Sunil Kumar Yadav, Ulrich Reitebuch and Konrad Polthier**Mesh Denoising based on Normal Voting Tensor and Binary Optimization**

To appear in: IEEE Transactions on Visualization and Computer Graphics (Volume: PP, Issue: 99)

Sunil Kumar Yadav, Seyedamirhosein Motamedi, Timm Oberwahrenbrock, Frederike Cosima Oertel, Konrad Polthier, Friedemann Paul, Ella Maria Kadas, and Alexander U. Brandt **CuBe: parametric modeling of 3D foveal shape using cubic Bézier**

To appear in: Biomedical Optics Express, Vol. 8, Issue 9, pp. 4181-4199, 2017

Martin Skrodzki and Konrad Polthier, **Turing-Like Patterns Revisited: A Peek Into The Third Dimension**

To appear in: Proceedings of Bridges, 2017

Faniry Razafindrazaka and Konrad Polthier, **Optimal Base Complexes for Quadrilateral Meshes**

In: Computer Aided Geometric Design, pp. 63-74, 2017

[pdf, 15 MB][BibTex]

Konstantin Poelke and Konrad Polthier

**Discrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary**

In: TopoInVis 2017 proceedings

[Extended Abstract, pdf, 1 MB][BibTex]

Martin Skrodzki, Ulrich Reitebuch and Konrad Polthier,

**Chladni Figures Revisited: A Peek Into The Third Dimension**

In: Proceedings of Bridges, pp. 481-484, 2016

Konstantin Poelke and Konrad Polthier,

**Boundary-aware Hodge decompositions for piecewise constant vector fields**

In: Computer-Aided Design (78), pp. 126-136, 2016

*1st price at SPM 2016 best paper awards*

[Article] [Preprint pdf, 6 MB][BibTex]

Anna Wawrzinek and Konrad Polthier,

**Integration of generalized B-spline functions on Catmull–Clark surfaces at singularities**

In: Computer-Aided Design (78), pp. 60-70, 2016

Konrad Polthier, Faniry Razafindrazaka**Discrete Geometry for Reliable Surface Quad-Remeshing**. In: Applications + Practical Conceptualization + Mathematics = fruitful Innovation, Proceedings of the Forum of Mathematics for Industry 2014. Springer. 2014

[preprint pdf, 10.7 MB] [BibTex]

Sebastian Götschel, Christoph von Tycowicz, Konrad Polthier, Martin Weiser**Reducing Memory Requirements in Scientific Computing and Optimal Control**. In: Multiple Shooting and Time Domain Decomposition Methods. Springer. 2015

[preprint pdf, 828 KB] [BibTex]

Faniry Razafindrazaka, Ulrich Reitebuch, Konrad Polthier**Perfect Matching Quad Layouts for Manifold Meshes**. Symposium on Geometry Processing (SGP), Graz 2015

[preprint pdf, 0.5 MB] [BibTex]

Faniry Razafindrazaka, Konrad Polthier**Realization of Regular Maps of Large Genus**. in: Topological and Statistical Methods for Complex Data. Mathematics and Visualization series. Pages 239-252. Springer. 2015

[pdf, 11.7 MB] [BibTex]

Christian Schulz, Christoph von Tycowicz, Hans-Peter Seidel, and Klaus Hildebrandt**Animating Deformable Objects using Sparse Spacetime Constraints**. ACM Transactions on Graphics (SIGGRAPH 2014), Volume 33, Issue 4, July 2014, pages 109:1-109:10.

[pdf, 8.5 MB] [BibTex]

Konrad Polthier, John M. Sullivan, Günter M. Ziegler, Hans-Christian Hege**Visualization**. In: MATHEON-Mathematics for Key Technology. EMS Series in Industrial and Applied Mathematics 1. European Mathematical Society 2014. Page 335-339

[pdf, 1.9 MB] [BibTex]

Konrad Polthier, Alexander Bobenko, Klaus Hildebrandt, Ralf Kornhuber, Christoph von Tycowicz, Harry Yserentant, Günter M. Ziegler**Geometry Processing**. in: MATHEON-Mathematics for Key Technology. EMS Series in Industrial and Applied Mathematics 1. European Mathematical Society 2014. Page 341-355

[pdf, 6.35 MB] [BibTex]

Felix Kälberer, Matthias Nieser, Konrad Polthier**Showcase 22, Mathematics in Hollywood**. In: MATHEON-Mathematics for Key Technology. EMS Series in Industrial and Applied Mathematics 1. European Mathematical Society 2014. Page 356-357

[pdf, 717 KB] [BibTex]

John M. Sullivan, Ulrich Pinkall, Konrad Polthier**Mathematical Visualization**, in: MATHEON-Mathematics for Key Technology. EMS Series in Industrial and Applied Mathematics 1. European Mathematical Society 2014. Page 381-392

[pdf, 12.7 MB] [BibTex]

Konstantin Poelke, Zoi Tokoutsi, Konrad Polthier**Complex Polynomial Mandalas and their Symmetries. **Proceedings of Bridges 2014, Tessellations Publishing, Page 433-436

[pdf, 4.5 MB] [BibTex]

Faniry Razafindrazaka, Konrad Polthier**Regular Surfaces and Regular Maps. **Proceedings of Bridges 2014, Tessellations Publishing, Page 225-234

[pdf, 1.5 MB] [BibTex]

Niklas Krauth, Matthias Nieser, Konrad Polthier**Differential-Based Geometry and Texture Editing with Brushes**. Journal of Mathematical Imaging and Vision, Volume 48, Issue 2 (2014), Page 359-368

[preprint pdf, 10.4 MB] [supplementary video] [BibTex]

Eduardo Colli, Fidel R. Nemenzo, Konrad Polthier, Christiane Rousseau **Mathematics is everywhere**. Proceedings of the International Congress of Mathematicians. Pages 799-811.

[pdf, 1.64 MB] [BibTex]

Faniry Razafindrazaka, Konrad Polthier**The 6-ring. **Bridges 2013, July 27-31, Enschede.

[pdf, 2.24 MB] [BibTex]

Faniry Razafindrazaka, Konrad Polthier**Regular map smoothing. **DGCI 2013, March 20-22, Seville.

[pdf, 0.3 MB] [BibTex]

Christoph von Tycowicz, Christian Schulz, Hans-Peter Seidel, Klaus Hildebrandt**An Efficient Construction of Reduced Deformable Objects**. ACM Transactions on Graphics (SIGGRAPH Asia 2013), Volume 32, Issue 6.

[preprint pdf, 11 MB] [supplementary video] [DOI] [BibTex]

Esfandiar Nava-Yazdani, Konrad Polthier**De Casteljauʼs algorithm on manifolds. **Computer Aided Geometric Design, Volume 30, Issue 7, October 2013, Pages 722-732

Klaus Hildebrandt, Konrad Polthier**Consistent discretizations of the Laplace–Beltrami operator and the Willmore energy of surfaces**. Oberwolfach Reports, Workshop 1228: Discrete Differential Geometry, 2012.

[BibTex]

Konstantin Poelke, Konrad Polthier

**Domain Coloring of Complex Functions: An Implementation-Oriented Introduction. **IEEE Computer Graphics and Applications, vol. 32, no. 5, pp. 90-97, Sept.-Oct., 2012

[preprint pdf, 1,2 MB] [DOI] [BibTex]

Ulrich Bauer, Carsten Lange, Max Wardetzky

**Optimal topological simplification of discrete functions on surfaces**. Discrete and Computational Geometry 47 (2012), pp 347-377.

Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier

**Interactive spacetime control of deformable objects.** ACM Transactions on Graphics 31(4) (SIGGRAPH 2012) Article No. 71.

[preprint pdf, 3.7 MB] [supplementary video, 76 MB] [DOI] [BibTex]

Hao Pan, Yi-King Choi, Yang Liu, Wenchao Hu, Qiang Du, Konrad Polthier, Caiming Zhang, Wenping Wang

**Robust Modeling of Constant Mean Curvature Surfaces.** ACM Transactions on Graphics 31(4) (SIGGRAPH 2012) Article No. 85.

[preprint pdf, 1.4 MB] [DOI] [BibTex]

Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier

**Interactive Surface Modeling using Modal Analysis.** ACM Transactions on Graphics, Volume 30, Issue 5, October 2011, pages 119:1-119:11. Will be presented at SIGGRAPH 2012.

[low-res pdf, 2.0 MB, high-res pdf, 15 MB] [video, 57 MB] [DOI] [BibTex]

Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier

**Modal Shape Analysis beyond Laplacian.** Computer Aided Geometric Design, Volume 29, Issue 5, June 2012, Pages 204–218.

[preprint pdf, 2.9 MB] [supplementary video, 6.4 MB] [DOI] [BibTex]

Anna Wawrzinek, Klaus Hildebrandt, Konrad Polthier

**Koiter's Thin Shells on Catmull-Clark Limit Surfaces.** Proceedings of the 16th International Workshop on Vision, Modeling, and Visualization 2011.

Klaus Hildebrandt, Konrad Polthier

**Generalized Shape Operators on Polyhedral Surfaces.** Computer Aided Geometric Design, Volume 28, Issue 5, June 2011, p. 321-343.

[preprint pdf, 1.2 MB] [DOI] [BibTex]

**Minkowski decompositions of associahedra** presented at 23rd FPSAC 2011, Reykjavik (611-622 of proceedings).

[pdf, 0.5 MB] [BibTex]

**Combinatorics of Minkowski decompositions of associahedra** presented at 23rd CCCG2011, Toronto (pp 611-622 of proceedings).

[pdf, 0.5 MB] [BibTex]

Klaus Hildebrandt, Konrad Polthier

**On approximation of the Laplace–Beltrami operator and the Willmore energy of surfaces.** Computer Graphics Forum, Volume 30, Issue 5, August 2011, Pages 1513-1520. Proceedings of ACM Siggraph/Eurographics Symposium on Geometry Processing 2011.** 1st prize best paper award** at SGP 2011

[pdf, 0.3 MB] [DOI] [BibTex]

Matthias Nieser, Ulrich Reitebuch, Konrad Polthier

**CubeCover - Parameterization of 3D Volumes**. Computer Graphics Forum, Volume 30, Issue 5, August 2011, Pages 1397-1406. Proceedings of ACM Siggraph/Eurographics Symposium on Geometry Processing 2011.

[pdf, 3.3 MB] [DOI] [BibTex]

Christoph von Tycowicz, Felix Kälberer, Konrad Polthier

**Context-Based Coding of Adaptive Multiresolution Meshes.** Computer Graphics Forum, Volume 30, Issue 8, pages 2231-2245, December 2011.

[pdf, 1.4 MB] [DOI] [BibTex]

Matthias Nieser, Jonathan Palacios, Konrad Polthier, Eugene Zhang

**Hexagonal Global Parameterization of Arbitrary Surfaces.** IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 6, pp. 865-878, June 2012, doi:10.1109/TVCG.2011.118.

[preprint pdf, 4.8 MB] [DOI] [BibTex]

Matthias Nieser, Konstantin Poelke, Konrad Polthier

**Automatic Generation of Riemann Surface Meshes.** Advances in Geometric Modeling and Processing, Lecture Notes in Computer Science 6130, Springer Berlin/Heidelberg, pp 161-178, 2010.

[pdf, 2.6 MB] [DOI] [BibTex]

Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier

**Eigenmodes of surface energies for shape analysis**. Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010), Lecture Notes in Computer Science 6130, Springer, pp 296-314.

[pdf, 10.6 MB] [DOI] [BibTex]

Ulrich Bauer, Konrad Polthier, Max Wardetzky

**Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines**. Discrete and Computational Geometry Vol. 43, pp: 798-823 (2010).

[pdf, 0.7 MB] [DOI] [BibTex]

Matthias Nieser, Konrad Polthier, Christian Schulz

**Patch Layout from Feature Graph**. Computer-Aided Design 42(3), pp. 213 - 220, 2010.

[pdf, 5.6 MB] [DOI][BibTex]

Felix Kälberer, Konrad Polthier, Christoph von Tycowicz

**Lossless Compression of Adaptive Multiresolution Meshes** . Sibgrapi 2009 Technical Paper.

[pdf, 3.3 MB] [DOI] [BibTex]

Matthias Nieser, Konrad Polthier

**Parameterizing Singularities of Positive Integral Index**. LNCS - Mathematics of Surfaces XIII, Springer 2009, vol. 5654/2009, pp. 265-277.

[pdf, 2.8 MB] [DOI] [BibTex]

Felix Kälberer, Matthias Nieser, Konrad Polthier

**Stripe Parameterization of Tubular Surfaces**. Topological Data Analysis and Visualization: Theory, Algorithms and Applications, V. Pascucci and H. Hagen and J. Tierny and X. Tricoche (eds.) Springer 2011.

Carsten Lange, Konrad Polthier und Udo Simon

**Zur Geometrie von Frühstückseiern**. Mathematische Semesterberichte, (56) 1-14, 2009.

[pdf, 294 KB] [DOI] [BibTex]

Konstantin Poelke, Konrad Polthier

**Lifted Domain Coloring**. Computer Graphics Forum, Volume 28, Number 3, June 2009 , pp. 735-742(8).

Nantel Bergeron, Christophe Hohlweg, Carsten Lange und Hugh Thomas

**Isometry classes of generalised associahedra.** Séminaire Lotharingien de Combinatoire, 61A (special issue in memoriam Pierre Leroux) (2009), Article B61Aa, 13pp.

[pdf, 0.4 MB] [BibTex]

Christophe Hohlweg, Carsten Lange, Hugh Thomas

**Permutahedra and generalised associahedra**. Advances in Mathematics 226 (2011), pp.608-640

[pdf, 550 KB] [DOI] [BibTex]

**Detection of Planar Regions in Volume Data for Topology Optimization**. Proceedings of Geometry Modelling and Processing 2008, F. Chen and B. Jüttler (eds.), pp. 119–126, Lecture Notes in Computer Science, vol. 4975, Springer.

[pdf, 2.1MB] [DOI] [BibTex]

Max Wardetzky, Saurabh Mathur, Felix Kälberer, Eitan Grinspun

**Discrete Laplace operators: No free lunch**. Symposium on Geometry Processing, 2007, pp. 33-37.

[pdf, 164 KB] [BibTex]

Miklos Bergou, Saurabh Mathur, Max Wardetzky, Eitan Grinspun

**TRACKS: Toward Directable Thin Shells**. Proceedings of SIGGRAPH, 2007.

[pdf, 1.3 MB] [Video, 53.7MB] [DOI] [BibTex]

Akah Garg, Eitan Grinspun, Max Wardetzky, Denis Zorin

**Cubic Shells**. Symposium on Computer Animation, 2007, pp. 91-98.

[pdf, 0.6 MB] [BibTex]

Ulrich Bauer and Konrad Polthier

**Parametric Reconstruction of Bent Tube Surfaces**. CyberWorld 2007 Conference Proceedings, Workshop "New Advances in Shape Analysis and Geometric Modeling", IEEE 2007.

[pdf, 3.48 MB] [DOI] [BibTex]

Felix Kälberer, Matthias Nieser and Konrad Polthier

**QuadCover - Surface Parameterization using Branched Coverings**. Computer Graphics Forum, Eurographics 2007.

[pdf, 1.84 MB] [DOI] [BibTex]

Klaus Hildebrandt and Konrad Polthier

**Constraint-based fairing of surface meshes**. Proceedings of the Eurographics and ACM Symposium on Geometry Processing 2007.

Christophe Hohlweg and Carsten Lange

**Realizations of the associahedron and cyclohedron**, Discrete and Computational Geometry 37: 517-543 (2007).

[pdf, 1.45 MB] [BibTex]

**On second-order characteristics of germ-grain models with convex grains**, in *Mathematika*, 2006, 53 (2), 255-286, ISSN 00255793

[BibTex]

Max Wardetzky, Miklos Bergou, David Harmon, Denis Zorin, Eitan Grinspun

**Discrete Quadratic Curvature Energies**, in Computer Aided Geometric Design (CAGD), 2007, pp. 499-518

[pdf, 1.21 MB] [Video, 5.9 MB] [Project] [DOI] [BibTex]

Klaus Hildebrandt, Konrad Polthier and Max Wardetzky

On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces. Geometriae Dedicata 123 (2006), pp. 89-112.

[pdf, 3.37 MB] [BibTex]

Convergence of the cotan Formula - an Overview. Discrete Differential Geometry (A. I. Bobenko, John M. Sullivan, Peter Schröder, Günter Ziegler, eds.), Birkhäuser Basel, 2007.

[pdf, 0.2 MB] [DOI] [BibTex]

The surface pair correlation function for stationary Boolean models, *Advances in Applied Probability (SGSA)* 39(1), 2007, pp. 1-15.

[BibTex]

Felix Ballani, Dietrich Stoyan and Susann Wolf

On two damage accumulation models and their size effects, *Journal of Applied Probability* 44(1), 2007, pp. 99-114.

[BibTex]

Miklos Bergou, Max Wardetzky, David Harmon, Denis Zorin, Eitan Grinspun

A Quadratic Bending Model for Inextensible Surfaces, Symposium on Geometry Processing, 2006.

[pdf, 0.63 MB] [Project] [BibTex]

Klaus Hildebrandt, Konrad Polthier and Eike Preuss

Evolution of 3d Curves under Strict Spatial Constraints. Ninth International Conference on Computer Aided Design and Computer Graphics (CAD/CG 2005).

[pdf, 0.2 MB] [DOI] [BibTex]

Klaus Hildebrandt, Konrad Polthier and Max Wardetzky

Smooth Feature Lines on Surface Meshes. Eurographics Symposium on Geometry Processing (2005).

[pdf, 1.6 MB] [BibTex]

Felix Kälberer, Konrad Polthier, Ulrich Reitebuch and Max Wardetzky

FreeLence - Coding with Free Valences. Eurographics 2005.

[pdf, 1.72 MB] [BibtTex]

Klaus Hildebrandt and Konrad Polthier

Anisotropic Filtering of Non-Linear Surface Features, Eurographics 2004.

[pdf, 2.42 MB] [simulations] [models] [BibTex]

Carsten Lange and Konrad Polthier

Anisotropic Smoothing of Point Sets. Special Issue of CAGD 2005.

[pdf, 3.52 MB] [simulations] [DOI] [BibTex]

Computational Aspects of Discrete Minimal Surfaces. In: Global Theory of Minimal Surfaces, Proc. of the Clay Mathematics Institute Summer School, J. Hass, D. Hoffman, A. Jaffe, H. Rosenberg, R. Schoen, M. Wolf (Eds.), CMI/AMS, 2005.

[pdf, 1.45 MB] [BibTex]

Mirek Majewski and Konrad Polthier

Using MuPAD and JavaView to Visualize Mathematics on the Internet. In: Proc. of the 9th Asian Technology Conference in Mathematics, (2004), pp. 465-474.

[pdf, 0.67 MB] [BibTex]

Polyhedral Surfaces of Constant Mean Curvature, Habilitationsschrift, TU-Berlin (Febr. 2002).

[Chapters1+3+4.pdf, 1.4 MB], [BibTex]

Konrad Polthier and Eike Preuss

Identifying Vector Fields Singularities using a Discrete Hodge Decomposition. In: Visualization and Mathematics III, eds: H.C. Hege, K. Polthier, Springer Verlag, 2003.

[pdf, 2.4 MB] [BibTex]