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.
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.
Dr. Fernando Jiménez Alburquerque +