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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.
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J. Wallner and H. Pottmann.
Geometric
computing for freeform architecture.
J. Math. Industry 1 (2011), #4,1-19.
[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.
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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.
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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.
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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].
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H. Pottmann and J. Wallner.
The focal geometry
of circular and conical meshes.
Adv. Comp. Math 29 (2008), 249-268.
[Zbl], [MR], [doi].
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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].
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W. Wang, J. Wallner, and Y. Liu.
An angle criterion
for conical mesh vertices.
J. Geometry Graphics 11 (2007), 199-208.
[Zbl], [MR].
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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].
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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].
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