基于支持向量机的Laplacian网格曲面孔洞修补算法

Hole repairing algorithm in triangular mesh surface based on support vector machines and Laplacian

针对三角网格曲面上的孔洞修复问题,提出了一种空间修补算法。在提取孔洞边界特征后进行边界预处理,建立孔洞边界特征平面,并将孔洞边界向该平面投影;通过二维三角化在特征平面上对孔洞多边形进行修补;以孔洞边界周围的网格顶点坐标及其Laplacian坐标作为训练样本,通过最小二乘支持向量机推断出填充顶点的Laplacian坐标;以推断得到的填充顶点Laplacian坐标为基础建立线性方程组,求解得到填充顶点坐标,以实现孔洞的准确修补。实例验证说明该算法可以很好的恢复缺失部分曲面的几何特征。

Aiming at repairing the triangular mesh holes, a new hole filling algorithm in space is presented. The holes boundary are extracted and pretreated, and the characteristic plane of the hole is established, on which boundary is projected; holes on characteristic plane through two-dimensional triangulation are repaired. The Eucliden-coordinate and Lapacian of mesh points of the hole boundary are chosen as training sample for support vector machines and deduced Lapacian of filling points; coordinate of filling point is calculated wsing linear equations based on deduced Lapacian of filling points to file the hole precisely. Examples prove that this algorithm furbishes up geometric details of missing area of triangular mesh surface.