Measurements of Arc Length's by Shortest Polygonal Jordan Curves
نویسندگان
چکیده
Arc length's may be measured by numeric integration if the curves are given by analytic formulas. This report deals with an alternative way. A shortest polygonal Jordan curve may be used to estimate arc length's. This theoretically known result is illustrated in this report. Measured convergence of error values is discussed for a few examples of curves. A new error measure (approximation effectiveness) is proposed and discussed. 1 CITR, Tamaki Campus, University Of Auckland, Auckland, New Zealand Measurements of Arc Length's by Shortest Polygonal Jordan Curves Reinhard Klette and Nan Yang Department of Computer Science, The University of Auckland CITR, Tamaki Campus Private Bag 92019, Auckland, New Zealand Abstract: Arc length's may be measured by numeric integration if the curves are given by analytic formulas. This report deals with an alternative way. A shortest polygonal Jordan curve may be used to estimate arc length's. This theoretically known result is illustrated in this report. Measured convergence of error values is discussed for a few examples of curves. A new error measure (approximation e ectiveness) is proposed and discussed.
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