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一种从等参线网格中生成双三次、 G^1 连续的 B 样条船壳曲面的方法

Generation of Discrete Bicubic G^1 B-Spline Ship Hullform Surfaces from a Given Curve Network Using Virtual Iso-Parametric Curves

  • 摘要: 本文中我们提出一种从船壳网格中插值生成 离散双三次 、 G 1 连续的 B 样条曲面方法。首先,网格中的曲线分为两种类型 : 边界曲线和参考曲线。其中边界曲线对应于可用于张量积 B 样条曲面的具有矩形结构的曲线集合。其次,在曲面片内部,曲面拟合点和边界方向导数可以从参考曲线中通过构建虚拟等参线的方法得到。最后,通过曲面拟合算法得到 离散 G 1 连续的 B 样条曲面。为证实方法的有效性,我们展示了几个用本文中提出的方法得到的光滑 船壳 曲面实例。

     

    Abstract: We propose a method that automatically generates discrete bicubic G^1 continuous B-spline surfaces thatinterpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and ``reference curves''. The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches, surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing ``virtual'' iso-parametric curves. Finally, a discrete G^1 continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.

     

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