ConicCurv: A curvature estimation algorithm for planar polygons

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Fuentes, R. Díaz, Sarlabous, J. Estrada, Mederos, V. Hernández
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866913760898187264
author Fuentes, R. Díaz
Sarlabous, J. Estrada
Mederos, V. Hernández
author_facet Fuentes, R. Díaz
Sarlabous, J. Estrada
Mederos, V. Hernández
contents ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and Bézier rational conic curves. The curvature values estimated by ConicCurv are invariant to Euclidean changes of coordinates and reproduce the exact curvature values if the data are sampled from a conic. We show that ConicCurv< has convergence order $3$ and, if the sample points are uniformly arc-length distributed, the convergence order is $4$. The performance of ConicCurv is compared with some of the most frequently used algorithms to estimate curvatures and its performance is illustrated in the calculation of the elastic energy of subdivision curves and the location of L-curves corners.
format Preprint
id arxiv_https___arxiv_org_abs_2503_20938
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle ConicCurv: A curvature estimation algorithm for planar polygons
Fuentes, R. Díaz
Sarlabous, J. Estrada
Mederos, V. Hernández
Numerical Analysis
53Z50, 53A15, 68W25, 65D15, 65F22
ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and Bézier rational conic curves. The curvature values estimated by ConicCurv are invariant to Euclidean changes of coordinates and reproduce the exact curvature values if the data are sampled from a conic. We show that ConicCurv< has convergence order $3$ and, if the sample points are uniformly arc-length distributed, the convergence order is $4$. The performance of ConicCurv is compared with some of the most frequently used algorithms to estimate curvatures and its performance is illustrated in the calculation of the elastic energy of subdivision curves and the location of L-curves corners.
title ConicCurv: A curvature estimation algorithm for planar polygons
topic Numerical Analysis
53Z50, 53A15, 68W25, 65D15, 65F22
url https://arxiv.org/abs/2503.20938