Discretization of Surfaces with Constant Ratio of Principal Curvatures

Fernando Jiménez Alburquerque, Christian Müller, Helmut Pottmann


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.


Dr. Fernando Jiménez Alburquerque   +

University: TU München

Prof. Dr. Christian Müller   +

Projects: C01
University: TU Wien, Institute of Discrete Mathematics and Geometry, 104
Address: Wiedner Hauptstr. 8-10, 1040 Vienna, AUSTRIA
Tel: +43 1 58801104465
Fax: +43 1 5880110493
E-Mail: cmueller[at]geometrie.tuwien.ac.at
Website: https://www.dmg.tuwien.ac.at/geom/ig/mueller/index.php

Prof. Dr. Helmut Pottmann   +

Projects: C01
University: TU Wien
E-Mail: pottmann[at]geometrie.tuwien.ac.at
Website: http://www.dmg.tuwien.ac.at/pottmann/
University: King Abdullah University of Science and Technology
E-Mail: helmut.pottmann[at]kaust.edu.sa