Asymptotic decider
In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology,[1] but can also be considered an algorithm in its own right.[2]
Principle
The algorithm first divides the scalar field into uniform cubes. It draws topologically correct contours on the sides (interface) of the cubes. These contours can then be connected to polygons and triangulated. The triangles of all cubes form the isosurfaces and are thus the output of the algorithm.[1] Sometimes there is more than one way to connect adjacent constructs. This algorithm describes a method for resolving these ambiguous configurations in a consistent manner.[3]
See also
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References
- Notes
- 1 2 Nielson & Hamann 1991, p. 83.
- ↑ Seng et al. 2005, abstract. "The asymptotic decider algorithm was employed to solve the ambiguity problem associated with the MC algorithm."
- ↑ Nielson & Hamann 1991, p. 84.
- Bibliography
- Nielson, Gregory M.; Hamann, Bernd (1991). Nielson, Gregory M.; Rosenblum, Larry, eds. The asymptotic decider: resolving the ambiguity in marching cubes. Proceedings of the 2nd conference on Visualization '91 (VIS '91). Los Alamitos, CA: IEEE Computer Society. pp. 83–91. ISBN 978-0-8186-2245-8.
- Seng Dewen; Li Zhongxue; Li Cuiping; Li Chumin (2005). "Application of marching cubes algorithm in visualization of mineral deposits". Journal of Beijing University of Science and Technology (English Edition). 12 (3). Abstract.
Further reading
- Charles D. Hansen; Chris R. Johnson (2004). Visualization Handbook. Academic Press. pp. 7–12. ISBN 978-0-12-387582-2.
- A. Lopes; K. Bordlie (2005). "Interactive approaches to contouring and isosurfaces for geovisualization". In Jason Dykes; Alan M. MacEachren; M. J. Kraak. Exploring Geovisualization. Elsevier. pp. 352–353. ISBN 978-0-08-044531-1.