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.
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References
Alexa, M., Cohen-Or, D., Levin, D.: As-rigid-as-possible shape interpolation. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’00), New Orleans, pp. 157–164. ACM/Addison-Wesley, New York (2000)
Balay, S., Brown, J., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page (2011). http://www.mcs.anl.gov/petsc
Benson, S., McInnes, L. C., Moré, J., Munson, T., Sarich, J.: TAO user manual (revision 1.9) (2007). http://www.mcs.anl.gov/tao
Bo, P., Pottmann, H., Kilian, M., Wang, W., Wallner, J.: Circular arc structures. ACM Trans Graph. 30(#101), 1–11 (2011). Proc. SIGGRAPH
Bommes, D., Zimmer, H., Kobbelt, L.: Mixed-integer quadrangulation. In ACM SIGGRAPH 2009 Papers (SIGGRAPH ’09), New Orleans, pp. 77:1–77:10. ACM, New York (2009).
Glymph, J., Shelden, D., Ceccato, C., Mussel, J., Schober, H.: A parametric strategy for free-form glass structures using quadrilateral planar facets. Autom. Constr. 13(2), 187–202 (2004). Conference of the Association for Computer Aided Design in Architecture
McNeel. Paneling tool documentation (2014). http://wiki.mcneel.com/labs/panelingtools.
Nieser, M., Palacios, J., Polthier, K., Zhang, E.: Hexagonal global parameterization of arbitrary surfaces. IEEE Trans. Vis. Comput. Graph. 18(6), 865–878 (2012)
Schiftner, A., Höbinger, M., Wallner, J., Pottmann, H.: Packing circles and spheres on surfaces. ACM Trans. Graph. 28(5), #139,1–8 (2009). Proc. SIGGRAPH Asia
Sechelmann, S., Rörig, T.: VaryLab web page (2013). http://www.varylab.com
Sechelmann, S., Rörig, T., Bobenko, A.I.: Quasiisothermic mesh layout. In Hesselgren, L., Sharma, S., Wallner, J., Baldassini, N., Bompas, P., Raynaud, J. (eds.) Advances in Architectural Geometry 2012, pp. 243–258. Springer, Vienna (2013)
Sommer, H.: JpetscTao, JNI wrapper (2010). http://jpetsctao.zwoggel.net/
Springborn, B., Schröder, P., Pinkall, U.: Conformal equivalence of triangle meshes. ACM Trans. Graph. 27(3), 77:1–77:11 (2008)
Troche, C.: Planar hexagonal meshes by tangent plane intersection. In: Advances in Architectural Geometry 2008, pp. 57–64. Springer, Vienna (2008)
Zimmer, H., Campen, M., Herkrath, R., Kobbelt, L.: Variational tangent plane intersection for planar polygonal meshing. In: Hesselgren, L., Sharma, S., Wallner, J., Baldassini, N., Bompas, P., Raynaud, J. (eds.) Advances in Architectural Geometry 2012, pp. 319–332. Springer, Vienna (2013).
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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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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DOI: https://doi.org/10.1007/978-3-319-11418-7_13
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