A C 2 Polar Jet Subdivision (2009)
Konrad Polthier, Alla Sheffer (editors, K. Karčiauskas, A. Myles, J. Peters
We describe a subdivision scheme that acts on control nodes that each carry a vector of values. Each vector defines partial derivatives, referred to as jets in the following and subdivision computes...
Partial Matching of 3D Shapes with Priority-Driven Search Abstract (2009)
Konrad Polthier, Alla Sheffer (editors, T. Funkhouser, P. Shilane
Priority-driven search is an algorithm for retrieving similar shapes from a large database of 3D objects. Given a query object and a database of target objects, all represented by sets of local 3D...
A Decomposition-based Representation for 3D Simplicial Complexes Abstract (2009)
Konrad Polthier, Alla Sheffer (editors, Annie Hui, Lucas Vaczlavik, Leila De Floriani
We define a new representation for non-manifold 3D shapes described by three-dimensional simplicial complexes, that we call the Double-Level Decomposition (DLD) data structure. The DLD data structure...
Konrad Polthier, Alla Sheffer (editors, Nonobtuse Remeshing, Mesh Decimation, H. Zhang
Quality meshing in 2D and 3D domains is an important problem in geometric modeling and scientific computing. We are concerned with triangle meshes having only nonobtuse angles. Specifically, we...
Uniform convergence of discrete curvatures from nets of curvature lines (2009)
Bauer, Ulrich, Polthier, Konrad, Wardetzky, Max
We study "Steiner-type" discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform pointwise convergence to smooth principal curvatures. We provide...
Konrad Polthier, Alla Sheffer (editors, Nonobtuse Remeshing, Mesh Decimation, H. Zhang
Quality meshing in 2D and 3D domains is an important problem in geometric modeling and scientific computing. We are concerned with triangle meshes having only nonobtuse angles. Specifically, we...
Designing Quadrangulations with Discrete Harmonic Forms (2008)
Konrad Polthier, Alla Sheffer (editors, Y. Tong, P. Alliez
We introduce a framework for quadrangle meshing of discrete manifolds. Based on discrete differential forms, our method hinges on extending the discrete Laplacian operator (used extensively in...
WUCSE-2006-29: Smooth Surface Reconstruction using Charts for Medical Data (2008)
Konrad Polthier, Alla Sheffer (editors
Paper ID 74 We present a surface reconstruction technique that constructs a smooth, C k, analytic surface from scattered data. The technique is robust to noise and both poorly and non-uniformly...
Error Bounds and Optimal Neighborhoods for MLS Approximation Abstract (2008)
Konrad Polthier, Alla Sheffer (editors, Yaron Lipman, Daniel Cohen-or, David Levin
In recent years, the moving least-square (MLS) method has been extensively studied for approximation and reconstruction of surfaces. The MLS method involves local weighted least-squares polynomial...
PriMo: Coupled Prisms for Intuitive Surface Modeling Abstract (2008)
Konrad Polthier, Alla Sheffer (editors, Mario Botsch, Mark Pauly, Markus Gross, Leif Kobbelt
We present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh...
Abstract Overfitting Control for Surface Reconstruction (2008)
Konrad Polthier, Alla Sheffer (editors, Yunjin Lee, Seungyong Lee, Ioannis Ivrissimtzis, Hans-peter Seidel
This paper proposes a general framework for overfitting control in surface reconstruction from noisy point data. The problem we deal with is how to create a model that will capture as much detail as...
Peter Peels, Anita Klooster, Paul De Haas, Wil Kortsmit, Konrad Polthier, Tom Verhoeff
onder auspiciën van het Wiskundig Genootschap
Hierarchical Error-Driven Approximation of Implicit Surfaces from Polygonal Meshes (2008)
Konrad Polthier, Alla Sheffer (editors, Takashi Kanai, Yutaka Ohtake, Kiwamu Kase
This paper describes an efficient method for the hierarchical approximation of implicit surfaces from polygonal meshes. A novel error function between a polygonal mesh and an implicit surface is...
Eurographics Symposium on Geometry Processing (2006) (2008)
Konrad Polthier, Alla Sheffer (editors, I. Ginkel, G. Umlauf
In this paper the problem of curvature behavior around extraordinary points of a Loop subdivision surface is addressed. A variant of Loop’s algorithm with small stencils is used that generates...
Visualizing Maple Plots with JavaViewLib (2008)
Steven Peter Dugaro, Konrad Polthier
Abstract. JavaViewLib is a new Maple package combined with the JavaView visualization toolkit that adds new interactivity to Maple plots in both web pages and worksheets. It provides a superior...
Constraint-based fairing of surface meshes (2008)
Er Belyaev, Michael Garl, Klaus Hildebrandt, Konrad Polthier
We propose a constraint-based method for the fairing of surface meshes. The main feature of our approach is that the resulting smoothed surface remains within a prescribed distance to the input mesh....
Probabilistic Fingerprints for Shapes (2008)
Konrad Polthier, Alla Sheffer (editors, Niloy J. Mitra, Leonidas Guibas, Joachim Giesen, Mark Pauly
We propose a new probabilistic framework for the efficient estimation of similarity between 3D shapes. Our framework is based on local shape signatures and is designed to allow for quick pruning of...
ABSTRACT The Video “Geodesics and Waves” (2008)
Konrad Polthier, Martin Steffens
The video Geodesics and Waves introduces the concepts of straightest geodesics and geodesic flow on polyhedral surfaces. It is the third in a series of videos presenting research results from the...
Robust Principal Curvatures on Multiple Scales (2008)
Konrad Polthier, Alla Sheffer (editors, Yong-liang Yang, Yu-kun Lai, Shi-min Hu, Helmut Pottmann
Geometry processing algorithms often require the robust extraction of curvature information. We propose to achieve this with principal component analysis (PCA) of local neighborhoods, defined via...
Defining and Computing Curve-skeletons with Medial Geodesic Function (2008)
Konrad Polthier, Alla Sheffer (editors, Tamal K. Dey, Jian Sun
Many applications in geometric modeling, computer graphics, visualization and computer vision benefit from a reduced representation called curve-skeletons of a shape. These are curves possibly with...
Smooth Feature Lines on Surface Meshes (2008)
M. Desbrun, H. Pottmann (editors, Klaus Hildebrandt, Konrad Polthier, Max Wardetzky
Feature lines are salient surface characteristics. Their definition involves third and fourth order surface derivatives. This often yields to unpleasantly rough and squiggly feature lines since third...
Smooth Feature Lines on Surface Meshes (2008)
M. Desbrun, H. Pottmann (editors, Klaus Hildebrandt, Konrad Polthier, Max Wardetzky
Feature lines are salient surface characteristics. Their definition involves third and fourth order surface derivatives. This often yields to unpleasantly rough and squiggly feature lines since third...
Partial Matching of 3D Shapes with Priority-Driven Search Abstract (2008)
Konrad Polthier, Alla Sheffer (editors, T. Funkhouser, P. Shilane
Priority-driven search is an algorithm for retrieving similar shapes from a large database of 3D objects. Given a query object and a database of target objects, all represented by sets of local 3D...
Reliable Implicit Surface Polygonization using Visibility Mapping (2008)
Konrad Polthier, Alla Sheffer (editors, Gokul Varadhan, Shankar Krishnan, Liangjun Zhang, Dinesh Manocha
We present a new algorithm to compute a topologically and geometrically accurate triangulation of an implicit surface. Our approach uses spatial subdivision techniques to decompose a manifold...
Selectively refinable subdivision meshes (2008)
Konrad Polthier, Alla Sheffer (editors
We introduce RGB triangulations, an extension of red-green triangulations that can support selective refinement over subdivision meshes generated through quadrisection of triangles. Our purpose is to...
Abstract Poisson Surface Reconstruction (2008)
Konrad Polthier, Alla Sheffer (editors, Michael Kazhdan, Matthew Bolitho
We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial...
Constraint-based fairing of surface meshes (2008)
Er Belyaev, Michael Garl, Klaus Hildebrandt, Konrad Polthier
We propose a constraint-based method for the fairing of surface meshes. The main feature of our approach is that the resulting smoothed surface remains within a prescribed distance to the input mesh....
We propose a simple concept for distributed computing. In a first stage this allows stand-alone programs to communicate and exchange data across computer networks. Existing stand-alone programs need...
Konrad Polthier, Alla Sheffer (editors, Miklós Bergou, Max Wardetzky, David Harmon, ...
Relating the intrinsic Laplacian to the mean curvature normal, we arrive at a model for bending of inextensible surfaces. Due to its constant Hessian, our isometric bending model reduces cloth...
(Guest Editors) FreeLence- Coding with Free Valences (2008)
Felix Kälberer, Konrad Polthier, Ulrich Reitebuch, Max Wardetzky
We introduce FreeLence, a novel and simple single-rate compression coder for triangle manifold meshes. Our method uses free valences and exploits geometric information for connectivity encoding....
(Guest Editors) FreeLence- Coding with Free Valences (2008)
Felix Kälberer, Konrad Polthier, Ulrich Reitebuch, Max Wardetzky
We introduce FreeLence, a novel and simple single-rate compression coder for triangle manifold meshes. Our method uses free valences and exploits geometric information for connectivity encoding....
Publication of Interactive Visualizations with (2007)
Konrad Polthier, Samy Khadem, Eike Preuß, Ulrich Reitebuch
Abstract. JavaView is a 3D geometry viewer and a numerical software library written in Java which allows one to publish interactive geometries and mathematical experiments in online web pages. Its...
Mathematical Visualization and Online Experiments (2007)
Abstract. The future of mathematical communication is strongly related with the internet. On a number of examples, the present paper gives a futuristic outlook how mathematical visualization imbedded...
Publication of Interactive Visualizations (2007)
With Javaview Konrad, Konrad Polthier, Samy Khadem, Eike Preu, Ulrich Reitebuch
JavaView is a 3D geometry viewer and a numerical software library written in Java which allows one to publish interactive geometries and mathematical experiments in online web pages. Its numerical...
Visualizing Maple Plots with JavaViewLib (2007)
Steven Peter Dugaro, Konrad Polthier
JavaViewLib is a new Maple package combined with the JavaView visualization toolkit that adds new interactivity to Maple plots in both web pages and worksheets. It provides a superior viewing...
Combinatorial Image Analysis (2006)
Reulke, Ralf, Knauer, Uwe, Eckardt, Ulrich, Flach, Boris, Polthier, Konrad
This volume presents the proccedings of the 11th International Workshop on Combinatorial Image Analysis. IWCIA 2006 was the 11th in a series of international workshopfs devoted to combinatorial image...
Folding meshes: Hierarchical mesh segmentation based on planar symmetry (2006)
Konrad Polthier, Alla Sheffer (editors, Patricio Simari, Evangelos Kalogerakis, Karan Singh
Meshes representing real world objects, both artist-created and scanned, contain a high level of redundancy due to (possibly approximate) planar reflection symmetries, either global or localized to...
Spherical Barycentric Coordinates (2006)
Konrad Polthier, Alexander Belyaev, Alla Sheffer (editors, Torsten Langer, Er Belyaev, Hans-peter Seidel, ...
We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar...
On Transfinite Barycentric Coordinates (2006)
Konrad Polthier, Alla Sheffer (editors, Alexander Belyaev
A general construction of transfinite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The Gordon-Wixom...
Folding meshes: Hierarchical mesh segmentation based on planar symmetry (2006)
Konrad Polthier, Alla Sheffer (editors, Patricio Simari, Evangelos Kalogerakis, Karan Singh
Meshes representing real world objects, both artist-created and scanned, contain a high level of redundancy due to (possibly approximate) planar reflection symmetries, either global or localized to...
Alla Sheffer, Konrad Polthier, Barbara Cutler, Jean-daniel Boissonnat
These proceedings are available only in electronic version
Overfitting Control for Surface Reconstruction (2006)
Lee, Yunjin, Lee, Seungyong, Ivrissimtzis, Ioannis, Seidel, Hans-Peter, Fellner, Dieter W., Spencer, Stephen N., ...
This paper proposes a general framework for overfitting control in surface reconstruction from noisy point data. The problem we deal with is how to create a model that will capture as much detail as...
On Transfinite Barycentric Coordinates (2006)
Belyaev, Alexander, Sheffer, Alla, Polthier, Konrad
A general construction of trans_nite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The Gordon-Wixom interpolation...
A Comparison of Shape Matching Methods for Contour Based Pose Estimation (2006)
Rosenhahn, Bodo, Brox, Thomas, Cremers, Daniel, Seidel, Hans-Peter, Reulke, Ralf, Eckhardt, Ulrich, ...
In this paper, we analyze two conceptionally different approaches for shape matching: the well-known iterated closest point (ICP) algorithm and variational shape registration via level sets. For the...
Spherical Barycentric Coordinates (2006)
Langer, Torsten, Belyaev, Alexander, Seidel, Hans-Peter, Fellner, Dieter W., Spencer, Stephen N., Sheffer, Alla, ...
We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar...
Anisotropic smoothing of point sets (2005)
Carsten Lange, Konrad Polthier, Tu Berlin, Tu Berlin
Figure 1: The initial point set of the Venus torso (a) was disturbed with a 3 % normal and tangential noise to produce the initial noisy point set (b). Figures (c) and (d) show the point set after 20...
Anisotropic smoothing of point sets (2005)
Carsten Lange, Konrad Polthier, Tu Berlin, Tu Berlin
Figure 1: The initial point set of the Venus torso (a) was disturbed with a 3 % normal and tangential noise to produce the initial noisy point set (b). Figures (c) and (d) show the point set after 20...
Anisotropic filtering of non-linear surface features (2004)
Klaus Hildebrandt, Konrad Polthier
Dedicated to the 65 th birthday of Prof. Dr. Hermann Karcher A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non-linear...
Anisotropic filtering of non-linear surface features (2004)
Klaus Hildebrandt, Konrad Polthier
A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non-linear geometric features such as curved surface regions and feature...
Identifying Vector Fields Singularities using a Discrete Hodge Decomposition (2003)
Summary. We derive a Hodge decomposition of discrete vector fields on polyhedral surfaces, and apply it to the identification of vector field singularities. This novel approach allows us to easily...
Visualizing Mathematics - Online (2002)
Modern mathematical visualization has always been related with special graphics workstation although visualization was always part of mathematics. Here we start from historical roots...
Unstable Periodic Discrete Minimal Surfaces (2002)
this paper we define the new alignment energy for non-conforming triangle meshes, and describes its use to compute unstable conforming discrete minimal surfaces. Our algorithm makes use of the...
Computational Aspects of Discrete Minimal Surfaces (2002)
ids. ii Printer: Opaque this Introduction to Polyhedral Meshes Polyhedral meshes belong to the most basic structures for the representation of geometric shapes not only in numerics and computer...
Polyhedral Surfaces of Constant Mean Curvature (2002)
Contents Preface vii 1 Introduction to Polyhedral Meshes 1 1.1 SimplicialComplexes................... 2 1.2 TopologicalProperties.................. 6 1.3 DistanceandMetric ................... 8 1.4...
Detecting Vector Field Singularities from Potentials (2001)
. We present an algorithm for the automatic detection of vector eld singularities based on potential functions derived from a Hodge decomposition of the eld. It allows one to easily detect and...
EG-Models - A New Journal for Digital Geometry Models (2001)
Michael Joswig, Konrad Polthier
The archive Electronic Geometry Models is a new electronic journal for the publication of digital geometry models from a broad range of mathematical topics. The geometry models are distinguished...
Digital models and computer assisted proofs (2000)
Michael Joswig, Konrad Polthier
The first collection of reviewed electronic geometry models is available online at the new Internet server
Variational Approach to Vector Field Decomposition (2000)
. For the feature analysis of vector elds we decompose a given vector eld into three components: a divergence-free, a rotation-free, and a harmonic vector eld. This Hodgetype decomposition splits a...
Variational Approach to Vector Field Decomposition (2000)
. For the feature analysis of vector fields we decompose a given vector field into three components: a divergence-free, a rotation-free, and a harmonic vector field. This Hodgetype decomposition...
Variational approach to vector field decomposition (2000)
Abstract. For the feature analysis of vector fields we decompose a given vector field into three components: a divergence-free, a rotation-free, and a harmonic vector field. This Hodgetype...
Smooth View-Dependent Rendering in Animations (1999)
Axel Friedrich, Konrad Polthier, Markus Schmies, Axel Friedrich Ý, Konrad Polthier Þ, Markus Schmies Ü
View-dependent rendering allows interactive visualization of larger scenes. A well-known artifact is the popping problem in animations resulting from temporal differences in the level of detail...
Geodesic Flow on Polyhedral Surfaces (1999)
Konrad Polthier And, Konrad Polthier, Markus Schmies
On a curved surface the front of a point wave evolves in concentric circles which start to overlap and branch after a certain time.
Videomath Festival ( 1998 : Berlín), Hege, Hans-Christian (ed.), Polthier, Konrad (ed.)
Colección de veinte programas en que se presentan, de manera visual, temas generales de las matemáticas. Se incluyen problemas de topología y geometría; se ilustran las teorías de Arquímedes,...
Videomath Festival at ICM'98 : A Collection of Mathematical Videos (1998)
Videomath Festival ( 1998 : Berlín), Hege, Hans-Christian (ed.), Polthier, Konrad (ed.)
Colección de veinte programas en que se presentan, de manera visual, temas generales de las matemáticas. Se incluyen problemas de topología y geometría; se ilustran las teorías de Arquímedes,...
Interpolating triangle hierarchies (1998)
Axel Friedrich, Konrad Polthier, Markus Schmies
We consider interpolation between keyframe hierarchies. We impose a set of weak constraints that allows smooth interpolation between two keyframe hierarchies in an animation or, more generally,...
Interpolation of Triangle Hierarchies (1998)
Axel Friedrich, Konrad Polthier, Markus Schmies
We consider interpolation between keyframe hierarchies. We impose a set of weak constraints that allows smooth interpolation between two keyframe hierarchies in an animation or, more generally,...
Interpolation of Triangle Hierarchies (1998)
Axel Friedrich Konrad, Axel Friedrich, Konrad Polthier, Markus Schmies
We consider interpolation between keyframe hierarchies. We impose a set of weak constraints that allows smooth interpolation between two keyframe hierarchies in an animation or, more generally,...
Compact constant mean curvature surfaces with low genus (1997)
Große-Brauckmann, Karsten, Polthier, Konrad
We describe numerical experiments that suggest the existence of certain new compact surfaces of constant mean curvature. They come in three dihedrally symmetric families, with genus ranging from 3 to...
An algorithm for discrete constant mean curvature surfaces (1997)
Konrad Polthier, Wayne Rossman
Abstract. We define triangulated piecewise linear constant mean curvature surfaces using a variational characterization. These surfaces are critical for area amongst continuous piecewise linear...
An Algorithm for Discrete Constant Mean Curvature Surfaces (1997)
Bernd Oberknapp, Konrad Polthier
. We present a new algorithm for computing discrete constant mean curvature surfaces in R 3 . It is based on the definition of a discrete version of the conjugate surface construction for cmc...
An algorithm for discrete constant mean curvature surfaces (1997)
Konrad Polthier, Wayne Rossman
We define triangulated piecewise linear constant mean curvature surfaces using a variational characterization. These surfaces are critical for area amongst continuous piecewise linear variations...
Construction of Triply Periodic Minimal Surfaces (1996)
Hermann Karcher, Konrad Polthier
We discuss the construction of triply period minimal surfaces. This includes concepts for constructing new examples as well as a discussion of numerical computations based on the new concept of...
Numerical Examples of Compact Constant Mean Curvature Surfaces (1995)
Karsten Große-Brauckmann, Konrad Polthier
We construct new examples of compact constant mean curvature surfaces numerically. A conjugate surface method allows to explicitly construct examples. We employ the numerical algorithm of Oberknapp...
Deutsche Forschungsgemeinschaft (dfg, Hans-christian Hege, Konrad Polthier
International Workshop with support of the
Deutsche Forschungsgemeinschaft (dfg, Hans-christian Hege, Konrad Polthier
International Workshop with support of the
Thesis (doctoral)--Universität Bonn, 1993.
Karsten Große-brauckmann, Konrad Polthier
We construct new examples of compact constant mean curvature surfaces numerically. A conjugate surface method allows to explicitly construct examples. We employ the numerical algorithm of Oberknapp...
Computing discrete minimal surfaces and their conjugates (1993)
Pinkall, Ulrich, Polthier, Konrad
We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the...
Computing Discrete Minimal Surfaces and Their Conjugates (1993)
Ulrich Pinkall, Strasse Des Juni, Konrad Polthier
ABSTRACT. We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in R 3, S 3 and H 3. The algorithm makes no restriction on the...
Computing Discrete Minimal Surfaces and Their Conjugates (1993)
Ulrich Pinkall, Konrad Polthier
We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in R³, S³ and H³. The algorithm makes no...