Home > Table of Contents


Proceedings of the 2nd International Symposium on Information Processing (ISIP 2009)

Huangshan, China, August 21-23, 2009

Editors: Fei Yu, Jian Shu, and Guangxue Yue

AP Catalog Number: AP-PROC-CS-09CN002

ISBN: 978-952-5726-02-2 (Print), 978-952-5726-03-9 (CD-ROM)

Page(s): 437-440

C2 Nearly Arc-length Parameterizations

Fang Kui, Shen Yue, Wang Juan, and Wu Quanyuan

Full text: PDF


Based on the piecewise rational interpolating polynomial monotonicity preserving interpolation, adopting the numerical quadrature to calculate the arc length si at everyone  of  the ordered vector point on the parametric curve, an approximating scheme for the inverse one of arc length function of the parametric curve is constructed, which  passes  through the n+1 points. A C2 nearly arc-length parameterization is presented by substituting the approximating scheme for the parameter t. The nearly Arc-length Parameterization passes through the n+1 vector-valued points, and has its accurate arc length parameters at every one of the ordered vector points. Moreover, our further study shows that the nearly Arc‑length Parameterization carries the exactly same geometric shape because it comes form a kind of parametric transformation of the original curve. Therefore, this process provides a key to the difficult problem of the arc length parameterization of parametric curve.


Index Terms

CAD, Monotonicity preserving approximation, arc-length parameterization

Copyright @ 2009 ACADEMY PUBLISHER All rights reserved