Karakus, FatmaPripoae, Cristina-LilianaPripoae, Gabriel-Teodor2025-03-232025-03-2320252227-7390https://doi.org/10.3390/math13030328https://hdl.handle.net/11486/4683We 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.eninfo:eu-repo/semantics/openAccesscurvature of plane curvescos-sine integralcos-sine special functioncurvature controlpseudo-spiralfinding arc-length parametrizationsArticle13310.3390/math130303282-s2.0-85217672879Q1WOS:001418657900001Q1