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This research project as described by the list of publications
below has a long history, and the hosting institution
of this web page (TU Graz) has only contributed a small part.
It has been supported by FWF Grant No. P12252 at TU Wien.
Work was performed within the
National research network S92 "Industrial Geometry", funded by
Austrian Science Fund (FWF) in 2005-2010, especially subproject
Computational Differential Geometry.
From 2012, work on developable surfaces is performed within the framework
of the SFB-Transregio programme
Discretization in Geometry
and Dynamics which is supported by Deutsche Forschungsgemeinschaft
in general and by the Austrian Science Fund (FWF, via project I705) in
particular.
Developable surfaces are characterized
by being unfoldable into the plane without stretching or tearing.
For all practical purposes this is the same as being composed
of special kinds of ruled surfaces.
We are e.g. concerned with approximation of surfaces by developables,
and in the segmention of freeform surfaces into developable strips.
From the mathematical viewpoint, a series of curves which have
the property that the ruled strips generated by them are developable
(a developable strip model) represents
a semidiscrete conjugate net, so there is an intimate connection
to discrete (actually, semidiscrete) differential geometry.
The property of being developable is highly relevant for
manufacturing, which makes such surfaces useful in various
applied areas, from mechanican engineering to architecture.
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C. Tang, P. Bo, J. Wallner, and H. Pottmann.
Interactive design of
developable surfaces.
ACM Trans. Graphics 35/2 (2016), #12, 1-12.
[doi].
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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.
[doi].
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H. Pottmann, A. Schiftner, P. Bo, H. Schmiedhofer, W. Wang, N. Baldassini, and
J. Wallner.
Freeform surfaces
from single curved panels.
ACM Trans. Graphics 27/3 (2008), #76,1-10, Proc. SIGGRAPH.
[doi].
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H. Pottmann, A. Schiftner, and J. Wallner.
Geometry of
architectural freeform structures.
Int. Math. Nachr. 209 (2008), 15-28.
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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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M. Peternell.
Recognition and reconstruction of developable surfaces from point clouds.
In 2004 Geometric Modeling and Processing, Theory and Applications,
pages 301-310. IEEE Computer Society, 2004, ISBN 0-7695-2078-2.
Proceedings of the GMP conference in Beijing, April 13-15, 2004.
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M. Peternell.
Developable surface fitting to point clouds.
Comput. Aided Geom. Design 21/8 (2004), 785-803.
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S. Leopoldseder.
Cone spline
surfaces and spatial arc splines - a sphere geometric approach.
Adv. Comput. Math. 17 (2002), 49-66.
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S. Leopoldseder.
Algorithms on cone
spline surfaces and spatial sculating arc splines.
Comput. Aided Geom. Design 18 (2001), 505-530.
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H. Pottmann and J. Wallner.
Approximation
algorithms for developable surfaces.
Comput. Aided Geom. Design 16 (1999), 539-556.
[Zbl], [MR], [doi].
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H.-Y. Chen, I.-K. Lee, S. Leopoldseder, H. Pottmann, T. Randrup, and J.
Wallner.
On surface
approximation using developable surfaces.
Graph. Models Img. Processing 61 (1999), 110-124.
[Zbl].
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S. Leopoldseder and H. Pottmann.
Approximation of
developable surfaces with cone spline surfaces.
Computer-Aided Design 30 (1998), 571-582.
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S. Leopoldseder.
Cone spline
surfaces and spatial arc splines.
PhD thesis, Technische Universität Wien, 1998.
Advisor: Helmut Pottmann.
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H. Dirnböck and H. Stachel.
The
development of the oloid.
J. Geom. Graphics 1 (1997), 105-118.
[Zbl], [MR].
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H. Pottmann and G. Farin.
Developable rational Bézier and B-spline surfaces.
Comput. Aided Geom. Design 12 (1995), 513-531.
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J. Hoschek and H. Pottmann.
Interpolation and approximation with developable B-spline surfaces.
In M. Dæhlen, T. Lyche, and L. L. Schumaker, editors, Mathematical
Methods for Curves and Surfaces, pages 255-264. Vanderbilt University
Press, Nashville, TN, 1995.
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H. Pottmann.
Studying NURBS curves and surfaces with classical geometry.
In M. D. hlen, T. Lyche, and L. L. Schumaker, editors, Mathematical Methods
for Curves and Surfaces, pages 413-438. Vanderbilt University Press,
Nashville, TN, 1995.
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H. Pottmann.
Rational curves and surfaces with rational offsets.
Comput. Aided Geom. Design 12 (1995), 175-192.
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