Institute of Geometry

Johannes Wallner

Univ.Prof. Dr.
Phone:+43-316-873-8440
Fax:+43-316-873-8448
Email: tugraz.at at j.wallner

Since January 2007, I am a professor of Geometry at TU Graz. Before that time I was with TU Wien, where I also got my Ph.D. Since October 2009 I am again affiliated with TU Wien, as a part time professor at the geometric modeling and industrial geometry group.

Research interests

Discretization in Geometry and Dynamics	SFB/Transregio (FWF Grant I-705)	[active]
Doctoral College Discrete Mathematics	FWF grant No. W1230	[active]
Multivariate subdivision processes	FWF grant No. P19780
Smoothness of nonlinear subdivision algorithms	FWF grant No. P18575
Computational Differential Geometry	FWF grant No. S9209
Freeform surfaces in architecture	Visual Computing grant (FFG)
Geometries and their Groups
Kinematics and Configuration spaces
Geometric Tolerancing	FWF grant No. P15911
Geometric Spline Theory
Geometry of NC Milling	FWF grant No. P13938
Modeling of Developable Surfaces	FWF grant No. P12252
Computational Line Geometry.	FWF grant No. P13648

Conferences

Advances in Architectural Geometry (Imperial College, London, 18-19.9.2014)
Geometry Workshop (Strobl, 28.-31.8.2013)
1st Workshop on Discretization in Geometry and Dynamics (Obergurgl 16.-22.12.2012)
Advances in Architectural Geometry (Paris, 27.-30.9.2012)
Discrete Differential Geometry (Oberwolfach, 8.7.-14.7.2012)
8th Int. Conf. on Mathematical Methods for Curves and Surfaces (Oslo, 28.6.-3.7.2012)
New Trends in Approximation Theory (Ein Gedi, Israel, 4.-7.1.2012)

Publications

for a complete list, click here

Books

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.
C. Ceccato, L. Hesselgren, M. Pauly, H. Pottmann, and J. Wallner. Advances in Architectural Geometry 2010. Springer, 2010. ISBN 978-3-7091-0308-1.
H. Pottmann and J. Wallner. Computational Line Geometry. Mathematics + Visualization. Springer, Heidelberg, 2010. ISBN 978-3-642-04017-7. 2nd printing. [Zbl], [MR].

Recent manuscripts

M. Barton, L. Shi, M. Kilian, J. Wallner, and H. Pottmann. Circular arc snakes and kinematic surface generation. Computer Graphics Forum 32/2 (2013), 1-10, Proc. Eurographics.
O. Karpenkov and J. Wallner. On offsets and curvatures for discrete and semidiscrete surfaces. Beitr. Algebra Geom. (2014), to appear. [doi].
C. Müller and J. Wallner. Semidiscrete isothermic surfaces. Results Math. (2013), to appear. [doi].
J. Wallner. On convergent interpolatory subdivision schemes in Riemannian geometry. Geometry Preprint 2012/02, TU Graz, April 2012.

Publications 2012

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.
P. Grohs and J. Wallner. Definability and stability of multiscale decompositions for manifold-valued data. J. Franklin Institute 349 (2012), 1648-1884. [doi], [arxiv:1001.1517].
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.
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].
J. Wallner. On the semidiscrete differential geometry of A-surfaces and K-surfaces. J. Geometry 103 (2012), 161-176. [doi].

Publications 2011

J. Wallner, E. Nava Yazdani, and A. Weinmann. Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces. Adv. Comp. Math 34 (2011), 201-218. [MR], [doi].
P. Bo, H. Pottmann, M. Kilian, W. Wang, and J. Wallner. Circular arc structures. ACM Trans. Graphics 30 (2011), #101,1-11, Proc. SIGGRAPH. [doi].
J. Wallner and H. Pottmann. Geometric computing for freeform architecture. J. Math. Industry 1 (2011), #4,1-19. [doi].
B. Deng, H. Pottmann, and J. Wallner. Functional webs for freeform architecture. Computer Graphics Forum 30/5 (2011), 1369-1378, Proc. Symp. Geometry Processing. [doi].
J. Wallner. Circular arc structures. In V. Caselles et al., editors, Trends in Mathematical Imaging and Surface Processing, Oberwolfach Reports, pages 41-43. 2011. Abstracts from the workshop held January 30--February 5th, 2011. [doi].

Publications 2010

A. Bobenko, H. Pottmann, and J. Wallner. A curvature theory for discrete surfaces based on mesh parallelity. Math. Annalen 348 (2010), 1-24. [MR], [doi], [arxiv:0901.4620].
C. Ceccato, L. Hesselgren, M. Pauly, H. Pottmann, and J. Wallner. Advances in Architectural Geometry 2010. Springer, 2010. ISBN 978-3-7091-0308-1.
N. Dyn, P. Grohs, and J. Wallner. Approximation order of interpolatory nonlinear subdivision schemes. J. Comput. Appl. Math. 223 (2010), 1697-1703. [MR], [doi].
C. Müller and J. Wallner. Oriented mixed area and discrete minimal surfaces. Discrete Comput. Geom. 43 (2010), 303-320. [Zbl], [MR], [doi].
H. Pottmann and J. Wallner. Computational Line Geometry. Mathematics + Visualization. Springer, Heidelberg, 2010. ISBN 978-3-642-04017-7. 2nd printing. [Zbl], [MR].
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].
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.
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].

Publications 2009

P. Grohs and J. Wallner. Interpolatory wavelets for manifold-valued data. Appl. Comput. Harmon. Anal. 27 (2009), 325-333. [Zbl], [MR], [doi].
H. Pottmann, J. Wallner, Q. Huang, and Y.-L. Yang. Integral invariants for robust geometry processing. Comput. Aided Geom. Design 26 (2009), 37-60. [Zbl], [MR], [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].
R. Tichy and J. Wallner. Johannes Frischauf - eine schillernde Persönlichkeit in Mathematik und Alpinismus. Int. Math. Nachr. 210 (2009), 21-32. [Zbl].
J. Wallner. Semidiscrete surface representations. In A. Bobenko et al., editors, Discrete Differential Geometry, Oberwolfach Reports. 2009. Abstracts from the workshop held January 12--17, 2009. [doi].
J. Wallner and H. Pottmann. Geometrische Struktur und Freiformarchitektur. IBDG 27/1 (2009), 34-38.

Publications 2008

P. Grohs and J. Wallner. Log-exponential analogues of univariate subdivision schemes in Lie groups and their smoothness properties. In M. Neamtu and L. L. Schumaker, editors, Approximation Theory XII: San Antonio 2007, pages 181-190. Nashboro Press, 2008, ISBN 978-0-9728482-9-9. [Zbl], [MR].
M. Pauly, N. J. Mitra, J. Wallner, H. Pottmann, and L. Guibas. Discovering structural regularity in 3D geometry. ACM Trans. Graphics 27/3 (2008), #43,1-11, Proc. SIGGRAPH. [doi].
H. Pottmann, A. Schiftner, and J. Wallner. Geometry of architectural freeform structures. Int. Math. Nachr. 209 (2008), 15-28.
H. Pottmann and J. Wallner. The focal geometry of circular and conical meshes. Adv. Comp. Math 29 (2008), 249-268. [Zbl], [MR], [doi].
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].
J. Wallner and H. Pottmann. Infinitesimally flexible meshes and discrete minimal surfaces. Monatshefte Math. 153 (2008), 347-365. [Zbl], [MR], [doi].

Teaching

see here