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Reference TypeConference Paper (Conference Proceedings)
Last Update1998: (UTC) administrator
Metadata Last Update2013: (UTC) administrator
Citation KeyWalterFour:1996:ApArLe
TitleApproximate arc length parametrization
FormatImpresso, On-line.
Access Date2022, Jan. 29
Number of Files1
Size188 KiB
Context area
Author1 Walter, Marcelo
2 Fournier, Alain
EditorVelho, Luiz
Albuquerque, Arnaldo de
Lotufo, Roberto A.
Conference NameSimpósio Brasileiro de Computação Gráfica e Processamento de Imagens, 9 (SIBGRAPI)
Conference LocationCaxambu
Date29 out. - 1 nov. 1996
PublisherSociedade Brasileira de Computação
Publisher CityPorto Alegre
Book TitleAnais
Tertiary TypeArtigo
OrganizationSBC - Sociedade Brasileira de Computação; UFMG - Universidade Federal de Minas Gerais
History (UTC)2008-07-17 14:17:55 :: administrator -> banon ::
2010-08-28 20:04:48 :: banon -> administrator ::
2013-04-05 16:31:16 :: administrator -> banon :: 1996
2013-04-05 16:51:52 :: banon -> administrator :: 1996
2013-04-19 14:14:54 :: administrator -> banon :: 1996
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Is the master or a copy?is the master
Content Stagecompleted
Keywordsarc-length parametrization
curve design
bezier parametric curves
AbstractCurrent 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.
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