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  <doc>
    <id>867</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-06-30</completedDate>
    <publishedDate>2005-06-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Evolution of 3d Curves under Strict Spatial Constraints</title>
    <abstract language="eng">We present a new algorithm for fairing of space curves with respect spatial constraints based on a vector valued curvature function. Smoothing with the vector valued curvature function is superior to standard Frenet techniques since the individual scalar components can be modeled similar to curvature-based curve smoothing techniques in 2d. This paper describes a curve smoothing flow that satisfies strict spatial constraints and allows simultaneous control of both curvature functions.</abstract>
    <identifier type="serial">05-33</identifier>
    <identifier type="opus3-id">867</identifier>
    <note>kein Volltext, Artikel ist in Verlagspublikation erschienen, der Preprint wurde offensichtlich vor längerer Zeit zurückgezogen (keine urn). Kossick 20. 11. 13</note>
    <enrichment key="SourceTitle">Appeared in: Proceedings of the Ninth International Conference on Computer Aided Design and Computer Graphics, IEEE Computer Society, 2005, ISBN 0-7695-2473-7, pp. 40-45</enrichment>
    <author>Klaus Hildebrandt</author>
    <author>Konrad Polthier</author>
    <author>Eike Preuß</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-33</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>curve fairing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>curve smoothing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>curvature smoothing flow</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65D10">Smoothing, curve fitting</collection>
    <collection role="msc" number="65D17">Computer aided design (modeling of curves and surfaces) [See also 68U07]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
  </doc>
  <doc>
    <id>858</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-04-08</completedDate>
    <publishedDate>2005-04-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces</title>
    <abstract language="eng">We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in Euclidian $3$-space. The notion of totally normal convergence is shown to be equivalent to the convergence of either one of the following: surface area, intrinsic metric, and Laplace-Beltrami operators. We further s how that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justification for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation.</abstract>
    <identifier type="serial">05-24</identifier>
    <identifier type="opus3-id">858</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8587</identifier>
    <enrichment key="SourceTitle">Appeared in: Geometriae Dedicata 123 (2006) 89-112</enrichment>
    <author>Klaus Hildebrandt</author>
    <author>Konrad Polthier</author>
    <author>Max Wardetzky</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-24</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Discrete Geometry</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Differential Geometry</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Numerical Analysis</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/858/ZR-05-24.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/858/ZR-05-24.ps</file>
  </doc>
  <doc>
    <id>4183</id>
    <completedYear>1998</completedYear>
    <publishedYear>1998</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>book</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">VideoMath - Festival at ICM 98</title>
    <parentTitle language="eng">Springer VideoMath</parentTitle>
    <identifier type="isbn">978-3-540-21385-7</identifier>
    <author>Hans-Christian Hege</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="visalgo">Visual Data Analysis in Science and Engineering</collection>
    <collection role="persons" number="hege">Hege, Hans-Christian</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3976</id>
    <completedYear>2001</completedYear>
    <publishedYear>2001</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>other</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">MathInsight 2002</title>
    <author>Hans-Christian Hege</author>
    <author>Konrad Polthier</author>
    <author>Martin Rumpf</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="visalgo">Visual Data Analysis in Science and Engineering</collection>
    <collection role="persons" number="hege">Hege, Hans-Christian</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3907</id>
    <completedYear>2004</completedYear>
    <publishedYear>2004</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>391</pageFirst>
    <pageLast>400</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>23(3)</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace>Grenoble, France</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Anisotropic filtering of non-linear surface features</title>
    <parentTitle language="eng">Computer Graphics Forum</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8003</enrichment>
    <author>Klaus Hildebrandt</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>4269</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-10-11</completedDate>
    <publishedDate>2013-10-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reducing Memory Requirements in Scientific Computing and Optimal Control</title>
    <abstract language="eng">In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42695</identifier>
    <enrichment key="SourceTitle">submitted to "Multiple Shooting and Time Domain Decomposition Methods", Springer Series "Contributions in Mathematical and Computational Sciences"</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-64</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh compression</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>compression</value>
    </subject>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="68P05">Data structures</collection>
    <collection role="msc" number="68P30">Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4269/ZR13-64.pdf</file>
  </doc>
  <doc>
    <id>4611</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>263</pageFirst>
    <pageLast>287</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reducing Memory Requirements in Scientific Computing and Optimal Control</title>
    <parentTitle language="eng">Multiple Shooting and Time Domain Decomposition Methods</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0297-zib-42695</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <editor>T. Carraro</editor>
    <author>Christoph von Tycowicz</author>
    <editor>M. Geiger</editor>
    <author>Konrad Polthier</author>
    <editor>S. Koerkel</editor>
    <author>Martin Weiser</author>
    <editor>R. Rannacher</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
  </doc>
  <doc>
    <id>6909</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>722</pageFirst>
    <pageLast>732</pageLast>
    <pageNumber/>
    <edition/>
    <issue>7</issue>
    <volume>30</volume>
    <type>article</type>
    <publisherName>CAGD</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2013-10-01</completedDate>
    <publishedDate>2013-10-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">De Casteljau's Algotithm on Manifolds</title>
    <abstract language="eng">This paper proposes a generalization of the ordinary de Casteljau algorithm to manifold-valued data including an important special case which uses the exponential map of a symmetric space or Riemannian manifold. We investigate some basic properties of the corresponding Bézier curves and present applications to curve design on polyhedra and implicit surfaces as well as motion of rigid body and positive definite matrices. Moreover, we apply our approach to construct canal and developable surfaces.</abstract>
    <parentTitle language="eng">Computer Aided Geometric Design</parentTitle>
    <identifier type="doi">10.1016/j.cagd.2013.06.002</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69096</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Computer Aided Geometric Design</enrichment>
    <enrichment key="AcceptedDate">2013-10-01</enrichment>
    <submitter>Esfandiar Nava-Yazdani</submitter>
    <author>Esfandiar Nava-Yazdani</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="navayazdani">Navayazdani, Esfandiar</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6909/1-s2.0-S0167839613000551-main.pdf</file>
  </doc>
  <doc>
    <id>548</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1997-09-05</completedDate>
    <publishedDate>1997-09-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Visualization and Mathematics '97</title>
    <abstract language="eng">This report contains paper abstracts of the workshop "Visualization and Mathematics" held in Berlin-Dahlem in September 1997. The meeting serves as a forum for an international community of researchers and practitioners on the application of visualization techniques in mathematics and on mathematical concepts in visualization. It is the second symposium in a series of workshops bringing together mathematicians and experts from scientific visualization. The themes of the workshop include: \begin{itemize} \item - applications in differential geometry and partial differential equations \item - algorithmic aspects of adaptive and hierarchical techniques in space and time \item - time control of animated objects and corresponding algorithms \item - algorithmic representation of objects for display, storage and exchange \item - new visualization techniques for mathematical structures \item - integration of visualization with symbolic and numerical computation. \end{itemize}</abstract>
    <identifier type="serial">TR-97-06</identifier>
    <identifier type="opus3-id">549</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5480</identifier>
    <enrichment key="SourceTitle">Proceedings of this workshop appeared as: Hans-Christian Hege, Konrad Polthier (eds.) Mathematical Visualization - Algorithms and Applications. Berlin: Springer 1998. ISBN 3-540-63991-8</enrichment>
    <author>Hans-Christian Hege</author>
    <author>Konrad Polthier</author>
    <series>
      <title>ZIB-Report</title>
      <number>TR-97-06</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="hege">Hege, Hans-Christian</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/548/TR-97-06.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/548/TR-97-06.pdf</file>
  </doc>
  <doc>
    <id>517</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1995-05-02</completedDate>
    <publishedDate>1995-05-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Visualization and Mathematics. International Workshop</title>
    <abstract language="eng">International Workshop with support of the Deutsche Forschungsgemeinschaft (DFG) and Max-Planck-Gesellschaft (MPG) Berlin (Dahlem), Germany, May 30 - June 2, 1995</abstract>
    <identifier type="serial">TR-95-02</identifier>
    <identifier type="opus3-id">518</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5179</identifier>
    <enrichment key="SourceTitle">Proceedings of this workshop appeared as: Hans-Christian Hege, Konrad Polthier (eds.) Visualization and Mathematics - Experiments, Simulation and Environments. Berlin: Springer 1997. ISBN 3-540-61269-6</enrichment>
    <author>Hans-Christian Hege</author>
    <author>Konrad Polthier</author>
    <series>
      <title>ZIB-Report</title>
      <number>TR-95-02</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/517/TR-95-02.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/517/TR-95-02.pdf</file>
  </doc>
  <doc>
    <id>850</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-03-08</completedDate>
    <publishedDate>2005-03-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Anisotropic Smoothing of Point Sets</title>
    <abstract language="eng">The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive a shape operator, principal curvature properties of a point set, and an anisotropic Laplacian of the surface. This anisotropic Laplacian reflects curvature properties which can be understood as the point set analogue of Taubin's curvature-tensor for polyhedral surfaces. We combine these discrete tools with techniques from geometric diffusion and image processing. Several applications demonstrate the efficiency and accuracy of our method.</abstract>
    <identifier type="serial">05-16</identifier>
    <identifier type="opus3-id">850</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8508</identifier>
    <enrichment key="SourceTitle">Appeared in: Computer Aided Geometric Design 22 (2005) 680-692. Special issue: Geometric Modelling and Differential Geometry</enrichment>
    <author>Carsten Lange</author>
    <author>Konrad Polthier</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-16</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>point sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anisotropic mean curvature</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anisotropic sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shape operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>principal curvatures</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anisotropic Laplace</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mean curvature flow</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>f</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="ccs" number="I.3.5">Computational Geometry and Object Modeling</collection>
    <collection role="msc" number="53A10">Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/850/ZR-05-16.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/850/ZR-05-16.ps</file>
  </doc>
  <doc>
    <id>800</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-06-15</completedDate>
    <publishedDate>2004-06-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Anisotropic Filtering of Non-Linear Surface Features</title>
    <abstract language="eng">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 lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well-known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non-linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.</abstract>
    <identifier type="serial">04-25</identifier>
    <identifier type="opus3-id">801</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8003</identifier>
    <enrichment key="SourceTitle">Appeared in: Computer Graphics Forum - Eurographics Vol. 23 (2004) 3, Blackwell Publishing</enrichment>
    <author>Klaus Hildebrandt</author>
    <author>Konrad Polthier</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-25</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh smoothing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>principal curvature</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>feature lines</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anisotropic smoothing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>prescribed mean curvature</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="ccs" number="I.3.5">Computational Geometry and Object Modeling</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/800/ZR-04-25.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/800/ZR-04-25.pdf</file>
  </doc>
  <doc>
    <id>801</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-06-15</completedDate>
    <publishedDate>2004-06-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Compressing Triangle Meshes using Geometric Infomation</title>
    <abstract language="eng">We introduce FreeLence, a lossless single-rate connectivity compression algorithm for triangle surface meshes. Based upon a geometry-driven traversal scheme we present two novel and simple concepts: free-valence connectivity encoding and entropy coding based on geometric context. Together these techniques yield significantly smaller rates for connectivity compression than current state of the art approaches - valence-based algorithms and Angle- Analyzer, with an average of $36\%$ improvement over the former and an average of $18\%$ over the latter on benchmark 3D models, combined with the ability to well adapt to the regularity of meshes. We also prove that our algorithm exhibits a smaller worst case entropy for a class of "'well-behaved"' triangle meshes than valence-driven connectivity encoding approaches.</abstract>
    <identifier type="serial">04-26</identifier>
    <identifier type="opus3-id">802</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8016</identifier>
    <enrichment key="SourceTitle">&lt;strong&gt;Revised Version (NOV 2005)&lt;/strong&gt;&lt;a href= "ftp://ftp.zib.de/pub/zib-publications/reports/ZR04261.ps.Z" &gt;&lt;img SRC="/PaperWeb/abstracts/icons/postscript.gif" border="0"&gt;&lt;/a&gt; &lt;a href= "ftp://ftp.zib.de/pub/zib-publications/reports/ZR04261.pdf" &gt;&lt;im</enrichment>
    <author>Felix Kälberer</author>
    <author>Konrad Polthier</author>
    <author>Ulrich Reitebuch</author>
    <author>Max Wardetzky</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-26</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mesh Compression</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Connectivity Encoding</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Polygonal Meshes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Context-based Entropy Coding</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="ccs" number="I.3.5">Computational Geometry and Object Modeling</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/801/ZR-04-26.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/801/ZR-04-26.pdf</file>
  </doc>
  <doc>
    <id>3882</id>
    <completedYear>2004</completedYear>
    <publishedYear>2004</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>465</pageFirst>
    <pageLast>474</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Using MuPAD and JavaView to visualize mathematics on the Internet</title>
    <parentTitle language="eng">Proc. of the 9th Asian Technology Conference in Mathematics</parentTitle>
    <author>Mirek Majewski</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3852</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computational aspects of discrete minimal surfaces</title>
    <parentTitle language="eng">Global Theory of Minimal Surfaces, Proc. of the Clay Mathematics Institute Summer School, CMI/AMS</parentTitle>
    <author>Konrad Polthier</author>
    <editor>J. Hass</editor>
    <editor>D. Hoffman</editor>
    <editor>A. Jaffe</editor>
    <editor>H. Rosenberg</editor>
    <editor>R. Schoen</editor>
    <editor>M. Wol</editor>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3843</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>40</pageFirst>
    <pageLast>45</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Evolution of 3D curves under strict spatial constraints</title>
    <parentTitle language="eng">IEEE Proceedings on Ninth International Conference on Computer Aided Design and Computer Graphics (CAD/CG 2005)</parentTitle>
    <identifier type="doi">10.1109/CAD-CG.2005.38</identifier>
    <author>Klaus Hildebrandt</author>
    <author>Konrad Polthier</author>
    <author>Eike Preuß</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3859</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Anisotropic fairing of point sets</title>
    <parentTitle language="eng">Special Issue of CAGD 2005</parentTitle>
    <identifier type="doi">10.1016/j.cagd.2005.06.010</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-8508</enrichment>
    <author>Carsten Lange</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3865</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>469</pageFirst>
    <pageLast>478</pageLast>
    <pageNumber/>
    <edition/>
    <issue>Issue 3</issue>
    <volume>24</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Free Lence - Coding with free valences</title>
    <parentTitle language="eng">Computer Graphics Forum</parentTitle>
    <identifier type="doi">10.1111/j.1467-8659.2005.00872.x</identifier>
    <author>Felix Kälberer</author>
    <author>Konrad Polthier</author>
    <author>Ulrich Reitebuch</author>
    <author>Max Wardetzky</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>3866</id>
    <completedYear>2005</completedYear>
    <publishedYear>2005</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>85</pageFirst>
    <pageLast>90</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Smooth feature lines on surface meshes</title>
    <parentTitle language="eng">Third Eurographics Symposium on Geometry Processing</parentTitle>
    <author>Klaus Hildebrandt</author>
    <author>Konrad Polthier</author>
    <author>Max Wardetzky</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5479</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>71:1</pageFirst>
    <pageLast>71:8</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>31</volume>
    <type>article</type>
    <publisherName>ACM</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Interactive spacetime control of deformable objects</title>
    <abstract language="eng">Creating motions of objects or characters that are physically plausible and follow an animator’s intent is a key task in computer animation. The spacetime constraints paradigm is a valuable approach to this problem, but it suffers from high computational costs. Based on spacetime constraints, we propose a technique that controls the motion of deformable objects and offers an interactive response. This is achieved by a model reduction of the underlying variational problem, which combines dimension reduction, multipoint linearization, and decoupling of ODEs. After a preprocess, the cost for creating or editing a motion is reduced to solving a number of one-dimensional spacetime problems, whose solutions are the wiggly splines introduced by Kass and Anderson [2008]. We achieve interactive response using a new fast and robust numerical scheme for solving a set of one-dimensional problems based on an explicit representation of the wiggly splines.</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2185520.2185567</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Klaus Hildebrandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="visalgo">Visual Data Analysis in Science and Engineering</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5480</id>
    <completedYear/>
    <publishedYear>2011</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>119:1</pageFirst>
    <pageLast>119:11</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>30</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Interactive surface modeling using modal analysis</title>
    <abstract language="eng">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].</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2019627.2019638</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">https://nbn-resolving.org/urn:nbn:de:0296-matheon-8349</enrichment>
    <author>Klaus Hildebrandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5481</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>204</pageFirst>
    <pageLast>2018</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>29</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modal Shape Analysis beyond Laplacian</title>
    <abstract language="eng">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.</abstract>
    <parentTitle language="eng">Computer Aided Geometric Design</parentTitle>
    <identifier type="doi">10.1016/j.cagd.2012.01.001</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0296-matheon-9678</enrichment>
    <author>Klaus Hildebrandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5482</id>
    <completedYear/>
    <publishedYear>2011</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2231</pageFirst>
    <pageLast>2245</pageLast>
    <pageNumber/>
    <edition/>
    <issue>8</issue>
    <volume>30</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Context-based Coding of Adaptive Multiresolution Meshes</title>
    <abstract language="eng">Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent-child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of state-of-the-art coders by a factor of 2 to 7. For efficient compression of vertex positions we adapt popular wavelet-based coding schemes to the adaptive triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state-of-the-art coders, we use a zerotree to encode the resulting coefficients. Using improved context modeling we enhanced the zerotree compression, cutting the overall geometry data rate by 7% below those of the successful Progressive Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression factors that are 4 times greater than those of coders which can handle irregular meshes.</abstract>
    <parentTitle language="eng">Computer Graphics Forum</parentTitle>
    <identifier type="doi">10.1111/j.1467-8659.2011.01972.x</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0296-matheon-8389</enrichment>
    <author>Christoph von Tycowicz</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Felix Kälberer</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5483</id>
    <completedYear/>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>296</pageFirst>
    <pageLast>314</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>6130</volume>
    <type>incollection</type>
    <publisherName>Springer Berlin / Heidelberg</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Eigenmodes of Surface Energies for Shape Analysis</title>
    <abstract language="eng">In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Furthermore, we design a quadratic energy, such that the eigenmodes of the Hessian of this energy are sensitive to the extrinsic curvature of the surface. &#13;
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 the surface. In addition, we discuss a spectral quadrangulation scheme for surfaces.</abstract>
    <parentTitle language="eng">Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010)</parentTitle>
    <identifier type="doi">10.1007/978-3-642-13411-1_20</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0296-matheon-7325</enrichment>
    <author>Klaus Hildebrandt</author>
    <editor>Bernard Mourrain</editor>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <editor>Scott Schaefer</editor>
    <author>Christoph von Tycowicz</author>
    <editor>Guoliang Xu</editor>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5484</id>
    <completedYear/>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>80</pageFirst>
    <pageLast>87</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Lossless Compression of Adaptive Multiresolution Meshes</title>
    <abstract language="eng">We present a novel coder for lossless compression of adaptive multiresolution meshes that exploits their special hierarchical structure. The heart of our method is a new progressive connectivity coder that can be combined with leading geometry encoding techniques. The compressor uses the parent/child relationships inherent to the hierarchical mesh. We use the rules that accord to the refinement scheme and store bits only where it leaves freedom of choice, leading to compact codes that are free of redundancy. To illustrate our scheme we chose the widespread red-green refinement, but the underlying concepts can be directly transferred to other adaptive refinement schemes as well. The compression ratio of our method exceeds that of state-of-the-art coders by a factor of 2 to 3 on most of our benchmark models.</abstract>
    <parentTitle language="eng">XXII Brazilian Symposium on Computer Graphics and Image Processing</parentTitle>
    <identifier type="doi">10.1109/SIBGRAPI.2009.53</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0296-matheon-5855</enrichment>
    <author>Felix Kälberer</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5488</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>341</pageFirst>
    <pageLast>355</pageLast>
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