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Discrete Differential Geometry
Our research focuses on quadrilateral meshes with planar faces, and especially conical meshes.
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One aspect of this topic, motivated by the interesting geometry properties of conical meshes, is mesh optimisation and geometric modelling of surfaces for architecture (e.g., developables and PL structures which possess planar offset and support structures).
Another topic is investigating conical meshes from the viewpoint of Laguerre geometry, and consistency/integrability.
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Publications
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J. Wallner and H. Pottmann. Infinitesimally flexible meshes and discrete minimal surfaces. Technical Report 162, Geometry Preprint Series, Vienna Univ. of Technology, August 2006.
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H. Pottmann and J. Wallner. The focal geometry of circular and conical meshes. Adv. Comp. Math (2007), to appear.
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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.
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W. Wang, J. Wallner, and Y. Liu. An angle criterion for conical mesh vertices. Technical Report 157, Geometry Preprint Series, Vienna Univ. of Technology, April 2006.
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J. Wallner. Computing quadrilateral and conical meshes. In A. Bobenko, R. K. J. Sullivan, and G. Ziegler, editors, Discrete differential Geometry, volume 3 of Oberwolfach Reports. 2006. Abstracts from the workshop held March 6--10, 2006.
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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 (2006), submitted.
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Quick Links
Johannes Wallner
Affine Differential Geometry
Developable Surfaces
Nonlinear Subdivision
Geometric Spline Theory
Geometric Tolerancing
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