Geometry of equilibrium curves and surfaces for discrete anisotropic energy
In this paper, we propose piecewise linear constant anisotropic mean curvature (CAMC) curves and surfaces based on a variational characterization. These curves (resp. surfaces) are equilibrium for the anisotropic energy amongst continuous piecewise linear variations which preserve the boundary condi...
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| Veröffentlicht in: | JSIAM Letters 2022, Vol.14, pp.57-60 |
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| creator | Jikumaru, Yoshiki |
| description | In this paper, we propose piecewise linear constant anisotropic mean curvature (CAMC) curves and surfaces based on a variational characterization. These curves (resp. surfaces) are equilibrium for the anisotropic energy amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the non-minimal case) the area (resp. volume) to one side of the curves (resp. surfaces). Our discrete CAMC surfaces are a generalization of discrete CMC surfaces defined by the variational principle. We also show a stability result of discrete CAMC surfaces including the result for discrete CMC surfaces. |
| doi_str_mv | 10.14495/jsiaml.14.57 |
| format | Article |
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| source | J-STAGE Free; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | anisotropic mean curvature anisotropic surface energy discrete surface first variation stability |
| title | Geometry of equilibrium curves and surfaces for discrete anisotropic energy |
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