Empirical Analysis of Surface Interpolation by Spatial Environment Graphs
An empirical analysis of a new algorithm for reconstruction of surfaces from three-dimensional point clouds is presented. The particular features of the algorithm are the reconstruction of open surfaces with boundaries from data sets of variable density, and the treatment of sharp edges, that is, locations of infinite curvature. The empirical data in particular confirm a formal analysis which has been performed for compact surfaces of limited curvature without boundary.
KeywordsLine Segment Empirical Analysis Dihedral Angle Sharp Edge Triangular Mesh
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- 1.U. Adamy, J. Giesen and M. John, New Techniques for Topologically Correct Surface Reconstruction, Proceedings of IEEE Visualization 2000, IEEE Computer Society Press, 2000.Google Scholar
- 2.N. Amenta, M. Bern and M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proceedings of SIGGRAPH’98, 1998, 415–421.Google Scholar
- 3.N. Amenta, S. Choi, T.K. Dey and N. Leekha, A simple algorithm for homeomorphic surface reconstruction, In Proc. 16th ACM Sympos. Comput. Geom., 2000.Google Scholar
- 5.D.G. Kirkpatrick, J.D. Radke, A framework for computational morphology, in: G.T. Toussaint (ed.), Computational Geometry, Elsevier Science Publisher B.V., North-Holland, 1985, 217–248.Google Scholar
- 8.R. Mend, Reconstruction of Surfaces from Unorganized Three-Dimensional Point Clouds, PhD thesis, Informatik VII, University of Dortmund, Germany, 2001.Google Scholar
- 9.R. Mend and H. Müller, Graph-Based Surface Reconstruction Using Structures in Scattered Point Sets, Proceedings of CGI ‘88 (Computer Graphics International), Hannover, Germany, 1998, 298–311.Google Scholar
- 10.R. Mencl, H. Müller, Interpolation and Approximation of Surfaces from Three-Dimensional Scattered Data Points, Proceedings of Scientific Visualization - Dagstuhl ‘87, IEEE Computer Society Press, 2000.Google Scholar
- 11.R. Mend, H. Müller, Surface interpolation by spatial environment graphs, In: Data Visualization: The State of the Art, Kluwer Academic Publishers, 2002.Google Scholar
- 12.F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction, Springer Verlag, 1985.Google Scholar
- 13.J.D. Radke, On the shape of a set of points, in: Computational Morphology, G.T. Toussaint (ed.), Elsevier Science Publisher B.V., North Holland, 1988, 105–136.Google Scholar
- 14.S.V. Rao, Some studies on beta-skeletons, PhD thesis, Dept. of Computer Science Engineering, Indian Institute of Technology, India, 1998.Google Scholar
- 15.R.C. Veltkamp, Closed Object Boundaries from Scattered Points, Lecture Notes in Computer Science 885, Springer Verlag, 1994.Google Scholar