Abstract
This paper builds on recent progress in computing with geometric constraints, which is particularly relevant to architectural geometry. Not only do various kinds of meshes with additional properties (like planar faces, or with equilibrium forces in their edges) become available for interactive geometric modeling, but so do other arrangements of geometric primitives, like honeycomb structures. The latter constitute an important class of geometric objects, with relations to “Lobel” meshes, and to freeform polyhedral patterns. Such patterns are particularly interesting and pose research problems which go beyond what is known for meshes, e.g. with regard to their computing, their flexibility, and the assessment of their fairness.
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Barnes, M. R.: Form finding and analysis of tension structures by dynamic relaxation. Int. J. Space Struct. 14(2), 89–104 (2009)
Block, P.: Thrust network analysis: exploring three-dimensional equilibrium. PhD thesis, MIT (2009)
Block, P., Lachauer, L.: Closest-fit, compression-only solutions for free form shells. In: Proceedings of the IABSE – IASS London Symposium, London, 8pp, 2011
Block, P., Ochsendorf, J.: Thrust network analysis: a new methodology for three-dimensional equilibrium. J. Int. Assoc. Shell Spat. Struct. 48(3), 167–173 (2007)
Bouaziz, S., Schwartzburg, Y., Weise, T., Pauly, M.: Shaping discrete geometry with projections. Comput. Graph. Forum 31, 1657–1667 (2012)
de Goes, F., Alliez, P., Owhadi, H., Desbrun, M.: On the equilibrium of simplicial masonry structures. ACM Trans. Graph. 32(#93), 1–10 (2013)
Deng, B., Bouaziz, S., Deuss, M., Zhang, J., Schwartzburg, Y., Pauly, M.: Exploring local modifications for constrained meshes. Comput. Graph. Forum 32, 11–20 (2013)
Deng, B., Bouaziz, S., Deuss, M., Kaspar, A., Schwartzburg, Y., Pauly, M.: Interactive design exploration for constrained meshes. Comput.-Aided Des. (2014). doi:10.1016/j.cad.2014.01.004
Eigensatz, M., Kilian, M., Schiftner, A., Mitra, N., Pottmann, H., Pauly, M.: Paneling architectural freeform surfaces. ACM Trans. Graph. 29(#45), 1–10 (2010)
Jiang, C., Wang, J., Wallner, J., Pottmann, H.: Freeform honeycomb structures. Comput. Graph. Forum 33(5) (2014). Proc. SGP
Lachauer, L., Block, P.: Compression support structures for slabs. In: Hesselgren, L. et al. (eds.) Advances in Architectural Geometry 2012, pp. 135–146. Springer, Vienna (2012)
Liu, Y., Pottmann, H., Wallner, J., Yang, Y.-L., Wang, W. Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graph. 25(3), 681–689 (2006)
Liu, Y., Pan, H., Snyder, J., Wang, W., Guo, B.: Computing self-supporting surfaces by regular triangulation. ACM Trans. Graph. 32(#92), 1–10 (2013)
Lobel, A.: Formes et structures engendrées par des éléments identiques, vol. 1–6. A. Lobel, Bourg-la-Reine (1993). ISBN 2-9514254-0-6
Panozzo, D., Block, P., Sorkine-Hornung, O.: Designing unreinforced masonry models. ACM Trans. Graph. 32(#91), 1–12 (2013)
Poranne, R., Ovreiu, E., Gotsman, C.: Interactive planarization and optimization of 3D meshes. Comput. Graph. Forum 32(1), 152–163 (2013)
Schiftner, A., Balzer, J.: Statics-sensitive layout of planar quadrilateral meshes. In: Ceccato, C. et al. (eds.) Advances in Architectural Geometry 2010, pp. 221–236. Springer, Vienna (2010).
Schiftner, A., Höbinger, M., Wallner, J., Pottmann, H.: Packing circles and spheres on surfaces. ACM Trans. Graph. 28(#139), 1–8 (2009)
Singh, M., Schaefer, S.: Triangle surfaces with discrete equivalence classes. ACM Trans. Graph. 29(#46), 1–7 (2010)
Tang, C., Sun, X., Gomes, A., Wallner, J., Pottmann, H.: Form-finding with polyhedral meshes made simple. ACM Trans. Graph. 33(#70) (2014). Proc. SIGGRAPH
Van Mele, T., Block, P.: A novel form finding method for fabric formwork for concrete shells. J. Int. Assoc. Shell Spatial Struct. 52, 217–224 (2011)
Vouga, E., Höbinger, M., Wallner, J., Pottmann, H.: Design of self-supporting surfaces. ACM Trans. Graph. 31(#87), 1–11 (2012)
Zadravec, M., Schiftner, A., Wallner, J.: Designing quad-dominant meshes with planar faces. Comput. Graph. Forum 29, 1671–1679 (2010)
Acknowledgements
This research was supported by KAUST base funding, NAWI Graz funding, by the DFG-Collaborative Research Center, TRR 109 Discretization in Geometry and Dynamics, through grants I 705 N-26 and I 706-N26 of the Austrian Science Fund (FWF), by FWF project P 23735-N13 and by the European Community’s 7th Framework Programme under grant agreement 286426 (GEMS).
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Jiang, C., Tang, C., Tomičí, M., Wallner, J., Pottmann, H. (2015). Interactive Modeling of Architectural Freeform Structures: Combining Geometry with Fabrication and Statics. 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_7
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DOI: https://doi.org/10.1007/978-3-319-11418-7_7
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