Applied Geometry

Christian Müller

Associate Professor

Head of research area Applied Geometry [www]

Applied Geometry
Wiedner Hauptstr. 8-10/104
A-1040 Vienna, Austria

Phone:

+43-1-58801-104465
Fax:

+43-1-58801-10493
Email:

cmueller at geometrie tuwien ac at
Web:

http://www.geometrie.tuwien.ac.at/mueller/

Education — Professional Experience — Research Interests: Show Details Hide Details

Education

PhD, Graz University of Technology, 04/2010 (Adv.: J. Wallner)
MSc, Graz University of Technology and University of Graz, 02/2007 (Adv.: O. Röschel)

Professional Experience

Assistant Professor, Institute of Discrete Mathematics and Geometry, TU Wien, since 02/2018
Visiting Associate, California Institute of Technology, Pasadena, CA, 02/2018 - 08/2018
Research Assistant, Institute of Discrete Mathematics and Geometry, TU Wien, 02/2011 - 01/2018
Research Visits, Fukuoka University and Kobe University, 07/2014 and 02/2016
Postdoc Fellow, EU Project, ModueleWorks GmbH, Aachen 08 - 10/2012 and 08 - 09/2015
FWF Project Assistant, Project Applications of Higher Geometries (PI: H. Pottmann), 05/2010 - 01/2011
Research Assistant, Institute of Geometry, TU Graz, 03/2007 - 04/2010

Research Interests

Discrete Differential Geometry
Computational Geometry
Geometry Processing
Geometry

Projects

Title:

Discrete geometric structures motivated by applications
Funded by:

FWF Austrian Science Fund [I 4868]
Duration:

10/2020 - 09/2024
Web:

http://www.discretization.de/en/projects/C01/

Title:

Discrete geometric structures motivated by applications in architecture
Funded by:

FWF Austrian Science Fund [I 2978]
Duration:

2020 - 2021
Web:

http://www.discretization.de/en/projects/C01/

Title:

Discrete surfaces with prescribed mean curvature
Funded by:

FWF Austrian Science Fund [P 29981]
Duration:

09/2017 - 02/2023
Web:

http://www.geometrie.tuwien.ac.at/mueller/projects/pmc/

Title:

Generating surfaces from curvature — a playful approach
Funded by:

FWF Austrian Science Fund [TCS 52]
Duration:

08/2018 - 07/2021
Web:

http://www.geometrie.tuwien.ac.at/mueller/projects/tcs/

Workshops Discrete Geometric Structures

Discrete Geoemtric Structures 2022
Discrete Geoemtric Structures 2024
Discrete Geoemtric Structures 2026

Courses

List of my courses in [TISS]

Preprints

Isometric surfaces in isotropic 3-space

C. Müller and H. Pottmann

Preprint (2025).

arXiv BibTeX

Discrete Lorentz surfaces and s-embeddings II: maximal surfaces

N.C. Affolter, F. Dellinger, C. Müller, D. Polly and N. Smeenk

Preprint, submitted (2025).

arXiv BibTeX

Klein-Arnold tensegrities

O. Karpenkov, F. Mohammadi, C. Müller, and B. Schulze

Preprint, submitted (2024).

arXiv BibTeX

A Differential Approach to Maxwell-Cremona Liftings

O. Karpenkov, F. Mohammadi, C. Müller and B. Schulze

Preprint, submitted (2024).

arXiv BibTeX

Publications

Discrete Lorentz surfaces and s-embeddings I: isothermic surfaces

N.C. Affolter, F. Dellinger, C. Müller, D. Polly and N. Smeenk

J. Geom. Phys., to appear (2025).

arXiv BibTeX

Sphericity and Geometric Properties of Ratios in Möbius and Laguerre Geometry

C. Müller and R. Rasoulzadeh-Mijic

Beitr. Algebra Geom. to appear (2025), 24p.

DOI BibTeX

Designing triangle meshes with controlled roughness

V. Ceballos Inza, P. Fykouras, F. Rist, D. Häseker, M. Hojjat, C. Müller and H. Pottmann

ACM Trans. Graphics 43, 6 (2024), 166:1-20, Proc. SIGGRAPH.

PDF BibTeX

Approximation by Meshes with Spherical Faces

A.S. Ramos Cisneros, A. Aikyn, M. Kilian, H. Pottmann, and C. Müller

ACM Trans. Graphics 43, 6 (2024), 179:1-17, Proc. SIGGRAPH.

PDF BibTeX

The Geometry of Discrete Asymptotic-Geodesic 4-Webs in Isotropic 3-Space

C. Müller and H. Pottmann

Monatsh. Math. 203, 223-246 (2024).

DOI BibTeX

Meshes with Spherical Faces

M. Kilian, A.S. Ramos Cisneros, C. Müller and H. Pottmann

ACM Trans. Graphics 42, 6 (2023), 177:1-177:19.

DOI PDF BibTeX

Smooth and Discrete Cone-Nets

M. Kilian C. Müller, and J. Tervooren

Results Maths 78, 110 (2023).

DOI BibTeX

Equilibrium stressability of multidimensional frameworks

O. Karpenkov, C. Müller, G. Panina, B. Servatius, H. Servatius, and D. Siersma

Eur. J. Math. 8, 33-61 (2022).

DOI BibTeX

Advanced Computational Design - digitale Methoden für die frühe Entwurfsphase

M. Wimmer, I. Kovacic, P. Ferschin, F. Rist, M. Hensel, K. Schinegger, S. Rutzinger, H. Kaufmann, M. Kilian, C. Müller, I. Izmestiev, G. Nawratil, J. Füssl, M. Stavric, D. Hahn, G. Suter

Bautechnik 99, H. 10, S. 720-730 (2022).

DOI BibTeX

Geometric criteria for realizability of tensegrities in higher dimensions

O. Karpenkov and C. Müller

SIAM J. Discrete Math. 35-2 (2021), pp. 637-660.

arXiv DOI BibTeX

Discrete Curvature and Torsion from Cross-Ratios

C. Müller and A. Vaxman

Ann. Mat. Pura Appl., 200, 1935-1960 (2021).

DOI arXiv BibTeX

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.

PDF BibTeX

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.

PDF BibTeX

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.

PDF DOI BibTeX

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.

PDF BibTeX

Canonical Möbius Subdivision

A. Vaxman, C. Müller and O. Weber

ACM Trans. Graphics (Proc. SIGGRAPH ASIA), 37(6), 227:1-227:15, 2018.

PDF BibTeX

Regular Meshes from Polygonal Patterns

A. Vaxman, C. Müller and O. Weber

ACM Trans. Graphics (Proc. SIGGRAPH), 36(4), 2017.

PDF BibTeX

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).

BibTeX DOI

Semi-discrete isothermic surfaces

F. Burstall, U. Hertrich-Jeromin, C. Müller and W. Rossman

Geom. Dedicata, 183 (2016), no. 1, 43-58.

arXiv BibTeX DOI

Planar discrete isothermic nets of conical type

C. Müller

Beitr. Algebra Geom. 57 (2016), no. 2, 459-482.

PDF BibTeX DOI

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)

PDF BibTeX

Semi-discrete Constant Mean Curvature Surfaces

C. Müller

Math. Z., 279 (2015), no. 1-2, 459-478.

PDF BibTeX DOI

On Discrete Constant Mean Curvature Surfaces

C. Müller

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

PDF BibTeX DOI

Discretizations of the hyperbolic cosine

C. Müller

Beitr. Algebra Geom., 54 (2013), no. 2, 509-531.

PDF BibTeX DOI

Semi-Discrete Isothermic Surfaces

C. Müller and J. Wallner

Results in Mathematics, 63 (2013), no. 3-4, 1395-1407.

PDF BibTeX DOI

Conformal hexagonal meshes

C. Müller

Geom. Dedicata 154 (2011), 27-46.

PDF BibTeX DOI

Oriented mixed area and discrete minimal surfaces

C. Müller and J. Wallner

Discrete Comput. Geom. 43 (2010), 303-320.

PDF BibTeX DOI