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...
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...
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...
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...
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...
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...
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...
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...