One part of this research is project `Computing Multilayer Freeform Surfaces', funded by the Österreichische Forschungsförderungsgesellschaft (FFG), which is conducted in cooperation with TU Wien and Waagner-Biro. Another part is the the project `Computational Differential Geometry', which is part of the National Research Network Industrial Geometry" (S92), funded by the Austrian Science Fund (FWF).

The implementation of freeform shapes in architecture is an area which encompasses great challenges in engineering as well as novel design ideas, and which consequently has high public exposure. However, the geometric basics of doubly curved surfaces realized as steel/glass constructions with planar faces remained largely unexplored. Planar quadrilateral faces and truly freeform geometries seemed mutually exclusive. Only recently the high potential of optimized mesh geometries has been realized: the aim of the present research project is the computation and interactive design of meshes with specific properties relevant for the construction process. They are not only capable of realizing the entire spectrum of freeform shapes, but at the same time provide the basis for a multi-layer support structure with planar faces and optimized joints without geometric torsion (Date: 10/2008)

• C. Jiang, H. Wang, V. Ceballos Inza, F. Dellinger, F. Rist, J. Wallner, and H. Pottmann. Using isometries for computational design and fabrication. ACM Trans. Graph. 40/4 (2021), #42,1-12, Proc. SIGGRAPH. [doi].
• D. Pellis, M. Kilian, F. Dellinger, J. Wallner, and H. Pottmann. Visual smoothness of polyhedral surfaces. ACM Trans. Graphics 38/4 (2019), 31:1-31:11, Proc. SIGGRAPH. [doi].
• H. Pottmann and J. Wallner. Freeform architecture and discrete differential geometry. In W. Kropatsch, N. Artner, and I. Janusch, editors, Discrete Geometry for Computer Imagery - DGCI 2017, volume 10502 of Lecture Notes in Computer Science, pages 3-8. Springer, 2017, ISBN 978-3-319-66271-8. [doi].
• D. Pellis, M. Kilian, J. Wallner, and H. Pottmann. Material-minimizing forms and structures. ACM Trans. Graphics 36/6 (2017), article 173, Proc. SIGGRAPH Asia. [doi].
• H. Pottmann and J. Wallner. Geometry and freeform architecture. In W. König, editor, Mathematics and Society, pages 131-151. European Math. Soc., 2016. [MR], [doi].
• C. Jiang, F. Günther, J. Wallner, and H. Pottmann. Measuring and controlling fairness of triangulations. In Advances in Architectural Geometry 2016, pages 24-39. vdf Hochschulverlag, Zürich, 2016. [doi].
• C. Tang, M. Kilian, P. Bo, J. Wallner, and H. Pottmann. Analysis and design of curved support structures. In Advances in Architectural Geometry 2016, pages 8-23. vdf Hochschulverlag, Zürich, 2016. [doi].
• H. Pottmann, M. Eigensatz, A. Vaxman, and J. Wallner. Architectural geometry. Computers and Graphics 47 (2015), 145-164. [doi].
• C. Jiang, C. Tang, M. Tomičić, J. Wallner, and H. Pottmann. Interactive modeling of architectural freeform structures - combining geometry with fabrication and statics. In P. Block, N. Mitra, J. Knippers, and W. Wang, editors, Advances in Architectural Geometry 2014, pages 95-108. Springer, 2015, ISBN 978-3-319-11417-0. [doi].
• C. Jiang, J. Wang, J. Wallner, and H. Pottmann. Freeform honeycomb structures. Computer Graphics Forum 33/5 (2014), 185-194, Proc. Symp. Geom. Processing. [doi].
• C. Tang, X. Sun, A. Gomes, J. Wallner, and H. Pottmann. Form-finding with polyhedral meshes made simple. ACM Trans. Graphics 33/4 (2014), #70,1-9, Proc. SIGGRAPH. [doi].
• H. Pottmann, C. Jiang, M. Höbinger, J. Wang, P. Bompas, and J. Wallner. Cell packing structures. Computer-Aided Design 60 (2015), 70-83, Special issue on Material Ecology. [doi].
• M. Barton, H. Pottmann, and J. Wallner. Detection and reconstruction of freeform sweeps. Computer Graphics Forum 33/2 (2014), 23-32, Proc. Eurographics. [doi].
• C. Jiang, J. Wang, P. Bompas, H. Pottmann, and J. Wallner. Freeform shading and lighting systems from planar quads. In C. Gengnagel, A. Kilian, J. Nembrini, and F. Scheurer, editors, Rethinking Prototyping - Proc. Design Modelling Symposium Berlin 2013, pages 335-346. epubli GmbH, Berlin, 2013, ISBN 978-3-8442-6845-4.
• J. Wang, C. Jiang, P. Bompas, J. Wallner, and H. Pottmann. Discrete line congruences for shading and lighting. Computer Graphics Forum 32/5 (2013), 53-62, Proc. Symposium Geometry Processing. [doi].
• L. Hesselgren, S. Sharma, J. Wallner, N. Baldassini, P. Bompas, and J. Raynaud. Advances in Architectural Geometry 2012. Springer, 2013. ISBN 978-3-7091-1250-2. [doi].
• E. Vouga, M. Höbinger, J. Wallner, and H. Pottmann. Design of self-supporting surfaces. ACM Trans. Graphics 31/4 (2012), #87, 1-11, Proc. SIGGRAPH. [doi].
• S. Flöry, Y. Nagai, F. Isvoranu, H. Pottmann, and J. Wallner. Ruled free forms. In L. Hesselgren et al., editors, Advances in Architectural Geometry 2012, pages 57-66. Springer, 2013. [doi].
• J. Wallner and H. Pottmann. Geometric computing for freeform architecture. J. Math. Industry 1 (2011), #4,1-19. [MR], [doi].
• C. Ceccato, L. Hesselgren, M. Pauly, H. Pottmann, and J. Wallner. Advances in Architectural Geometry 2010. Springer, 2010. ISBN 978-3-7091-0308-1. [doi].
• J. Wallner, A. Schiftner, M. Kilian, S. Flöry, M. Höbinger, B. Deng, Q. Huang, and H. Pottmann. Tiling freeform shapes with straight panels: Algorithmic methods. In C. Ceccato et al., editors, Advances in Architectural Geometry 2010, pages 73-86. Springer, 2010. [doi].
• M. Zadravec, A. Schiftner, and J. Wallner. Designing quad-dominant meshes with planar faces. Computer Graphics Forum 29/5 (2010), 1671-1679, Proc. Symp. Geometry Processing. [doi].
• H. Pottmann and J. Wallner. Freiformarchitektur und Mathematik. Mitt. DMV 18/2 (2010), 88-95. [Zbl], [MR].
• H. Pottmann, Q. Huang, B. Deng, A. Schiftner, M. Kilian, L. Guibas, and J. Wallner. Geodesic patterns. ACM Trans. Graphics 29/4 (2010), #43,1-10, Proc. SIGGRAPH. [doi].
• A. Schiftner, M. Höbinger, J. Wallner, and H. Pottmann. Packing circles and spheres on surfaces. ACM Trans. Graphics 28/5 (2009), #139,1-8, Proc. SIGGRAPH Asia. [doi].
• H. Pottmann, A. Schiftner, and J. Wallner. Geometry of architectural freeform structures. Int. Math. Nachr. 209 (2008), 15-28.
• A. Schiftner. Planar quad meshes from relative principal curvature lines. Master's thesis, TU Wien, 2007.
• H. Pottmann, Y. Liu, J. Wallner, A. Bobenko, and W. Wang. Geometry of multi-layer freeform structures for architecture. ACM Trans. Graphics 26/3 (2007), #65,1-11, Proc. SIGGRAPH. [doi].
• H. Pottmann, S. Brell-Cokcan, and J. Wallner. Discrete surfaces for architectural design. In P. Chenin, T. Lyche, and L. L. Schumaker, editors, Curves and Surface Design: Avignon 2006, pages 213-234. Nashboro Press, 2007, ISBN 978-0-9728482-7-5. [Zbl], [MR].
• H. Pottmann and J. Wallner. The focal geometry of circular and conical meshes. Adv. Comp. Math 29 (2008), 249-268. [Zbl], [MR], [doi].
• Y. Liu, H. Pottmann, J. Wallner, Y.-L. Yang, and W. Wang. Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graphics 25/3 (2006), 681-689, Proc. SIGGRAPH. [doi].
• W. Wang, J. Wallner, and Y. Liu. An angle criterion for conical mesh vertices. J. Geometry Graphics 11 (2007), 199-208. [Zbl], [MR].
• J. Wallner. Computing quadrilateral and conical meshes. In A. Bobenko et al., editors, Discrete Differential Geometry, volume 3 of Oberwolfach Reports. 2006. Abstracts from the workshop held March 6--10, 2006. [Zbl].
• H. Pottmann, J. Wallner, Y.-L. Yang, Y.-K. Lai, and S.-M. Hu. Principal curvatures from the integral invariant viewpoint. Comput. Aided Geom. Design 24 (2007), 428-442. [MR], [doi].