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.