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قیمت: 4500 تومان
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دانلود مقاله :
(2013) Two efficient algorithms for computing the characteristics of a subsegment of a digital straight line
نویسندگان :
Jacques-Olivier Lachauda, Mouhammad Said
فرمت: pdf
چکیده :
We address the problem of computing the exact characteristics of any subsegment of a Digital Straight Line (DSL) with known characteristics (a slope ab, a shift to origin μ). We present here two new algorithms that solve this problem, whose correctnesses are fully proved. Their principle is to descend/climb the Stern–Brocot tree of fractions in a topdown/
bottom-up way. The top-down algorithm SmartDSS has a time complexity which depends on the sum of the quotients of the continued fraction of the output slope and on the number of pattern repetitions. As a corollary, its time complexity is bounded by the sum of the quotients of the continued fraction of the input slope, Said and Lachaud (2009) [18]. The bottom-up algorithm ReversedSmartDSS has a time complexity proportional to the difference of depth of the input slope and the slope of the output segment, Said and Lachaud (2011) [17]. As a corollary, its complexity is thus logarithmic in the coefficients of the input slope. These algorithms are also efficient in practice, as shown by a series of experiments comparing these new lgorithms with standard arithmetic digital straight segment recognition.
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