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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)