Auto-Surface Reconstruction with Alpha Shape

In this paper, we present an algorithm for the reconstruction of piecewise linear surfaces from unorganized sample points with improved a-shape. Alpha-shapes is based on eficient, discrete mathematics which determine exact relationships between points, shapes, and spaces. It generates a family of shapes according to the selected a parameter. The method discussed in this paper might be applied for surface reconstruction, and the process is fully automatic. Koichi ~ a r a d a ~ Department of Engineering Hiroshima University 2.1 Interval Calculation Given the point set as input, we fust construct the Delaunay triangulation, called D. For each simplex Or E D there is a single interval such that Or belongs to the surface iff the a value is contained in this interval. Seeing Fig 2-1 for example, if a€ [r , R 1, line MN will be kept on the surface as l-simplex, this range is the interval of the line MN. For points M and N, their interval is [0 , r 1. Out of the interval, the simplex will not keep itself on the surface and will change to lower or higher order simplex. The details about the interval see reference [I].