<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <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>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>5571</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>34:1</pageFirst>
    <pageLast>34:10</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>34</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Real-time Nonlinear Shape Interpolation</title>
    <abstract language="eng">We introduce a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular, the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. To achieve this, we restrict the optimization to a low-dimensional subspace that is specifically designed for the shape interpolation problem. The construction of the subspace is based on two components: a formula for the calculation of derivatives of the interpolated shapes and a Krylov-type sequence that combines the derivatives and the Hessian of the objective functional. To make the computational cost for solving the reduced optimization problem independent of the resolution of the example shapes, we combine the dimensional reduction with schemes for the efficient approximation of the reduced nonlinear objective functional and its gradient. In our experiments, we obtain rates of 20-100 interpolated shapes per second even for the largest examples which have 500k vertices per example shape.</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2729972</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Christoph von Tycowicz</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Hans-Peter Seidel</author>
    <author>Klaus Hildebrandt</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5572</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>101</pageFirst>
    <pageLast>109</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Animating articulated characters using wiggly splines</title>
    <abstract language="eng">We propose a new framework for spacetime optimization that can generate artistic motion with a long planning horizon for complex virtual characters. The scheme can be used for generating general types of motion and neither requires motion capture data nor an initial motion that satisfies the constraints. Our modeling of the spacetime optimization combines linearized dynamics and a novel warping scheme for articulated characters. We show that the optimal motions can be described using a combination of vibration modes, wiggly splines, and our warping scheme. This enables us to restrict the optimization to low-dimensional spaces of explicitly parametrized motions. Thereby the computation of an optimal motion is reduced to a low-dimensional non-linear least squares problem, which can be solved with standard solvers. We show examples of motions created by specifying only a few constraints for positions and velocities.</abstract>
    <parentTitle language="eng">ACM SIGGRAPH / Eurographics Symposium on Computer Animation</parentTitle>
    <identifier type="doi">10.1145/2786784.2786799</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Christian Schulz</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Hans-Peter Seidel</author>
    <author>Klaus Hildebrandt</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</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>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>1</volume>
    <type>bookpart</type>
    <publisherName>EMS Publishing House</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Geometry processing</title>
    <parentTitle language="eng">MATHEON - Mathematics for Key Technologies</parentTitle>
    <identifier type="isbn">978-3-03719-137-8</identifier>
    <identifier type="doi">10.4171/137</identifier>
    <enrichment key="Series">EMS Series in Industrial and Applied Mathematics</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Konrad Polthier</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Alexander Bobenko</author>
    <author>Klaus Hildebrandt</author>
    <author>Ralf Kornhuber</author>
    <author>Christoph von Tycowicz</author>
    <author>Harry Yserentant</author>
    <author>Günter M. Ziegler</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>5883</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>35</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects</title>
    <abstract language="eng">We introduce techniques for the processing of motion and animations of non-rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in Rn to the processing of motion of non-rigid shapes. Following this principle, we introduce a discrete geometric flow for curves in shape space. The flow iteratively replaces every shape with a weighted average shape of a local neighborhood and thereby globally decreases an energy whose minimizers are discrete geodesics in shape space. Based on the flow, we devise a novel smoothing filter for motions and animations of deformable shapes. By shortening the length in shape space of an animation, it systematically regularizes the deformations between consecutive frames of the animation. The scheme can be used for smoothing and noise removal, e.g., for reducing jittering artifacts in motion capture data. We introduce a reduced-order method for the computation of the flow. In addition to being efficient for the smoothing of curves, it is a novel scheme for computing geodesics in shape space. We use the scheme to construct non-linear Bézier curves by executing de Casteljau's algorithm in shape space.</abstract>
    <parentTitle language="eng">Computer Graphics Forum</parentTitle>
    <identifier type="doi">10.1111/cgf.12832</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SourceTitle">Computer Graphics Forum 35 (2016) Issue 2</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-59504</enrichment>
    <author>Christopher Brandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Klaus Hildebrandt</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
</export-example>
