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基于Powell-Sabin样条细分的参数曲面重建方法

A Parameter Surface Reconstruction Method Based on Powell-Sabin Spline Subdivision

  • 摘要: 本文提出一种基于Powell-Sabin样条细分的参数曲面重建方法. 该方法将给定的三角网格进行一次Powell-Sabin样条细分得到加细网格, 然后利用均值参数化方法建立到参数域的映射, 同时在采样得到规则型值点作为参数曲面表面点的近似. 最后建立光顺条件下的B样条曲面能量函数, 求解出B样条曲面的控制点网格, 完成参数曲面重建. 结果表明本文方法能够捕获由给定三角网格呈现的几何细节, 能够在较小开销下实现理想的重建效果.

     

    Abstract: This paper proposes a method for reconstructing parameter surfaces based on Powell-Sabin splines subdivision. The method involves performing one iteration of Powell-Sabin subdivision on the given triangular mesh to obtain a refined mesh . Then, using the mean value parameterization method, a mapping is established from the refined mesh  to the parameter domain . Sampling regularly spaced points in the spline function space  to approximate the parameter surface points on the surface. Finally, an energy function for B-spline surfaces is established under smoothness conditions, and the control point grid for the B-spline surface is obtained by solving the function, thereby completing the parameter surface reconstruction. The results show that the proposed method can capture the geometric details presented by the given triangular mesh and achieve ideal reconstruction with relatively small computational costs.

     

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