### 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 | |

Publication status | Published - 2007 |

Event | 12th IMA International Conference on the Mathematics of Surfaces - Sheffield, United Kingdom Duration: 4 Sep 2007 → 6 Sep 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 | United Kingdom |

City | Sheffield |

Period | 4/09/07 → 6/09/07 |

## Fingerprint Dive into the research topics of 'Estimation of end curvatures from planar point data'. Together they form a unique fingerprint.

## 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). Springer-Verlag. https://doi.org/10.1007/978-3-540-73843-5_19