Oriented Mixed Area and Discrete Minimal Surfaces

Oriented Mixed Area and Discrete Minimal Surfaces,10.1007/s00454-009-9198-7,Discrete & Computational Geometry,Christian Müller,Johannes Wallner

Oriented Mixed Area and Discrete Minimal Surfaces   (Citations: 4)
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Recently a curvature theory for polyhedral surfaces has been estab- lished which associates with each face a mean curvature value computed from areas and mixed areas of that face and its corresponding Gauss image face. Therefore a study of minimal surfaces requires studying pairs of polygons with vanishing mixed area. We show that the mixed area of two edgewise parallel polygons equals the mixed area of a derived polygon pair which has only the half number of vertices. Thus we are able to recursively characterize vanishing mixed area for hexagons and other n-gons in an incidence-geometric way. We use these geometric results for the construction of discrete minimal surfaces and a study of equilibrium forces in their edges, especially those with the combinatorics of a hexagonal mesh.
Journal: Discrete & Computational Geometry - DCG , vol. 43, no. 2, pp. 303-320, 2010
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