密集散乱数据的三角形网格曲面逼近方法

介绍了一种密集三维散乱点群数据的三角形网格曲面逼近方法 .算法采用一定数量的球体在曲面空间的有效投影域上的排布来模拟 Voronoi多边形 ,从而实现平面域约束 Delaunay三角剖分 ,并利用 Hardy多二项式插值原理将其映射到曲面空间 .通过对球体集合的动力学数值仿真 ,解决了网格节点的位置确定和最佳网格节点数量确定的问题 .实际模拟结果表明 :算法结构清晰、实用 ,三角化结果品质良好 ,在数控加工和反求工程中有着广阔的应用前景 .

An Algorithm of Triangular Mesh Approximation of Dense 3D Scattered Data

A new way of constructing triangular mesh to approximate is discussed dense 3D scattered data. It allocates a set of spheres distributed in the projection space to mimic Voronoi polygons, from which constrained Delaunay triangulation can be generated by connecting the centers of spheres. According to the principle of Hardy's multiquadric interpolation, nodes of mesh in the domain can be mapped to object space. Moveover, the optimal position of nodes and population of spheres are solved via dynamic simulation and adaptive sphere population control. The experimental results testify that well shaped triangles can be created by this method and the approach can be widely used in NC machining and reverse engineering.