×

The surface evolver. (English) Zbl 0769.49033

Summary: The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The minimization is done by evolving the surface down the energy gradient. This paper describes the mathematical model used and the operations available to interactively modify the surface.

MSC:

49Q10 Optimization of shapes other than minimal surfaces

Software:

Surface Evolver

References:

[1] Almgren F., The Mathematical Intelligencer 4 pp 164– (1982) · Zbl 0492.53003 · doi:10.1007/BF03023550
[2] Almgren F., Scientific American pp 82– (1976) · doi:10.1038/scientificamerican0776-82
[3] Brakke K. A., The Motion of a Surface by Its Mean Curvature (1977) · Zbl 0386.53047
[4] Brakke K. A., Surface Evolver Manual
[5] Brakke K. A., Computing Optimal Geometries (1991)
[6] Brakke K. A., Journal of Geometric Analysis 2 pp 11– (1992) · Zbl 0725.53013 · doi:10.1007/BF02921333
[7] Brakke, K. A. ”Grain growth with the Surface Evolver”. Video Proceedings of the Workshop on Computational Crystal Growing. Edited by: Taylor, J. E. Providence, RI: American Mathematical Society. [Brakke 1992b]
[8] Callahan M., Computing Optimal Geometries (1991)
[9] Dobkin D., ”Primitives for the manipulation of three-dimensional subdivisions” (1987) · Zbl 0664.68023 · doi:10.1145/41958.41967
[10] Mittclmann H., ”Symmetric capillary surfaces in a cube”
[11] Morgan F., Comm. Part. Diff. Eq. 11 pp 1257– (1986) · Zbl 0617.49019 · doi:10.1080/03605308608820464
[12] Morgan F., ”Surfaces minimizing area plus length of singular curves” · Zbl 0816.49033 · doi:10.1090/S0002-9939-1994-1231039-1
[13] Press W., Numerical Recipes in C (1988) · Zbl 0661.65001
[14] Racz L. M., ”On some meniscus problems in materials processing”
[15] DOI: 10.1093/comjnl/21.3.243 · doi:10.1093/comjnl/21.3.243
[16] DOI: 10.2307/1970949 · Zbl 0335.49032 · doi:10.2307/1970949
[17] Taylor J. E., Seminar on Minimal Submanifolds pp 271– (1983)
[18] Taylor, J. E. ”Constructions and conjectures in crystalline nondiffercntiable geometry”. Proceedings of the Conference in Differential Geometry. Rio de Janeiro. Pittman Publishing Ltd. [Taylor 1988]
[19] Tegart, J. ”Three-dimensional fluid interfaces in cylindrical containers”. AIAA paper AIAA-91–2174, 27th Joint Propulsion Conference. Sacramento, CA. [Tegart 1991]
[20] Thompson W., Acta Math. 11 pp 121– (1887) · JFM 20.0523.01 · doi:10.1007/BF02612322
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.