Estimation of end curvatures from planar point data

Xinhui Ma; Robert J. Cripps

doi:10.1007/978-3-540-73843-5_19

Estimation of end curvatures from planar point data

Xinhui Ma, Robert J. Cripps

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Mathematics of Surfaces XII
Subtitle of host publication	Proceedings of 12th IMA International Conference, Sheffield, UK, September 4-6, 2007
Editors	Ralph Martin, Malcolm Sabin, Joab Winkler
Place of Publication	Berlin
Publisher	Springer-Verlag
Pages	307-319
Number of pages	12
ISBN (Electronic)	9783540738435
ISBN (Print)	9783540738428
DOIs	https://doi.org/10.1007/978-3-540-73843-5_19
Publication status	Published - 2007
Externally published	Yes
Event	12th IMA International Conference on the Mathematics of Surfaces - Sheffield, United Kingdom Duration: 4 Sept 2007 → 6 Sept 2007 Conference number: 12

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer-Verlag
Number	4647
ISSN (Print)	0302-9743

Conference

Conference	12th IMA International Conference on the Mathematics of Surfaces
Abbreviated title	IMA
Country/Territory	United Kingdom
City	Sheffield
Period	4/09/07 → 6/09/07

Access to Document

10.1007/978-3-540-73843-5_19

Cite this

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title = "Estimation of end curvatures from planar point data",

abstract = "Given a string of discrete planar points, the estimation of principal curvature vectors using circle fitting and Richardson{\textquoteright}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.",

author = "Xinhui Ma and Cripps, {Robert J.}",

year = "2007",

doi = "10.1007/978-3-540-73843-5_19",

language = "English",

isbn = "9783540738428",

series = "Lecture Notes in Computer Science",

publisher = "Springer-Verlag",

number = "4647",

pages = "307--319",

editor = "Ralph Martin and Malcolm Sabin and Joab Winkler",

booktitle = "Mathematics of Surfaces XII",

note = "12th IMA International Conference on the Mathematics of Surfaces, IMA ; Conference date: 04-09-2007 Through 06-09-2007",

}

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 proceeding › Conference contribution

TY - GEN

T1 - Estimation of end curvatures from planar point data

AU - Ma, Xinhui

AU - Cripps, Robert J.

N1 - Conference code: 12

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-540-73843-5_19

DO - 10.1007/978-3-540-73843-5_19

M3 - Conference contribution

SN - 9783540738428

T3 - Lecture Notes in Computer Science

SP - 307

EP - 319

BT - Mathematics of Surfaces XII

A2 - Martin, Ralph

A2 - Sabin, Malcolm

A2 - Winkler, Joab

PB - Springer-Verlag

CY - Berlin

T2 - 12th IMA International Conference on the Mathematics of Surfaces

Y2 - 4 September 2007 through 6 September 2007

ER -

Estimation of end curvatures from planar point data

Abstract

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Conference

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