针对非均匀b样条的节点设置问题,提出一种利用非均匀b样条曲面拟合离散数据的迭代算法,通过优化节点分布来改进拟合曲面的质量.该算法以带参数化的三角网格曲面为输入,在首次迭代中根据输入曲面的几何特征将其对应的参数域划分成若干个子区域,并使得每个子区域上累积的几何特征信息量近似相等,子区域的重心坐标将取为首次迭代的节点;在随后的迭代中,保证前次迭代生成的重心位置固定不变,并根据前次迭代得到的曲面拟合误差再次将区域划分成累积误差接近相等的子区域,新增加的子区域重心的坐标选为拟加入的节点.文中算法自适应地在曲面形状复杂或拟合误差大的区域引入更多的控制顶点,使得拟合曲面的质量得以逐步改进.实验结果表明,该算法快速有效,在拟合具有明显几何特征的输入数据时具有优势.Knot placement of non-uniform B-spline is studied, and an iterative surface fitting scheme is proposed by exploring the degrees of freedom of knots to improve the fitting surface's quality.Our algorithm takes as input triangular meshes with parameterization.In the first iteration, the parametric domain is partitioned into several sub-regions with equally accumulated surface geometric information, and the coordinates of the centroids are chosen as the candidates of knots; in the following iteration steps, we partition the regions according to the fitting errors analogously while the centroids generated by previous steps remain unchanged.The fitting surface's quality is progressively improved as more control points are adaptively introduced into the region of the surface with more features or larger fitting error.Several experiments demonstrate the efficacy of our method in fitting surface with distinct geometric features.国家自然科学基金(61100105;61100107;61170324;61272300); 福建省自然科学基金(2011J05007;2012J01291
