Summary
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.
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References
U. Adamy, J. Giesen and M. John, New Techniques for Topologically Correct Surface Reconstruction, Proceedings of IEEE Visualization 2000, IEEE Computer Society Press, 2000.
N. Amenta, M. Bern and M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proceedings of SIGGRAPH’98, 1998, 415–421.
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.
N. Amenta, S. Choi and R. K. Kolluri, The Power Crust, Unions of Balls, and the Medial Axis Transform, Computational Geometry: Theory and Applications, 2001, 19 (2–3), 127–153.
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.
W.E. Lorensen, H.E. Cline, Marching Cubes: A high resolution 3D-surface construction algorithm, Computer Graphics, 1987, 21 (4), 163–169.
R. Mencl, A Graph-Based Approach to Surface Reconstruction, Computer Graphics Forum, 1995, 14 (3), 445–456.
R. Mend, Reconstruction of Surfaces from Unorganized Three-Dimensional Point Clouds, PhD thesis, Informatik VII, University of Dortmund, Germany, 2001.
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.
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.
R. Mend, H. Müller, Surface interpolation by spatial environment graphs, In: Data Visualization: The State of the Art, Kluwer Academic Publishers, 2002.
F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction, Springer Verlag, 1985.
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.
S.V. Rao, Some studies on beta-skeletons, PhD thesis, Dept. of Computer Science Engineering, Indian Institute of Technology, India, 1998.
R.C. Veltkamp, Closed Object Boundaries from Scattered Points, Lecture Notes in Computer Science 885, Springer Verlag, 1994.
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Mencl, R., Müller, H. (2004). Empirical Analysis of Surface Interpolation by Spatial Environment Graphs. In: Brunnett, G., Hamann, B., Müller, H., Linsen, L. (eds) Geometric Modeling for Scientific Visualization. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07443-5_4
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DOI: https://doi.org/10.1007/978-3-662-07443-5_4
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