List of Publications

Publications 2013

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

Circular arc snakes and kinematic surface generation

M. Barton, L. Shi, M. Kilian, J. Wallner and H. Pottmann
Computer Graphics Forum 32 (2013), Proc. Eurographics

Smooth surfaces from bilinear patches: discrete affine minimal surfaces

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

Conchoid surfaces of quadrics

D. Gruber and M. Peternell
Journal of Symbolic Computation 59, 36-53, 2013

Conchoid surfaces of spheres

M. Peternell, D. Gruber and J. Sendra
Comput. Aided Geom. Design 30, 35-44, 2013

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.

List of Publications

Publications 2012

Ruled Laguerre minimal surfaces

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

Ruled Free Forms

S. Flöry, Y. Nagai, F. Isvoranu, H. Pottmann and J. Wallner
AAG, 2012

Intuitive Design Exploration of Constrained Meshes

X. Zhao, C.C. Tang, Y.L. Yang, H. Pottmann and N. Mitra
AAG, 2012

Darboux Cyclides and Webs from Circles

H. Pottmann, L. Shi and M. Skopenkov
Comput. Aided Geom. Design, 29: 77-97, 2012

Modeling Polyhedral Meshes with Affine Maps

A. Vaxman
Computer Graphics Forum, Vol. 31, Issue 5 (2012)

Design of self-supporting surfaces

E. Vouga, M. Höbinger, J. Wallner and H. Pottmann
ACM Trans. Graphics 31 (2012), Proc. SIGGRAPH.

Generalized Dupin Cyclides with Rational Lines of Curvature

M. Peternell
Proc. Conf. Avignon 2010 (Springer 2012)

List of Publications

Publications 2011

Shape Space Exploration of Constrained Meshes

Y.-L. Yang, Y.-J. Yang, H. Pottmann and N. J. Mitra
Proc. SIGGRAPH Asia (2011).

Functional webs for freeform architecture

B. Deng, H. Pottmann and J. Wallner
Computer Graphics Forum, Vol. 30, 2011

Circular arc structures

P. Bo, H. Pottmann, M. Kilian, W. Wang and J. Wallner
ACM Trans. Graphics 30 (2011), #101,1-11, Proc. SIGGRAPH.

Conformal hexagonal meshes

C. Müller
Geom. Dedicata 154 (2011)

Geometric Computing for Freeform Architecture

J. Wallner and H. Pottmann
J. Math. Industry (2011), Vol. 1

Conchoid surfaces of rational ruled surfaces

M. Peternell, D. Gruber, J. Sendra
Computer Aided Geometric Design, Vol. 28 (2011)

List of Publications

Publications 2010

Architectural Geometry as Design Knowledge

Pottmann, H.
Architectural Design (2010), Vol. 80, number 4

Advances in Architectural Geometry 2010

Ceccato, C.; Hesselgren, L.; Pauly, M.; Pottmann, H.; Wallner, J.
1st Edition., 2010, 242 p. 190 illus. in color., Hardcover ISBN: 978-3-7091-0308-1

Ruled Surfaces for Rationalization and Design in Architecture

S. Flöry and H. Pottmann
Proc. ACADIA, 2010

Designing Quad-dominant Meshes with Planar Faces

M. Zadravec, A. Schiftner, J. Wallner
Computer Graphics Forum 29/5 (2010), 1671-1679, Proc. Symp. Geometry Processing

Statics-Sensitive Layout of Planar Quadrilateral Meshes

A. Schiftner, J. Balzer
Proc. Advances in Architectural Geometry 2010

Tiling Freeform Shapes With Straight Panels: Algorithmic Methods

J. Wallner, A. Schiftner, M. Kilian, S. Floery, M. Hoebinger, B. Deng, Q. Huang, H. Pottmann
Proc. Advances in Architectural Geometry 2010

Case Studies in Cost-Optimized Paneling of Architectural Freeform Surfaces

M. Eigensatz, M. Deuss, A. Schiftner, M. Kilian, N. Mitra, H. Pottmann, M. Pauly
Proc. Advances in Architectural Geometry 2010

Freiformarchitektur und Mathematik

Helmut Pottmann and Johannes Wallner
Mitt. DMV, 18, 2, 88-95, 2010

Geodesic Patterns

H. Pottmann, Q. Huang, B. Deng, A. Schiftner, M. Kilian, L. Guibas, J. Wallner
ACM Trans.\ Graphics, Vol. 29, Nr.3, 2010

Paneling Architectural Freeform Surfaces

Michael Eigensatz, Martin Kilian, Alexander Schiftner, Niloy J. Mitra, Helmut Pottmann, Mark Pauly
SIGGRAPH 2010

Rational Two-Parameter Families of Spheres
and Rational Offset Surfaces

M. Peternell
J. Symbolic Computation 45 , 1-18, 2010.

Surface Fitting and Registration of Point Clouds using Approximations of the Unsigned Distance Function.

S. Flöry and M. Hofer
Computer Aided Geometric Design (CAGD)

A curvature theory for discrete surfaces based on mesh parallelity .

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

Edge offset meshes in Laguerre geometry.

H. Pottmann, P. Grohs, and B. Blaschitz.
Adv. Comp. Math. (2010)

List of Publications

Publications 2009

Geometry and New and Future Spatial Patterns

H. Pottmann
Architectural Design (2009), Vol. 79, number 6

Geometrische Struktur und Freiformarchitektur

J. Wallner and H. Pottmann
IBDG Vol. 27, Nr. 1, p. 34-38 (2009)

Rational offset surfaces and their modeling applications

Krasauskas, R. and Peternell, M.
IMA Volume 151: Nonlinear Computational Geometry, (eds.) I.Z. Emiris, F. Sottile, and Th. Theobald, p. 109-136, 2009.

Digital anastylosis of the Octagon in Ephesos

B. Thuswaldner, S. Flöry, R. Kalasek, M. Hofer, Q.-X. Huang, H. Thür
ACM Journal on Computing and Cultural Heritage (JOCCH) 2(1), 2009.

Fitting curves and surfaces to point clouds in the presence of obstacles

S. Flöry
Computer Aided Geometric Design (CAGD) 26(2): 192-202, 2009.

Packing circles and spheres on surfaces

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

Edge offset meshes in Laguerre geometry.

H. Pottmann, P. Grohs, and B. Blaschitz.
Adv. Comp. Math. (2009).

Integral invariants for robust geometry processing.

H. Pottmann, J. Wallner, Q. Huang, and Y.-L. Yang.
Comput. Aided Geom. Design, 26, 37-60 (2009)

Laguerre Minimal Surfaces, Isotropic Geometry and Linear Elasticity

H. Pottmann, P. Grohs and N.J. Mitra
Adv. Comp. Math, 31, 391-419 (2009).

Generalized Penetration Depth Computationbased on Kinematical Geometry

G. Nawratil, H. Pottmann and B. Ravani
Journal of Computer Aided Geometric Design, 26, 425-443 (2009).

List of Publications

Publications 2008

Geometry of Architectural Freeform Structures

H. Pottmann, A. Schiftner, and J. Wallner.
Int. Math. Nachr., Nr. 209/2008

On Generalized LN-Surfaces in 4-Space.

M. Peternell and B. Odehnal.
Proceedings of ISSAC08, 223-230, 2008

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).

4-Points Congruent Sets for Robust Pairwise Surface Registration.

D. Aiger, N.J.Mitra, and D. Cohen-Or.
ACM Trans. Graphics, 27/3, Proc. SIGGRAPH (2008).

Discovering Structural Regularity in 3D Geometry.

M. Pauly, N.J. Mitra, J. Wallner, H. Pottmann and L.J Guibas.
ACM Trans. Graphics, 27/3, Proc. SIGGRAPH (2008).

Curved Folding.

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

Constrained Curve Fitting on Manifolds.

S. Flöry, and M. Hofer.
Computer-Aided Design 40, 1(2008).

Infinitesimally flexible meshes and discrete minimal surfaces.

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

On quadratic two-parameter families of spheres and their envelopes

M. Peternell, B. Odehnal, M. L. Sampoli
Comput. Aided Geom. Design 25, 342-355 (2008).

Architectural Geometry

H. Pottmann, A. Asperl, M. Hofer and A. Kilian
Bentley Institute Press (2007), 724 pages, 2200 figures in color, ISBN 978-1-934493-04-5.

Convolution surfaces of quadratic triangular Bézier surfaces

M. Peternell and B. Odehnal
Comput. Aided Geom. Design (2008).

Subdivision Schemes for the fair Discretization of the Spherical Motion Group

G. Nawratil and H. Pottmann
Journal of Computational and Applied Mathematics 222 (2) 574-591 (2008).

The focal geometry of circular and conical meshes.

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

List of Publications

Publications 2007

Architectural Geometry

H. Pottmann, A. Asperl, M. Hofer and A. Kilian
Bentley Institute Press (2007), 724 pages, 2200 figures in color, ISBN 978-1-934493-04-5.

Minkowski sum boundary surfaces of 3D-objects

M. Peternell and T. Steiner
Graphical Models (2007).

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.

Discrete Surfaces in Isotropic Geometry

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

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

Symmetrization

Niloy J. Mitra, Leonidas Guibas and Mark Pauly
ACM Trans. Graphics 26/3 (2007), Proc. SIGGRAPH

Geometric Modeling in Shape Space

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

Dynamic Geometry Registration

Niloy J. Mitra, Simon Floery, Maks Ovsjanikov, Natasha Gelfand, Leonidas Guibas and Helmut Pottmann
Symposium on Geometry Processing 2007.

Approximating boundary-triangulated objects with balls.

O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, M. Peternell and H. Pottmann
In Proc. 23rd European Workshop on Computational Geometry.

Voronoi diagrams for oriented spheres.

F. Aurenhammer, J. Wallner, M. Peternell and H. Pottmann
In Proc. ISVD'07: 4th Int. Conf. Voronoi Diagrams in Science and Engineering.IEEE Computer Society, 2007.

A geometric method for automatic extraction of sulcal fundi.

C.-Y. Kao, M. Hofer, G. Sapiro, J. Stern, K. Rehm and D. A. Rottenberg
IEEE Trans. Medical Imaging.

Discrete surfaces for architectural design.

H. Pottmann, S. Brell-Cokcan and J. Wallner
In P. Chenin, T. Lyche and L. L. Schumaker, editors, Curves and Surface Design: Avignon 2006.

Robust feature classification and editing.

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

Fair webs

J. Wallner, H. Pottmann and M. Hofer
The Visual Computer.

List of Publications

Publications 2006

Surface fitting based on a feature sensitive parametrization.

Y. Lai, S.-H. Hu and H. Pottmann
Computer-Aided Design

Geometric modeling with conical meshes and developable surfaces.

Y. Liu, H. Pottmann, J. Wallner, Y.-L. Yang and W. Wang
In ACM Trans. Graphics Proc. SIGGRAPH

Constrained 3D shape reconstruction using a combination of surface fitting and registration.

Y. Liu, H. Pottmann and W. Wang
Computer-Aided Design

Fair polyline networks for constrained smoothing of digital terrain elevation data.

M. Hofer, G. Sapiro and J. Wallner
IEEE Trans. Geosc. Remote Sensing

$fracture$

Reassembling fractured objects by geometric matching.

Q.-X. Huang, S. Flöry, N. Gelfand, M. Hofer and H. Pottmann
ACM Trans. Graphics, Proc. SIGGRAPH 2006.

A geometric method for automatic extraction of sulcal fundi.

C.-Y. Kao, M. Hofer, G. Sapiro, J. Stern and D. A. Rottenberg
In Proc. ISBI'06 , IEEE (electronic), 2006

Equiform kinematics and the geometry of line elements.

B. Odehnal, H. Pottmann and J. Wallner
Beitr. Algebra Geom.

Sphere-geometric aspects of bisector surfaces

M. Peternell
Proceedings of the Conference Algebraic Geometry and Geometric Modeling 2006

Raumgeometrie - Konstruieren und Visualisieren

G. Pillwein, A. Asperl, R. Müllner and M. Wischounig
ÖBV-HPT-Verlag, Wien, 2006. ISBN 3-209-04745-6. 2 Bände. Lehr- und Übungsbuch für den Raumgeometrieunterricht in der AHS-Oberstufe.

Geometry and convergence analysis of algorithms for registration of 3D shapes

H. Pottmann, Q.-X. Huang, Y.-L. Yang and S.-M. Hu
Int. J. Computer Vision

Rational surfaces with linear normals and their convolutions with rational surfaces

M. L. Sampoli, M. Peternell and B. Jöttler
Comput. Aided Geom. Design

Intrinsic subdivision with smooth limits for graphics and animation

J. Wallner and H. Pottmann
ACM Trans. Graphics

Fitting B-spline curves to point clouds by squared distance minimization

W. Wang, H. Pottmann and Y. Liu
ACM Trans. Graphics

Robust principal curvatures on multiple scales

Y.-L. Yang, Y.-K. Lai, S.-M. Hu and H. Pottmann
In K. Polthier and A. Sheffer, editors, SGP 2006: 4th Eurographics Symposium on Geometry processing

List of Publications

Publications 2005

Robust global registration

N. Gelfand, N. J. Mitra, L. J. Guibas and H. Pottmann
In M. Desbrun and H. Pottmann, editors, SGP 2005: Third Eurographics Symposium on Geometry processing

3D shape recognition and reconstruction based on line element geometry

M. Hofer, B. Odehnal, H. Pottmann, T. Steiner and J. Wallner
In Tenth IEEE International Conference on Computer Vision IEEE Computer Society, 2005

Swept volumes

M. Peternell, H. Pottmann, T. Steiner and H. Zhao
Computer-Aided Design Appl. 2 ,

A geometric idea to solve the eikonal equation

M. Peternell and T. Steiner
n B. Jüttler, editor, SCCG '05: Proceedings of the 21st spring conference on Computer graphics, pages 43-48. ACM Press, 2005,

Industrial Geometry: Recent advances and applications in CAD

H. Pottmann, S. Leopoldseder, M. Hofer, T. Steiner and W. Wang
Computer-Aided Design 37/7 (2005),

A variational approach to spline curves on surfaces

H. Pottmann and M. Hofer
Comput. Aided Geom. Design 22/7 (2005)

Fair curve networks in nonlinear geometries

J. Wallner, H. Pottmann and M. Hofer
ACM SIGGRAPH 2005 Conference Abstracts and Applications

How to teach CAD

A. Asperl
Computer-Aided Design Appl. 2 (2005), 459-468.