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中文摘要：
针对残缺的三角网格模型，提出一种将网格模型的散乱数据点转化为有序阵列点再进行B样条曲面快速重建的算法．首先确定最小二乘平面上的一个矩形参数域，再构造出一个平面阵列点列，并部分映射到三维网格上；然后利用空间阵列点的邻域信息估计4个角点的空间坐标，并构造径向基函数曲面，用于补充空间阵列点列中残缺的数据；最后利用有序点列拟合的高效性构造B样条曲面．实验结果表明：该算法速度快、拟合精度高、鲁棒性强，重建的曲面具有良好的光顺性和可延伸性，适用于逆向工程中对经过数据分割后的网格模型的自由曲面重建．
英文摘要：
For a triangular mesh model with holes, a rapid B-spline surface reconstruction algorithm is developed by generating regularized grid points from scattered vertex points of the mesh. First, a rectangular parameter region is obtained on the least square plane and planar regularized grid points are constructed. Then most of the planar grid points are mapped back onto the mesh model and the spatial regularized grid points are obtained, where some points in the grid are missed. The neighbor information of the spatial grid points is used to evaluate the positions of the four corner points. Then a radial basis function surface is constructed and used to fill the missing points. Finally, a smooth B-spline surface is fitted to these spatial regularized grid points. The experimental data shows that the presented algorithm is fast, accurate and robust. The reconstructed surface has good smoothness and extensionality. It can be well applied to reconstruct B-spline surface from mesh model after data segmentation in reverse engineering.
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