自适应T样条曲面重建

Automatic reconstruction of T-spline surfaces

为了进行快速高精度的曲面重建,提出了一种新的基于T样条的曲面自动重建算法。由于T样条控制网格具有特殊性质,因此在使用T样条进行曲面重建时,一个关键的问题是如何构造好一个T网格。该新算法在进行曲面重建时,用三角网格的参数化方法,先将数据点同胚映射到平面,然后再利用平面四叉树细分的方法将无结构散乱数据自动生成合理有效的T网格,最后将曲面重构模型转化为最优化问题,并由最小二乘法求解,同时在误差较大的区域辅以T样条的局部修正,以使重建曲面与原网格面的最大误差小于指定的误差值。由于该新的曲面重建方法是一个基于细节的重建方法,因此采样点密集区域所插入的T网格点也就相应地增多,这样既抓住了网格曲面的特征,又能很好地减少过多的T网格控制顶点,这就提高了算法效率。另外,该新算法还具有高效、易操作、能适应复杂曲面重建、曲面自动生成且满足相应精度要求等优点。重构结果显示,该新的曲面重建算法不仅重构应用范围广,且重构精度高。

A new procedure for reconstructing a smooth parametric surfaces using T-Splines from a triangulation mesh was present in this paper . In our solution, a key ingredient is that the scheme for automatically extract a quad-dominant control mesh （T-mesh） and a parameterization of the data points over the T-mesh . We use the discrete conformal parameterlzatlon as the solution of choice for mapping the 3 D triangular mesh to a 2D domain, and we partition this two dimensional space by recursively subdividing it into four quadrants, then automatically constructing the T-mesh that we need for the reconstructing. By using least square approximation we can get the control point of the surface and finish our algorithm until the approximation error below a specified threshold. We use adaptive refinement of the T-mesh in order to satisfy user- specified error tolerances and demonstrate our method on real data.