Computational Differential Geometry
Concepts from differential geometry play a crucial role in a variety of geometry-related application areas such as geometric modeling, geometry processing, computer vision and image processing. The current focus of our research in computational differential geometry is on integral invariants, special discrete representations and the use of appropriate metrics for feature sensitive processing and computations in shape spaces.

This research is supported by


Semi-discrete Constant Mean Curvature Surfaces

C. Müller
Math. Z., (to appear).

Smooth surfaces from rational bilinear patches

L. Shi, J. Wang and H. Pottmann
Comput. Aided Geom. Design (2014), 31(1), 1-12.

Affine arc length polylines and curvature continuous uniform B-splines

F. Käferböck
Comput. Aided Geom. Design, Special Issue, (to appear).

On Discrete Constant Mean Curvature Surfaces

C. Müller
Discrete Comput. Geom., 51 (2014), no. 3, 516-538.

Discrete Line Congruences for Shading and Lighting

J. Wang, C. Jiang, P. Bompas, J. Wallner, and H. Pottmann
Computer Graphics Forum 32/5 (2013), Proc. Symposium Geometry Processing

Smooth surfaces from bilinear patches: discrete affine minimal surfaces

F. Käferböck and H. Pottmann
Comput. Aided Geom. Design 30(5): 476-489, 2013

Ruled Laguerre minimal surfaces

M. Skopenkov, H. Pottmann and P. Grohs
Math. Z. 272, 645-674, 2012

Discretizations of the hyperbolic cosine

C. Müller
Beitr. Algebra Geometrie 54 (2013), no. , 509-531.

Semi-Discrete Isothermic Surfaces

C. Müller and J. Wallner
Results Math.
63 (2013), no. 3-4, 1395-1407.

Conformal hexagonal meshes

C. Müller
Geom. Dedicata 154 (2011)

A curvature theory for discrete surfaces based on mesh parallelity .

Alexander I. Bobenko, Helmut Pottmann, and Johannes Wallner
Math. Annalen (2010)

Packing circles and sphere on surfaces

A. Schiftner, M. Höbinger, J. Wallner, H. Pottmann
to appear in ACM Trans. Graphics, 28/5, Proc. SIGGRAPH Asia (2009)
panels

Freeform surfaces from single curved panels.

H. Pottmann, A. Schiftner, P. Bo, H. Schmiedhofer, W. Wang, N. Baldassini, and J. Wallner.
ACM Trans. Graphics, 27/3, Proc. SIGGRAPH (2008).
fold

Curved Folding.

M. Kilian, S. Föry, Z. Chen, N. J. Mitra, A. Sheffer and H. Pottmann.
ACM Trans. Graphics, 27/3, Proc. SIGGRAPH (2008).
meshes

Integral invariants for robust geometry processing.

H. Pottmann, J. Wallner, Q. Huang, and Y.-L. Yang.
Comput. Aided Geom. Design (2008).
meshes

Infinitesimally flexible meshes and discrete minimal surfaces.

J. Wallner and H. Pottmann
Monatshefte Math., 153/347-365 (2008).
laguerre

Laguerre Minimal Surfaces, Isotropic Geometry and Linear Elasticity

H. Pottmann, P. Grohs and N.J. Mitra
Adv. Comp. Math.
robust

The focal geometry of circular and conical meshes.

H. Pottmann and J. Wallner
Adv. Comp. Math (2008).
principal

Principal curvatures from the integral invariant viewpoint

H. Pottmann, J. Wallner, Y.-L. Yang, Y.-K. Lai, and S.-M. Hu
Comput. Aided Geom. Design 24 (2007), 428-442.
isogeom

Discrete Surfaces in Isotropic Geometry

H. Pottmann, Y. Liu
The Mathematics of Surfaces XII(2007).
freeform

Geometry of multi-layer freeform structures for architecture

H. Pottmann, Y. Liu, J. Wallner, A. Bobenko and W. Wang
ACM Trans. Graphics 26/3 (2007), Proc. SIGGRAPH
freeform

Geometric Modeling in Shape Space

Martin Kilian, Niloy J. Mitra and Helmut Pottmann
ACM Trans. Graphics 26/3 (2007), Proc. SIGGRAPH
robust

Robust feature classification and editing.

Y.-K. Lai, Q.-Y. Zhou, S.-M. Hu, J. Wallner and H. Pottmann.
IEEE Trans. Vis. Comp. Graphics.