三角网格模型的细分曲面拟合

Subdivision Surface Fitting from Triangle Mesh

提出一种用Loop细分曲面拟合三角网格模型的新算法。首先对网格模型进行特征识别,然后把经过简化和形状优化的网格作为拟合细分曲面初始控制网格。通过对控制网格顶点的循环修正、网格形状优化、局部自适应细分来求解拟合细分曲面控制顶点。该算法不仅避免了求解线性方程组,克服了拟合控制网格的扭曲现象,而且达到了用较少的控制网格拟合出反映物体细节特征并满足精度要求的分片光滑(片内除奇异点C1外其余C2连续)的Loop细分曲面的目的。实例表明,该算法用于测量数据的曲面重构是有效可行的。

A new algorithm is used to fit the Loop subdivision surface from the triangle mesh. All features of the original mesh model are first identified. A shape-optimization mesh simplification method is presented to simplify the dense triangle mesh as an initial control mesh. The vertex within the control mesh for subdivision surface fitting is located by the iterative modification, the mesh shape optimization and the local adaptive subdivision. The method avoids the solution of the linear equation system, meanwhile the distortion of the fitting control mesh is overcome. Moreover, the size of the control mesh, corresponding to the Loop subdivision surface fitting is smaller. The surface is reconstructed according to the given precision. The example shows characteristics of the original model and piecewise smooth （C^2 continuous everywhere except for the extraordinary vertices C^1）. Experiments demonstrate that the algorithm is efficient and feasible on surface reconstruction from measured data.