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A novel approach for computing C2-continuous offset of NURBS curves

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Abstract

Computing offset curves is an important geometric operation in areas of CAD/CAM, robotics, cam design and many industrial applications. In this paper, an algorithm for computing offsets of NURBS curves using C2-continuous B-spline curves is presented. The progenitor curve in database is initially approximated by a line-fitting curve, and then the exact offset of this line-fitting curve is introduced as an initial offset. Based on the initial offset and a set of selected knots, an intended C2-continuous B-spline curve is subsequently constructed. The method uses a new error-measuring scheme, which is based on the convex hull property of Bézier curves and the idea of cumulative errors, to calculate the global error bound of offset approximation. The method obtains offset curves with C2 continuity and guarantees that the actual error bound is precisely within the prescribed tolerance. In addition, it also allows one to selectively parametrize the offset curve.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Chung-Hsing University, 250 Kuo-kuang Road, Taichung, 402, Taiwan

    S.-H.F. Chuang & J.-L. Shih

Authors
  1. S.-H.F. Chuang
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  2. J.-L. Shih
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Correspondence to S.-H.F. Chuang.

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Chuang, SH., Shih, JL. A novel approach for computing C2-continuous offset of NURBS curves. Int J Adv Manuf Technol 29, 151–158 (2006). https://doi.org/10.1007/s00170-004-2484-x

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  • DOI: https://doi.org/10.1007/s00170-004-2484-x

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