Abstract
This paper describes a new algorithm of computing the convex hull of a 3-dimensional object. The convex hull generated by this algorithm is an abstract polyhedron being described by a new data structure, the cell list, suggested by one of the authors. The correctness of the algorithm is proved and experimental results are presented.
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References
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry – Algorithms and Applications. Springer, Heidelberg (2000)
Clarkson, K.L., Mehlhorn, K., Seidel, R.: Four results on randomized incremental constructions. In: Comp. Geom.: Theory and Applications, pp. 185–221 (1993); Preliminary version in Proc. Symp. Theor. Aspects of Comp. Sci. (1992)
Klette, R., Sun, H.J.: A Global Surface Area Estimation Algorithm for Digital Regular Solids. University of Auckland, CITR-TR-69 (2001)
Kovalevsky, V.A.: Finite Topology as Applied to Image Analysis. Computer Vision, Graphics and Image Processing 45(2), 141–161 (1989)
Kovalevsky, V.A.: Digital Geometry based on the Topology of Abstract Cell Complexes. In: Proceedings of the Third International Colloquium Discrete Geometry for Computer Imagery, pp. 259–284. University of Strasbourg (1993)
Kovalevsky, V.A.: Algorithms and Data Structures for Computer Topology. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 37–58. Springer, Heidelberg (2002)
Kovalevsky, V.A.: Multidimensional Cell Lists for Investigating 3-Manifolds. Discrete Applied Mathematics 125(1), 25–43 (2002)
Lorensen, W.E., Cline, H.E.: Marching Cubes: A High-Resolution 3D Surface Construction Algorithm. Computer Graphics 21(4), 163–169 (1987)
Preparata, F.P., Shamos, M.I.: Computational Geometry – An Introduction. Springer, Heidelberg (1985)
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Kovalevsky, V., Schulz, H. (2004). Convex Hulls in a 3-Dimensional Space. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_14
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DOI: https://doi.org/10.1007/978-3-540-30503-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
Online ISBN: 978-3-540-30503-3
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