Skip to main content

Estimation of end curvatures from planar point data

Ma, Xinhui; Cripps, Robert J.

Authors

Robert J. Cripps



Contributors

Ralph Martin
Editor

Malcolm Sabin
Editor

Joab Winkler
Editor

Abstract

Given a string of discrete planar points, the estimation of principal curvature vectors using circle fitting and Richardson’s extrapolation principle has been considered by several authors. However, these methods can not be directly applied to end points, due to symmetry. This article extends these methods to cope with end points. The method is based on the construction of interpolating circles using the first (or last) four data points. Error analysis suggests that the accuracy of curvature estimation using circle fitting is determined by arc-lengths and derivatives of curvature with respect to arc-length. A comparison is made between the proposed four-point method and the well established three-point method.

Publication Date Sep 4, 2007
Journal Mathematics of Surfaces XII; Lecture Notes in Computer Science
Print ISSN 0302-9743
Electronic ISSN 1611-3349
Pages 307-319
Series Title Lecture Notes in Computer Science
Series Number 4647
Series ISSN 0302-9743
ISBN 9783540738428; 9783540738435
APA6 Citation Ma, X., & Cripps, R. J. (2007). Estimation of end curvatures from planar point data. In R. Martin, M. Sabin, & J. Winkler (Eds.), Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-73843-5_19
DOI https://doi.org/10.1007/978-3-540-73843-5_19
Keywords Curvature vector; Curvature error; Order error; Planar point; Test curf
Publisher URL https://link.springer.com/chapter/10.1007%2F978-3-540-73843-5_19
;