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",
      conference-year = "29 out. - 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 = "",
           targetfile = "a14.pdf",
                 type = "Modelagem Geom{\'e}trica",
        urlaccessdate = "2021, Nov. 29"