Discrete Geodesic Parallel Coordinates

Christian Müller, Davide Pellis, Helmut Pottmann, Florian Rist, Hui Wang


Geodesic parallel coordinates are orthogonal nets on surfaces where one of the two families of parameter lines are geodesic curves. We describe a discrete version of these special surface parameterizations and show that they are very useful for specific applications, most of which are related to the design and fabrication of surfaces in architecture. With the new dis- crete surface model, it is easy to control strip widths between neighboring geodesics. This facilitates tasks such as cladding a surface with strips of originally straight flat material or designing geodesic gridshells and timber rib shells. It is also possible to model nearly developable surfaces. These are characterized by geodesic strips with almost constant strip widths and are used for generating shapes that can be manufactured from materials which allow for some stretching or shrinking like felt, leather, or thin wooden boards. Most importantly, we show how to constrain the strip width param- eters to model a class of intrinsically symmetric surfaces. These surfaces are isometric to surfaces of revolution and can be covered with doubly-curved panels that are produced with only a few molds when working with flexible materials like metal sheets.


  • Hui Wang, Davide Pellis, Florian Rist, Helmut Pottmann, and Christian Müller.
    Discrete Geodesic Parallel Coordinates.
    ACM Trans. Graph., 38(6):173:1–173:13, November 2019.
    doi:10.1145/3355089.3356541, dgd:607.

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

Davide Pellis   +

University: TU Wien
E-Mail: davidepellis[at]gmail.com

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