by Noakes, L, Kozera, R and Klette, R
Abstract:
This paper* discusses the problem of how to approximate the length of a parametric curve γ : [0; T] → IRn from points qi = γ (ti), where the parameters ti are not given. Of course, it is necessary to make some assumptions about the distribution of the ti: in the present paper ε-uniformity. Our theoretical result concerns an algorithm which uses piecewise-quadratic interpolants. Experiments are conducted to show that our theoretical estimates are sharp, and that the assumption of ε-uniformity is needed. This work may be of interest in computer graphics, approximation and complexity theory, digital and computational geometry, and digital image processing.
Reference:
Length estimation for curves with ε-uniform sampling (Noakes, L, Kozera, R and Klette, R), In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer Verlag, volume 2124, 2001.
Bibtex Entry:
@inproceedings{noakes2001lengthsampling,
author = "Noakes, L and Kozera, R and Klette, R",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "518--526",
publisher = "Springer Verlag",
title = "Length estimation for curves with ε-uniform sampling",
volume = "2124",
year = "2001",
abstract = "This paper* discusses the problem of how to approximate the length of a parametric curve γ : [0; T] → IRn from points qi = γ (ti), where the parameters ti are not given. Of course, it is necessary to make some assumptions about the distribution of the ti: in the present paper ε-uniformity. Our theoretical result concerns an algorithm which uses piecewise-quadratic interpolants. Experiments are conducted to show that our theoretical estimates are sharp, and that the assumption of ε-uniformity is needed. This work may be of interest in computer graphics, approximation and complexity theory, digital and computational geometry, and digital image processing.",
isbn = "9783540425137",
issn = "0302-9743",
eissn = "1611-3349",
keyword = "Discrete curves",
keyword = "Length estimation",
keyword = "Quadratic interpolants",
language = "eng",
}