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Surface Panelization Using Periodic Conformal Maps

Abstract

We present a new method to obtain periodic conformal parameterizations of surfaces with cylinder topology and describe applications to architectural design and rationalization of surfaces. The method is based on discrete conformal maps from the surface mesh to a cylinder or cone of revolution. It accounts for a number of degrees of freedom on the boundary that can be used to obtain a variety of alternative panelizations. We illustrate different choices of parameters for nurbs surface designs. Further, we describe how our parameterization can be used to get a periodic boundary aligned hex-mesh on a doubly-curved surface and show the potential on an architectural facade case study. Here we optimize an initial mesh in various ways to consist of a limited number of planar regular hexagons that panel a given surface.

Keywords

  • Edge Length
  • Boundary Vertex
  • Freeform Surface
  • Triangle Mesh
  • Interior Vertex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

We would like to thank Boris Springborn for sharing his knowledge on discrete conformal maps and the anonymous referees for their comments. Thilo Rörig and Stefan Sechelmann are supported by SFB/TR 109: Discretization in Geometry and Dynamics and DFG Research Center Matheon.

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Correspondence to Thilo Rörig .

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Rörig, T., Sechelmann, S., Kycia, A., Fleischmann, M. (2015). Surface Panelization Using Periodic Conformal Maps. In: Block, P., Knippers, J., Mitra, N., Wang, W. (eds) Advances in Architectural Geometry 2014. Springer, Cham. https://doi.org/10.1007/978-3-319-11418-7_13

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