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

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.