Articles (complete list >>) |
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Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier: Interactive spacetime control of deformable objects. Conditionally accepted at SIGGRAPH 2012. |
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Hao Pan, Yi-King Choi, Yang Liu, Wenchao Hu, Qiang Du, Konrad Polthier, Caiming Zhang, Wenping Wang: Robust Modeling of Constant Mean Curvature Surfaces. Conditionally accepted at SIGGRAPH 2012.We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture and other engineering applications. Our method is based on a novel use of the CVT (centroidal Voronoi tessellation) optimization framework. We devise a CVT-CMC energy function defined as a combination of an extended CVT energy and a volume functional. We show that minimizing the CVT-CMC energy is asymptotically equivalent to minimizing mesh surface area with a fixed volume, thus defining a discrete CMC surface. The CVT term in the energy function ensures high mesh quality throughout the evolution of a CMC surface in an interactive design process for form finding. Our method is capable of modeling CMC surfaces with fixed or free boundaries and is robust with respect to input mesh quality and topology changes. Experiments show that the new method generates discrete CMC surfaces of improved mesh quality over existing methods |
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Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier: Interactive Surface Modeling using Modal Analysis. (low-res pdf, 2,0 MB, high-res pdf, 15 MB, video, 57 MB). ACM Transactions on Graphics, Volume 30, Issue 5, October 2011, pages 119:1-119:11. Will be presented at SIGGRAPH 2012 DOI:10.1145/2019627.2019638 (BibTex). We propose a framework for deformation-based surface modeling that is interactive, robust and intuitive to use. The deformations are described by a non-linear optimization problem that models static states of elastic shapes under external forces which implement the user input. Interactive response is achieved by a combination of model reduction, a robust energy approximation, and an efficient quasi-Newton solver. Motivated by the observation that a typical modeling session requires only a fraction of the full shape space of the underlying model, we use second and third derivatives of a deformation energy to construct a low-dimensional shape space that forms the feasible set for the optimization. Based on mesh coarsening, we propose an energy approximation scheme with adjustable approximation quality. The quasi-Newton solver guarantees superlinear convergence without the need of costly Hessian evaluations during modeling. We demonstrate the effectiveness of the approach on different examples including the test suite introduced in [Botsch and Sorkine 2008]. |
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Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier: Modal Shape Analysis beyond Laplacian. (preprint, 2,9 MB, supplementary video, 6,4 MB). Computer Aided Geometric Design, Volume 29, Issue 5, June 2012, Pages 204–218. DOI:10.1016/j.cagd.2012.01.001 (BibTex). In recent years, substantial progress in shape analysis has been achieved through methods that use the spectra and eigenfunctions of discrete Laplace operators. In this work, we study spectra and eigenfunctions of discrete differential operators that can serve as an alternative to the discrete Laplacians for applications in shape analysis. We construct such operators as the Hessians of surface energies, which operate on a function space on the surface, or of deformation energies, which operate on a shape space. In particular, we design a quadratic energy such that, on the one hand, its Hessian equals the Laplace operator if the surface is a part of the Euclidean plane, and, on the other hand, the Hessian eigenfunctions are sensitive to the extrinsic curvature (e.g. sharp bends) on curved surfaces. Furthermore, we consider eigenvibrations induced by deformation energies, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Based on these spectra and eigenmodes, we derive two shape signatures. One that measures the similarity of points on a surface, and another that can be used to identify features of surfaces. |
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| complete list of articles >> | |
Books (complete list >>)
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Bilder der Mathematik Edited by Georg Glaeser and Konrad Polthier available since August 2010 |
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Symposium on Geometry Processing 2009 (SGP09) Guest Editors: M. Alexa, M. Kazhdan and Konrad Polthier Order directly from Eurographics Publishing Press. |
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Topology-Based Methods in Visualization II Edited by Hans-Christian Hege, Konrad Polthier and Gerik Scheuermann available since 2009
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