@InProceedings{WalterFour:1996:ApArLe,
author = "Walter, Marcelo and Fournier, Alain",
title = "Approximate arc length parametrization",
booktitle = "Anais...",
year = "1996",
editor = "Velho, Luiz and Albuquerque, Arnaldo de and Lotufo, Roberto A.",
pages = "143--150",
organization = "Simp{\'o}sio Brasileiro de Computa{\c{c}}{\~a}o Gr{\'a}fica e
Processamento de Imagens, 9. (SIBGRAPI)",
publisher = "Sociedade Brasileira de Computa{\c{c}}{\~a}o",
address = "Porto Alegre",
keywords = "arc-length parametrization, approximation, curve design, bezier
parametric curves.",
abstract = "Current approaches to compute the arc length of a parametric curve
rely on table lookup schemes. We present an approximate
closed-form solution to the problem of computing an arc length
parametrization for any given parametric curve. Our solution
outputs a one or two-span Bezier curve which relates the length of
the curve to the parametric variable. The main advantage of our
approach is that we obtain a simple continuous function relating
the length of the curve and the parametric variable. This allows
the length to be easily computed given the parametric values.
Tests with our algorithm show that the maximum error in our
approximation is 8.7% and that the average of maximum errors is
1.9%. Our algorithm is fast enough to compute the closed-form
solution in a fraction of a second. After that a user can
interactively get an approximation of the arc length for an
arbitrary parameter value.",
conference-location = "Caxambu, MG, Brazil",
conference-year = "29 Oct.-1 Nov. 1996",
isbn = "85-244-0103-6",
language = "en",
organisation = "SBC - Sociedade Brasileira de Computa{\c{c}}{\~a}o; UFMG -
Universidade Federal de Minas Gerais",
ibi = "83LX3pFwXQZW44Lb/cMJwi",
url = "http://urlib.net/ibi/83LX3pFwXQZW44Lb/cMJwi",
targetfile = "a14.pdf",
type = "Modelagem Geom{\'e}trica",
urlaccessdate = "2024, May 02"
}