Research area — Projects — Publications

Head of research area Applied Geometry

Computational Fabrication
Computational Design • Shape Optimization • Exploration of Shape Collections • Fabrication-Aware Shape Modeling • Shape Modeling for Personal Fabrication
Geometry Education
Computational Line and Sphere Geometry • Geometric Modeling • Teacher Training
Discrete Differential Geometry and Applications
Semi-Discrete Surfaces • Discrete Isothermic / Minimal / CMC Surfaces • Computational Geometry • Hexagonal Meshes • Geometry Processing • Conformal Mesh Deformations
Geometry Processing and Shape  Optimization
Geometry Processing • Differential Geometry • Computational Design • Applications in Architecture

Active third-party funded research projects:

Publications 2022
Equilibrium stressability of multidimensional frameworks
O. Karpenkov, C. Müller, G. Panina, B. Servatius, H. Servatius, and D. Siersma
Eur. J. Math., (2022), to appear.
Publications 2021
Using Flexible Trapezoidal Quad-Surfaces for Transformable Design
K. Sharifmoghaddam, G. Nawratil, A. Rasoulzadeh, and J. Tervooren
IASS Annual Symposium and Spatial Structures Conference (Surrey, UK), 12p., (2021).
Analysis of a reduced-order model for the simulation of elastic geometric zigzag-spring meta-materials
K. Leimer and P. Musialski
Computers & Graphics, (2021), to appear.
Design and fabrication of multi-patch elastic geodesic grid structures
S. Pillwein, J. Kübert, F. Rist, and P. Musialski
Computers & Graphics 98, (2021), 218-230.
Generalized Deployable Elastic Geodesic Grids
S. Pillwein and P. Musialski
ACM Trans. Graphics 40, 6 (2021), 271:1-271:15.
Using isometries for computational design and fabrication
C. Jiang, H. Wang, V. Ceballos Inza, F. Dellinger, F. Rist, J. Wallner, and H. Pottmann
ACM Trans. Graphics 40, 4 (2021), 42:1-42:12, Proc. SIGGRAPH.
Computational design of Weingarten surfaces
D. Pellis, M. Kilian, H. Pottmann, and M. Pauly
ACM Trans. Graphics 40, 4 (2021), 114:1-114:11, Proc. SIGGRAPH.
Geometric criteria for realizability of tensegrities in higher dimensions
O. Karpenkov and C. Müller
SIAM J. Discrete Math. 35-2 (2021), pp. 637-660.
Discrete Curvature and Torsion from Cross-Ratios
C. Müller and A. Vaxman
Ann. Mat. Pura Appl., 200, 1935-1960 (2021).
Publications 2020
Reduced-Order Simulation of Flexible Meta-Materials
K. Leimer and P. Musialski
SCF '20: Proceedings of the ACM Symposium on Computational Fabrication (2020), 11p.
Design and Fabrication of Elastic Geodesic Grid Structures
S. Pillwein, J. Kübert, F. Rist, and P. Musialski
SCF '20: Proceedings of the ACM Symposium on Computational Fabrication (2020), 11p.
Computational Design of Cold Bent Glass Facades
K. Gavriil, R. Guseinov, J. Perez, D. Pellis, P. Henderson, F. Rist, H. Pottmann, and B. Bickel
ACM Trans. Graphics 39(6) 208:1-208:16, 2020. Proc. SIGGRAPH Asia.
Freeform quad-based kirigami
C. Jiang, F. Rist, H. Pottmann, and J. Wallner
ACM Trans. Graphics 39, 6 (2020), Proc. SIGGRAPH Asia.
Architectural freeform surfaces designed for cost-effective paneling through mold re-use
D. Pellis, M. Kilian, H. Wang, C. Jiang, C. Müller, and H. Pottmann
Advances in Architectural Geometry 2020.
Pose to Seat: Automated design of body-supporting surfaces
K. Leimer, A. Winkler, S. Ohrhallinger, and P. Musialski
Computer Aided Geometric Design, (2020).
On Elastic Geodesic Grids and Their Planar to Spatial Deployment
S. Pillwein, K. Leimer, M. Birsak and P. Musialski
ACM Trans. Graphics 39, 4 (2020), 1-12, Proc. SIGGRAPH.
Quad-mesh based isometric mappings and developable surfaces
C. Jiang, C. Wang, F. Rist, J. Wallner and H. Pottmann
ACM Trans. Graphics, 39(4), 2020, Proc. SIGGRAPH.
Principal Symmetric Meshes
D. Pellis, H. Wang, M. Kilian, F. Rist, H. Pottmann, and C. Müller
ACM Trans. Graphics 39, 4 (2020), 127:1-127:17, Proc. SIGGRAPH.
Simulation of Flexible Patterns by Structural Simplification
K. Leimer and P. Musialski
ACM SIGGRAPH 2020 Posters (2020), 39(2).
Discretizations of surfaces with constant ratio of principal curvatures
M.R. Jimenez, C. Müller and H. Pottmann
Discrete Comput. Geom. 63(3), (2020), 670-704.
Multi-nets: Classification of discrete and smooth surfaces with characteristic properties on arbitrary parameter rectangles
A.I. Bobenko, H. Pottmann, and T. Rörig
Discrete Comput. Geom. 63, (2020), 624-655.
Smooth polyhedral surfaces
F. Günther, C. Jiang, and H. Pottmann
Advances in Mathematics, 363, (2020).
Publications 2019
Curve-pleated Structures
C. Jiang, K. Mundilova, F. Rist, J. Wallner, and H. Pottmann
ACM Trans. Graphics 38,6 (Proc. SIGGRAPH ASIA), 2019.
Discrete Geodesic Parallel Coordinates
H. Wang, D. Pellis, F. Rist, H. Pottmann, and C. Müller
ACM Trans. Graphics 38,6 (2019), 173:1-173:13, Proc. SIGGRAPH ASIA.
Visual Smoothness of Polyhedral Surfaces
D. Pellis, M. Kilian, F. Dellinger, J. Wallner and H. Pottmann
ACM Trans. Graphics (Proc. SIGGRAPH), 2019.
Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces
K. Gavriil, A. Schiftner and H. Pottmann
Computer-Aided Design (2019), 111, 29-43.
Void Filling of Digital Elevation Models with Deep Generative Models
K. Gavriil, G. Muntingh and O.J.D. Barrowclough
to appear in IEEE Geoscience and Remote Sensing Letters, (2019).
Publications 2018
Sit & Relax: Interactive Design of Body-Supporting Surfaces
K. Leimer, M. Birsak, F. Rist and P. Musialski
Computer Graphics Forum, 37(7):349-359, 2018.
Best Paper Honorable Mention
Canonical Möbius Subdivision
A. Vaxman, C. Müller and O. Weber
ACM Trans. Graphics (Proc. SIGGRAPH ASIA), 37(6), 227:1-227:15, 2018.
Folding the Vesica Piscis
K. Mundilova and T. Wills
In Eve Torrence et al., editors, Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, (2018), 535-538.
Aligning principal stress and curvature directions
D. Pellis and H. Pottmann
In L. Hesselgren et al., editors, Advances in Architectural Geometry 2018, pages 34-53, 2018.
Design and Construction of Curved Support Structures with Repetitive Parameters
E. Schling, M. Kilian, H. Wang, J. Schikore, H. Pottmann
In L. Hesselgren et al., editors, Advances in Architectural Geometry 2018, pages 140-165, 2018.
Designing patterns using triangle-quad hybrid meshes
C-h. Peng, H. Pottmann, P. Wonka
ACM Trans. Graphics (Proc. SIGGRAPH), 37(4), 2018.
Cissoid constructions of augmented rational ruled surfaces
J.R. Sendra, M. Peternell and J. Sendra
Comput. Aided Geom. Design (2018), 60, 1-9.
String Art: Towards Computational Fabrication of String Images
M. Birsak, F. Rist, P. Wonka and P. Musialski
Computer Graphics Forum (Proc. EUROGRAPHICS), 37(2), 2018.
Publications 2017
Relation-Based Parametrization and Exploration of Shape Collections
K. Leimer, L. Gersthofer, M. Wimmer and P. Musialski
Computers & Graphics, 67:127-137, 2017.
Path Exploration on Mobile Devices
M. Birsak, P. Musialski, P. Wonka and M. Wimmer
IEEE Transactions on Visualization and Computer Graphics, PP(99):1-15, 2017.
Material-minimizing forms and structures
M. Kilian, D. Pellis, J. Wallner and H. Pottmann
ACM Trans. Graphics (Proc. SIGGRAPH Asia), 36(6), 2017.
Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining
P. Bo, M. Barton, and H. Pottmann
Computer Aided Design, (2017), 91, 84-94.
Regular Meshes from Polygonal Patterns
A. Vaxman, C. Müller and O. Weber
ACM Trans. Graphics (Proc. SIGGRAPH), 36(4), 2017.
Semi-Discrete Constant Mean Curvature Surfaces of Revolution in Minkowski Space
C. Müller and M. Yasumoto
Geometry, integrability and quantization XVIII, 191-202, Bulgar. Acad. Sci., Sofia, (2017).
String actuated curved folded surfaces
M. Kilian, A. Monszpart and N. J. Mitra
ACM TOG, 36(3) Article 25 (2017).
Publications 2016
Vertex normals and face curvatures of triangle meshes
X. Sun, C. Jiang, J. Wallner and H. Pottmann
In A. Bobenko, editor, Advances in Discrete Differential Geometry, pages 267-286, Springer 2016.
Geometry and freeform architecture
H. Pottmann and J. Wallner
In W. König, editor, Mathematics and Society, pages 131-151. EMS 2016.
Measuring and controlling fairness of triangulations
C. Jiang, F. Günther, J. Wallner and H. Pottmann
In S. Adriaenssens et al., editors, Advances in Architectural Geometry 2016, pages 24-39. VDF Hochschulverlag, ETH Zürich, 2016.
Analysis and design of curved support structures
C. Tang, M. Kilian, P. Bo, J. Wallner and H. Pottmann
In S. Adriaenssens et al., editors, Advances in Architectural Geometry 2016, pages 8-23. VDF Hochschulverlag, ETH Zürich, 2016.
Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution
Pengbo Bo, Michael Bartoň, Denys Plakhotnik and Helmut Pottmann
Computer Aided Design (2016), 79, 1-11.
Interactive design of developable surfaces
C. Tang, P. Bo, J. Wallner and H. Pottmann
ACM Trans. Graphics, 35(2), 2016, #12,1-12.
Semi-discrete isothermic surfaces
F. Burstall, U. Hertrich-Jeromin, C. Müller and W. Rossman
Geom. Dedicata, 183 (2016), no. 1, 43-58.
Planar discrete isothermic nets of conical type
C. Müller
Beitr. Algebra Geom. 57 (2016), no. 2, 459-482.
Publications 2015
Polyhedral Patterns
C. Jiang, C. Tang, A. Vaxman, P. Wonka and H. Pottmann
ACM Trans. Graphics (Proc. SIGGRAPH Asia), 34(6), 2015.
Conformal Mesh Deformations with Möbius Transformations
A. Vaxman, C. Müller and O. Weber
ACM Trans. Graphics (Proc. SIGGRAPH), 34(4), 2015.
Best Paper Award 2015 (Fac of Math and Geoinf — TU Wien)
Integrable PolyVector Fields
O. Diamanti, A. Vaxman, D. Panozzo, and O. Sorkine-Hornung
ACM Trans. Graphics (Proc. SIGGRAPH), 34(4), 2015.
Single breath-hold 3D measurement of left atrial volume using compressed sensing CMR and a non-model-based reconstruction approach
O. Vardoulis, P. Monney, D. Piccini, A. Bermano, A. Vaxman, C. Gotsman, J. Schwitter, M. Stuber, N. Stergiopulos and J. Schwitter
Journal of Cardiovascular Magnetic Resonance, 17(1), 2015.
Offsets, conchoids and pedal surfaces
M. Peternell, L. Gotthart, J. Sendra and J.R. Sendra
J. Geom. 106 (2015), 321-339.
Precise Gouging-free Tool Orientations for 5-Axis CNC Machining
Y.-J. Kim, G. Elber, M. Bartoň and H. Pottmann
Computer-Aided Design (2015), 15, 220-229.
Cell packing structures.
H. Pottmann, C. Jiang, M. Höbinger, J. Wang, P. Bompas and J. Wallner
Computer-Aided Design (2015), 60, 70-83.
Architectural Geometry
H. Pottmann, M. Eigensatz, A. Vaxman and J. Wallner
Computers and Graphics (2015), vol. 47, 145-164.
Semi-discrete Constant Mean Curvature Surfaces
C. Müller
Math. Z., 279 (2015), no. 1-2, 459-478.

Publications 2014
A Projective Framework for Polyhedral Mesh Modeling
A. Vaxman
Computer Graphics Forum, 33(8), 2014.
Interactive Modeling of Architectural Freeform Structures - Combining Geometry with Fabrication and Statics
C. Jiang, C. Tang, M. Tomičić, J. Wallner and H. Pottmann
AAG 2014.
Form-finding with Polyhedral Meshes Made Simple.
C. Tang, X. Sun, A. Gomes, J. Wallner, and H. Pottmann
ACM Trans. Graphics 33/4 (2014), Proc. SIGGRAPH.
On Discrete Constant Mean Curvature Surfaces
C. Müller
Discrete Comput. Geom., 51 (2014), no. 3, 516-538.
Designing N-PolyVector Fields with Complex Polynomials
O. Diamanti, A. Vaxman, D. Panozzo and O. Sorkine-Hornung
Computer Graphics Forum 33/5, (2014), Proc. Symp. Geom. Processing.
Freeform Honeycomb Structures
C. Jiang, J. Wang, J. Wallner and H. Pottmann
Computer Graphics Forum 33/5 (2014), Proc. Symp. Geom. Processing.
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 31 (2014), no. 7-8, 331-344.
Detection and reconstruction of freeform sweeps.
M. Barton, H. Pottmann and J. Wallner
Computer Graphics Forum 33/2 (2014), Proc. Eurographics.
Publications 2005 — 2013
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