三维稀疏散乱点集的直接三角剖分新方法

给出一种三维稀疏散乱点集在三维空间直接进行三角剖分的新方法——在形成初始三角形后对它周围的离散点循环三角化．通过在剖分过程中引入两相邻三角形的最小夹角、最优点搜索半径系数和最小张角这三个剖分参数,实现了任意三维稀疏散乱点集的完全剖分以及非封闭自由曲面边界的自动识别．针对某些特殊复杂曲面上稀疏散乱点集的剖分问题提出了“分部剖分”思想：根据曲面的特征在不同区域设置不同的剖分参数．实例表明,这种直接剖分方法能有效处理任意多连通封闭和非封闭自由曲面上的稀疏散乱点集的三角剖分问题．

A novel approach of direct triangulation of sparse 3D scattered data

A novel approach of direct triangulation of sparse 3D scattered data in 3D space,circulating triangulation of the surrounding points of the initial triangle is presented.Three triangulation parameters,the minimal angle of two adjacent triangles and the coefficient of radius for searching the optimized point and the minimal inner angle of the potential triangle are proposed to deal with the direct triangulation of arbitrary sparse 3D scattered data.The boundary of non-closed surface can be automatically recognized by means of the proposed parameters.The idea of "stepping triangulation" by setting different parameters in different areas is presented to deal with the triangulation of the scattered data on certain kind of special complex surface.The examples show that the presented approach of direct triangulation can effectively deal with the triangulation of arbitrary sparse 3D scattered data on both closed surface and non-closed surface.