𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Estimating derivatives and curvature of open curves

✍ Scribed by Luciano da Fontoura Costa

Book ID
104161558
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
287 KB
Volume
35
Category
Article
ISSN
0031-3203

No coin nor oath required. For personal study only.

✦ Synopsis

This article presents an e ective spectral approach to estimate derivatives and curvature of open parametric curves. As the method is based on the discrete Fourier transform, the discontinuities of the curve (as well as of its derivatives) must be controlled to minimize the Gibbs phenomenon. We address this problem by obtaining a smooth extension of the curve in such a way as to suitably close it, which is done through a variational approach taking into account the spectral energy of di erentiated versions of the extended curves. This novel method presents potential for applications in a broad class of problems, ranging from applied and experimental physics to image analysis.

πŸ“œ SIMILAR VOLUMES

Total curvature and length estimate for
Total curvature and length estimate for curves in CAT(K) spaces
✍ Chaiwat Maneesawarng; Yongwimon Lenbury πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 141 KB

We introduce the notion of total curvature of curves (which agrees with the usual one in the piecewise smooth case) in spaces of Alexandrov curvature bounded above. Basic properties of total curvature, including rectifiability of curves of finite total curvature and additivity of total curvature, ar

Curvature-dependent parameterization of
Curvature-dependent parameterization of curves and surfaces
✍ M. Kosters πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 760 KB

An efficient way of drawing parametric curves and surfaces is to approximate the curve or surface by a sequence of straight-line segments or a mesh of polygons, respectively. In such an approximation, many small line segments or polygons are needed in regions of high curvature, and fewer and larger