Modelling 3-Valent Meshes Using Hyperbolic Geometry

Marc Alexa, Jan E. Kyprianidis, Ronald Richter, Boris Springborn

Description

Polygon meshes with 3-valent vertices often occur as the frame of free-form surfaces in architecture, in which rigid beams are connected in rigid joints. For modelling such meshes, it is desirable to measure the deformation of the joints’ shapes. It is natural to represent joint shapes as points in hyperbolic 3-space. This endows the space of joint shapes with a geometric structure that facilitates computation. This structure can be used to optimize meshes towards different constraints, and it might be useful for other applications as well.

References

  • Ronald Richter, Jan Eric Kyprianidis, Boris Springborn, and Marc Alexa.
    Constrained Modelling of 3-Valent Meshes Using a Hyperbolic Deformation Metric.
    Computer Graphics Forum, 2016.
    doi:10.1111/cgf.12805.

Authors

Prof. Dr. Marc Alexa  

Prof. Dr. Jan E. Kyprianidis  

Ronald Richter  

Prof. Dr. Boris Springborn   +

Projects: A01
University: TU Berlin, Institut für Mathematik, MA 871
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31423617
Fax: +49 30 31479282
E-Mail: boris.springborn[at]tu-berlin.de
Website: http://page.math.tu-berlin.de/~springb/

See also

Hyperbolic Helicoids
Felix Knöppel
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Material-Minimizing Forms and Structures
Martin Kilian, Davide Pellis, Helmut Pottmann, Johannes Wallner
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Discretization of Surfaces with Constant Ratio of Principal Curvatures
Fernando Jiménez Alburquerque, Christian Müller, Helmut Pottmann
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Constant Mean Curvature Surfaces in Hyperbolic 3-Space
Nicholas Schmitt
images