Proceedings of the 2nd International Symposium on Information Processing (ISIP 2009) Huangshan, China, August 2123, 2009 Editors: Fei Yu, Jian Shu, and Guangxue Yue AP Catalog Number: APPROCCS09CN002 ISBN: 9789525726022 (Print), 9789525726039 (CDROM) Page(s): 437440 

C2 Nearly Arclength Parameterizations Fang Kui, Shen Yue, Wang Juan, and Wu Quanyuan 
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Abstract 

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 arclength parameterization is presented by substituting the approximating scheme for the parameter t. The nearly Arclength Parameterization passes through the n+1 vectorvalued 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, arclength parameterization 

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