Discretization of Surfaces with Constant Ratio of Principal Curvatures
Fernando Jiménez Alburquerque, Christian Müller, Helmut Pottmann
Description
Motivated by applications in architecture, surfaces with a constant ratio of principal curvatures were studied. These surfaces are a natural generalization of minimal surfaces, and can be constructed by applying a Christoffel-type transformation to appropriate spherical curvature line parametrizations, both in the smooth setting and in a discretization with principal nets. This Christoffel-type transformation can be linked to the discrete curvature theory for parallel meshes and characterize nets that admit these transformations. In the case of negative curvature, a discretization of asymptotic nets is presented. This case is suitable for design and computation, and forms the basis for a special type of architectural support structures, which can be built by bending flat rectangular strips of inextensible material, such as sheet metal.
References
-
Michael R. Jimenez, Christian Müller, and Helmut Pottmann.
Discretizations of Surfaces with Constant Ratio of Principal Curvatures.
Discrete Comput. Geom., 2019. accepted for publication.
URL: http://www.geometrie.tuwien.ac.at/ig/publications/constratio/constratio.pdf, doi:10.1007/s00454-019-00098-7.
