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Numerical Curve Length Calculation Using Polynomial Interpolation

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Abstract

In this paper we present a method and algorithm for computing curve length approximately using a fixed rule resulting from polynomial interpolation of the points on the curve. The method can applied efficiently calculating digital curves by considering the control points of the interpolation as the pixels centers points. In the paper several examples are presented and the calculated lengths are compared to other methods found in the literature and we have shown progress. We provided MATLAB® code to simulate the algorithm. The advantage of the proposed method is in the approximation of the digital curve with the continuous curve rather than with piecewise linear sections used by most other methods.

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Authors and Affiliations

  1. Department of Mathematics, New Mexico Institute of Mining and Technology, 801 Leroy Place, PO #3696, Socorro, NM, 87801, USA

    Sameh Abdelwahab Nasr Eisa

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  1. Sameh Abdelwahab Nasr Eisa
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Correspondence to Sameh Abdelwahab Nasr Eisa.

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Eisa, S.A.N. Numerical Curve Length Calculation Using Polynomial Interpolation. J Math Imaging Vis 49, 377–383 (2014). https://doi.org/10.1007/s10851-013-0471-2

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  • DOI: https://doi.org/10.1007/s10851-013-0471-2

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