A surface reconstruction algorithm using weighted alpha shapes

Abstract

This paper discusses a surface reconstruction method using the Delaunay triangulation algorithm. Surface reconstruction is used in various engineering applications to generate CAD model in reverse engineering, STL files for rapid prototyping and NC codes for CAM system from physical objects. The suggested method has two other components in addition to the triangulation: the weighted alpha shapes algorithm and the peel-off algorithm. The weighted alpha shapes algorithm is applied to restrict the growth of tetrahedra, where the weight is calculated based on the density of points. The peel-off algorithm is employed to enhance the reconstruction in detail. The results show that the increase in execution time due to the two additional processes is very small compared to the ordinary triangulation, which demonstrates that the proposed surface reconstruction method has great advantage in execution time for a large set of points. © Springer-Verlag Berlin Heidelberg 2005.