pixels to the line. These pixels form a digital straight line. This paper defines equation of a digital straight line as equation of the corresponding real straight line y = a*x + b, where a = p/q with (p, q) = 1 is the slope and b is the real-number offset. First, the paper provides an algorithm to digitize real straight lines, then discusses the relationships among slopes, offsets, permutations, and shifts of digital straight lines of different offsets. It will prove that digitization of y = a*x+b remains unchanged if b is in interval [i/q, (i+1)/q), for integer i. From one interval of b to the next interval of b, the digitization is shifted or permuted. Number of shifts and position of permutations are calculated by explicit formulas. The concept of parallel digital straight lines is discussed as a consequence of these mentioned-above results.
KeywordsComputer Graphic Pattern Anal Graphic Image Periodic Sequence Small Solution
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