基于灰色预测GM(1,1)模型的网格孔洞填补算法

针对三角网格曲面中存在的孔洞提出了一种填补算法.在空洞曲面的投影平面上,每次寻找孔洞多边形最小内角所在顶点,用GM(1,1)模型在孔洞内部插入新点,构造三角形并生成新的孔洞边界多边形,直到所有的孔洞边界多边形全部处理完.最后将平面三角面片返回到三维空间并用基于径向基函数的平滑算法对其进行平滑处理.实例表明用本算法进行孔洞填补能避免出现错误和狭长的三角形,而且和原孔洞边界能光滑连接,对曲率变化较大的孔洞也能得到满意的填补结果.

Hole-Filling Algorithm in Mesh Surface Based on Grey Model GM(1,1)

A hole-filling algorithm is presented.On the projection plane of hole surface,the vertex with the minimal internal angle is found firstly,and new points in hole are interpolated using grey model GM(1,1).Then new triangles are created and new boundary polygons are constructed.This process continues until all boundary polygons are managed.Finally the new triangles on projection plane are put back to 3D space and to fair them based on radial basis function.The results show this algorithm can avoid false and spiky triangles,and new triangles can join original surface smoothly.Moreover this method can achieve satisfied effect for those with large changed curvature.