Curvature Control for Plane Curves

Fatma Karakus, Cristina-Liliana Pripoae and Gabriel-Teodor Pripoae ()
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Fatma Karakus: Department of Mathematics, Faculty of Arts and Sciences, Sinop University, 57000 Sinop, Turkey
Cristina-Liliana Pripoae: Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, 010374 Bucharest, Romania
Gabriel-Teodor Pripoae: Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 3, 1-16

Abstract: We define a family of special functions (the CSI ones), which can be used to write any parameterized plane curve with polynomial curvature explicitly. These special functions generalize the Fresnel integrals, and may have an interest in their own right. We prove that any plane curve with polynomial curvature is asymptotically a pseudo-spiral. Using the CSI functions, we can approximate, locally, any plane curve; this approach provides a useful criterion for a (local) classification of plane curves. In addition, we present a new algorithm for finding an arc-length parametrization for any curve, within a prescribed degree of approximation.

Keywords: curvature of plane curves; cos-sine integral; cos-sine special function; curvature control; pseudo-spiral; finding arc-length parametrizations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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