Curvature Control for Plane Curves
[ X ]
Tarih
2025
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
curvature of plane curves, cos-sine integral, cos-sine special function, curvature control, pseudo-spiral, finding arc-length parametrizations
Kaynak
Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
13
Sayı
3
