Fabrication-Aware Freeform Design based on Shape Space Exploration

Research project funded by the Austrian science fund FWF.

Project details

FWF project: P 23735

Livetime: 2011/10/01 - 2015/10/31

www: http://www.geometrie.tuwien.ac.at/geom/ig/projects/freeformdesign/


Project leader: Helmut Pottmann
Project members: Bailin Deng
Yukie Nagai
Amir Vaxman
Florian Käferböck
Mathias Höbinger


Freeform surfaces play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction of architectural freeform structures remains a challenge. In order to make a freeform design realizable, an optimization process known as rationalization has to be applied. This means its decomposition into smaller parts, thereby meeting two competing objectives: feasibility, and consistency with the designer’s intentions. Depending on what constitutes the design, there have been different approaches to this problem (with strong involvement of our research group) which have led to different kinds of specific geometric and computational questions. Mostly these questions involve replacing smooth surfaces (possibly with an additional curve network on them) by other structures like meshes with special properties. The guiding thought in all considerations is the efficient manufacturing of the surface parts and their respective necessary supporting/connecting elements. Both simple geometry and repetition of elements contribute to this goal of efficiency. In any case, a rationalized design is the output of a possibly very complicated nonlinear optimization, and it is very hard to make changes to such a highly constrained geometric model.

The present project developed methodology for unifying two traditionally separate phases in freeform architecture, namely (i) shape design and (ii) rationalization in view of the actual fabrication. While motivated by architecture, such fabrication-aware design or design exploration makes sense in many other applications as well.

The applied method is shape space exploration. This means that we view the set of all feasible designs which fulfil the constraints (posed by manufacturing and other practical aspects) as points of a high-dimensional manifold (shape space). Then design exploration is accomplished by an efficient navigation in this manifold. The ideas come from computational differential geometry and nonlinear optimization. We developed efficient algorithms for interactive modelling while satisfying constraints from manufacturing and in the case of architecture also from statics. Besides Architecture, we mainly studied modelling of so-called developable surfaces since they play an important role in several manufacturing technologies and their treatment in CAD systems has so far been quite limited.


  1. M. Barton, L. Shi, H. Pottmann, M. Kilian, and J. Wallner. Circular arc snakes and kinematic surface generation. Computer Graphics Forum, 32, 2013. Proc. Eurographics
  2. O. Diamanti, A. Vaxman, D. Panozzo, and O. Sorkine-Hornung. Integrable polyvector fields. ACM Trans. Graphics 34(4), 2015. Proc. SIGGRAPH
  3. S. Flöry, Y. Nagai, F. Isvoranu, H. Pottmann, and J. Wallner. Ruled free forms. In L. Hesselgren et al., editors, Advances in Architectural Geometry, 57-66, 2012
  4. C. Jiang, J. Wang, J. Wallner, and H. Pottmann. Freeform honeycomb structures. Computer Graphics Forum, 33(5), 2014. Proc. Symp. Geom. Processing
  5. C. Jiang, C. Tang, M. Tomicic, J. Wallner, and H. Pottmann. Interactive modeling of architectural freeform structures - combining geometry with fabrication and statics. In P. Block, J. Knippers, and W. Wang, editors, Advances in Architectural Geometry. Springer, 2015
  6. C. Jiang, C. Tang, A. Vaxman, P. Wonka, and H. Pottmann. Polyhedral patterns. ACM Trans. Graphics, 34(6), 2015. Proc. SIGGRAPH Asia
  7. F. Käferböck and H. Pottmann. Smooth surfaces from bilinear patches: discrete affine minimal surfaces. Computer-Aided Geom. Design, 2013
  8. F. Käferböck. Affine arc length polylines and curvature continuous uniform B-splines. Computer-Aided Geom. Design 31, 2014, 331-344
  9. H. Pottmann. Architectural geometry and fabrication-aware design. Nexus Network Journal, 15:195-208, 2013
  10. H. Pottmann, M. Eigensatz, A. Vaxman, and J. Wallner. Architectural geometry. Computers and Graphics 47, 2015, 145-164
  11. C. Tang, X. Sun, A. Gomes, H. Pottmann, and J. Wallner. Form-finding with polyhedral meshes made simple. ACM Trans. Graphics, 33(4), 2014. Proc. SIGGRAPH
  12. C. Tang, P. Bo, J. Wallner, and H. Pottmann. Interactive design of developable surfaces. ACM Trans. Graphics. to appear
  13. A. Vaxman. Modeling polyhedral surfaces with affine maps. Computer Graphics Forum 31 (2012), 1647-1656. Proc. Symp. Geometry Processing
  14. A. Vaxman. A framework for polyhedral mesh modeling. Computer Graphics Forum 33 (2014), 121-131.
  15. A. Vaxman, C. Müller, and O. Weber. Conformal mesh deformations with Möbius transformations. ACM Trans. Graphics 34(4), 2015. Proc. SIGGRAPH
  16. E. Vouga, M. Höbinger, J. Wallner, and H. Pottmann. Design of self-supporting surfaces. ACM Trans. Graphics, 31:#87,1-11, 2012. Proc. SIGGRAPH
  17. Y. Yang, Y. Yang, H. Pottmann, and N. Mitra. Shape space exploration of constrained meshes. ACM Trans. Graphics, 30, 2011. Proc. SIGGRAPH Asia
  18. X. Zhao, C. Tang, Y. Yang, H. Pottmann, and N. Mitra. Intuitive design exploration of constrained meshes. In L. Hesselgren et al, editors, Advances in Architectural Geometry, 305-318. Springer, 2012