Abstract: 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 wel-l shaped triangles can be created by this method and the approach can be widely used in NC machining and reverse engineering.