Abstract
Reconstructing surfaces from a set of unorganised sample points in the 3D space is a very important problem in reverse engineering. Most algorithms first build a triangular mesh to obtain an approximate surface representation. In this paper we describe an algorithm which works by creating and merging local triangular complexes to obtain an unambiguous 2D-manifold triangulation. We use all the given sample points as vertices, which is a natural requirement. Our method is able to handle open boundaries and holes, different geni (for example tori) and unoriented surfaces in a computationally efficient way.
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References
Amenta, N., Bern, M., Kamvysselis, M.: A New Voronoi-based surface reconstruction algorithm. Comput. Graphics 415–421 (1998).
Bajaj C., Bernardini, F., Chen, J., Schikore, D.: Automatic reconstruction of 3D CAD models. Proc. of the Int. J. Conf. on Theory and Practice of Geometric Modeling, Blaubeuren, Germany, October 1996.
Bernardini, F.: Automatic reconstruction of CAD Models and properties from digital scans. Ph.D. Thesis, Purdue University, 1997.
Boissonnat, J.-D.: Geometric structures for three-dimensional shape representation. ACM Trans. Graphics 3, 266–286 (1984).
Choi, B. K., Shin, H. Y., Yoon, Y. I., Lee, J. W.: Triangulation of scattered data in 3D space. Comput. Aided Des. 20 239–248 (1988).
Edelsbrunner, H., Mücke, E. P.: Three-dimensional alpha shapes. ACM Trans. Graphics 13 43–72 (1994).
Edelsbrunner, H.: Weighted alpha shapes. Technical Report UIUCDCD-R- 92–1760. Comp. Sci. Dept., Univ. Illinois, Urbana, Ill, 1992.
Guo, B., Mennon, J., Willette, B.: Surface reconstruction using alpha shapes. Comput. Graphics 16 177–190 (1997).
Hoppe, H., et al.: Surface reconstruction from unorganised points. Comput. Graphics, 71–76 (1992).
Várady, T., Martin, R. R., Cox, J.: Reverse engineering of geometric models — an introduction. Comput. Aided Des. 29 255–268 (1997).
Veltkamp, R. C.: Boundaries through scattered points of unknown density. Graph. Models Image Proc. 57 441–452 (1995).
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© 2001 Springer-Verlag Wien
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Kós, G. (2001). An Algorithm to Triangulate Surfaces in 3D Using Unorganised Point Clouds. In: Brunnett, G., Bieri, H., Farin, G. (eds) Geometric Modelling. Computing, vol 14. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6270-5_12
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DOI: https://doi.org/10.1007/978-3-7091-6270-5_12
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83603-3
Online ISBN: 978-3-7091-6270-5
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