Estimation of end curvatures from planar point data

Xinhui Ma, Robert J. Cripps

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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.
Original languageEnglish
Title of host publicationMathematics of Surfaces XII
Subtitle of host publicationProceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007
EditorsRalph Martin, Malcolm Sabin, Joab Winkler
Place of PublicationBerlin
PublisherSpringer-Verlag
Pages307-319
Number of pages12
ISBN (Electronic)9783540738435
ISBN (Print)9783540738428
DOIs
Publication statusPublished - 2007
Event12th IMA International Conference on the Mathematics of Surfaces - Sheffield, United Kingdom
Duration: 4 Sep 20076 Sep 2007
Conference number: 12

Publication series

NameLecture Notes in Computer Science
PublisherSpringer-Verlag
Number4647
ISSN (Print)0302-9743

Conference

Conference12th IMA International Conference on the Mathematics of Surfaces
Abbreviated titleIMA
CountryUnited Kingdom
CitySheffield
Period4/09/076/09/07

Fingerprint

curvature
error analysis
symmetry
method

Cite this

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: Proceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007 (pp. 307-319). (Lecture Notes in Computer Science; No. 4647). Berlin: Springer-Verlag. https://doi.org/10.1007/978-3-540-73843-5_19
Ma, Xinhui ; Cripps, Robert J. / Estimation of end curvatures from planar point data. Mathematics of Surfaces XII: Proceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007. editor / Ralph Martin ; Malcolm Sabin ; Joab Winkler. Berlin : Springer-Verlag, 2007. pp. 307-319 (Lecture Notes in Computer Science; 4647).
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Ma, X & Cripps, RJ 2007, Estimation of end curvatures from planar point data. in R Martin, M Sabin & J Winkler (eds), Mathematics of Surfaces XII: Proceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007. Lecture Notes in Computer Science, no. 4647, Springer-Verlag, Berlin, pp. 307-319, 12th IMA International Conference on the Mathematics of Surfaces, Sheffield, United Kingdom, 4/09/07. https://doi.org/10.1007/978-3-540-73843-5_19

Estimation of end curvatures from planar point data. / Ma, Xinhui; Cripps, Robert J.

Mathematics of Surfaces XII: Proceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007. ed. / Ralph Martin; Malcolm Sabin; Joab Winkler. Berlin : Springer-Verlag, 2007. p. 307-319 (Lecture Notes in Computer Science; No. 4647).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Ma X, Cripps RJ. Estimation of end curvatures from planar point data. In Martin R, Sabin M, Winkler J, editors, Mathematics of Surfaces XII: Proceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007. Berlin: Springer-Verlag. 2007. p. 307-319. (Lecture Notes in Computer Science; 4647). https://doi.org/10.1007/978-3-540-73843-5_19