Surface Reconstruction

We describe the problem of surface reconstruction from the point clouds which is applied in many scientific and engineering applications. Our aim is to obtain a visualization of data from 3D scanning and document the real objects digitally. Digital documentation brings the possibility to manipulate with surfaces in mathematical and modelling computer software. It can help with reconstruction and documentation of historical buildings and sculptures with 3D scanners or restoring of monuments. We mention several known algorithms for surface reconstruction and focus on the algorithms which are necessary for pre-processing of the input set of points – Delaunay triangulation and Voronoi diagram and the thinning algorithm. We explain choice of software for implementation of the algorithms. Introduction The problem of surface reconstruction appeared in medical imaging. Recently digital documentation is very modern and expanding method in many scientific and engineering applications. The input is a finite set of points in the space, we know 3D coordinates. The input set is called point cloud in computer graphics. Real data can be obtained from 3D scanning of the real object and may contain as many as millions points. The output is a reconstructed surface so that the points of the input set lie on or close to surface. If it is possible we want to get the parametrical or implicit description and the final step is to create 3D model of reconstructed surface. How to obtain the output is the subject of our research; see Figures 1, 2. Figure 1. Example of the input set of points obtained by 3D scanning of the Corinthian column. On the left the real object, on the right the input set of points which represents the object. (the source: www.windform.it) WDS'09 Proceedings of Contributed Papers, Part I, 204–209, 2009. ISBN 978-80-7378-101-9 © MATFYZPRESS