Estimation of end curvatures from planar point data

Ma, Xinhui; Cripps, Robert J.

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.

Citation

Ma, X., & Cripps, R. J. (2007). Estimation of end curvatures from planar point data. In R. Martin, M. Sabin, & J. Winkler (Eds.), Mathematics of Surfaces XII; Lecture Notes in Computer Science (307-319). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-73843-5_19

• Publication Date: Sep 4, 2007
• Deposit Date: Apr 12, 2019
• 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
• Book Title: Mathematics of Surfaces XII; Lecture Notes in Computer Science
• ISBN: 9783540738428; 9783540738435
• DOI: https://doi.org/10.1007/978-3-540-73843-5_19
• Keywords: Curvature vector; Curvature error; Order error; Planar point; Test curf
• Public URL: https://hull-repository.worktribe.com/output/1582507
• Publisher URL: https://link.springer.com/chapter/10.1007%2F978-3-540-73843-5_19