TY - CHAP A1 - Oppermann, Leif A1 - Jacobs, R. A1 - Watkins, M. A1 - Shackford, R. A1 - Tycowicz, Christoph von A1 - Wright, M. A1 - Capra, M. A1 - Greenhalgh, Chris A1 - Benford, Steve T1 - Love City: A Text-Driven, Location-Based Mobile Phone Game Played Between 3 Cities T2 - Pervasive Gaming Applications - A Reader for Pervasive Gaming Research Y1 - 2007 SN - 978-3-8322-6224-2 VL - 2 SP - 285 EP - 312 PB - Shaker Verlag ER - TY - CHAP A1 - Greenhalgh, Chris A1 - Benford, Steve A1 - Drozd, Adam A1 - Flintham, Martin A1 - Hampshire, Alastair A1 - Oppermann, Leif A1 - Smith, Keir A1 - Tycowicz, Christoph von T1 - EQUIP2: A Platform for Mobile Phone-based Game Development T2 - Concepts and Technologies for Pervasive Games - A Reader for Pervasive Gaming Research Y1 - 2007 SN - 978-3-8322-6223-5 VL - 1 SP - 153 EP - 178 PB - Shaker Verlag ER - TY - JOUR A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Seidel, Hans-Peter A1 - Hildebrandt, Klaus T1 - Animating Deformable Objects Using Sparse Spacetime Constraints JF - ACM Transactions on Graphics N2 - We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and quickly (within a few seconds) generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Controlling the warped motion requires the derivative of the warp map. We derive a representation of the derivative that can be efficiently and robustly evaluated. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to very low-dimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion. Y1 - 2014 U6 - https://doi.org/10.1145/2601097.2601156 VL - 33 IS - 4 SP - 109:1 EP - 109:10 ER - TY - JOUR A1 - Tycowicz, Christoph von A1 - Schulz, Christian A1 - Seidel, Hans-Peter A1 - Hildebrandt, Klaus T1 - An Efficient Construction of Reduced Deformable Objects JF - ACM Transactions on Graphics N2 - Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for real-time simulation of deformable objects and interactive deformation-based editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches. Y1 - 2013 U6 - https://doi.org/10.1145/2508363.2508392 VL - 32 IS - 6 SP - 213:1 EP - 213:10 PB - ACM ER - TY - JOUR A1 - Hildebrandt, Klaus A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad T1 - Interactive spacetime control of deformable objects JF - ACM Transactions on Graphics N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1145/2185520.2185567 VL - 31 IS - 4 SP - 71:1 EP - 71:8 PB - ACM ER - TY - JOUR A1 - Hildebrandt, Klaus A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad T1 - Interactive surface modeling using modal analysis JF - ACM Transactions on Graphics N2 - 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]. Y1 - 2011 U6 - https://doi.org/10.1145/2019627.2019638 VL - 30 IS - 5 SP - 119:1 EP - 119:11 ER - TY - JOUR A1 - Hildebrandt, Klaus A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad T1 - Modal Shape Analysis beyond Laplacian JF - Computer Aided Geometric Design N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1016/j.cagd.2012.01.001 VL - 29 IS - 5 SP - 204 EP - 2018 ER - TY - JOUR A1 - Tycowicz, Christoph von A1 - Kälberer, Felix A1 - Polthier, Konrad T1 - Context-based Coding of Adaptive Multiresolution Meshes JF - Computer Graphics Forum N2 - 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. Y1 - 2011 U6 - https://doi.org/10.1111/j.1467-8659.2011.01972.x VL - 30 IS - 8 SP - 2231 EP - 2245 ER - TY - GEN A1 - Hildebrandt, Klaus A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad ED - Mourrain, Bernard ED - Schaefer, Scott ED - Xu, Guoliang T1 - Eigenmodes of Surface Energies for Shape Analysis T2 - Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010) N2 - 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. 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. Y1 - 2010 U6 - https://doi.org/10.1007/978-3-642-13411-1_20 VL - 6130 SP - 296 EP - 314 PB - Springer Berlin / Heidelberg ER - TY - CHAP A1 - Kälberer, Felix A1 - Tycowicz, Christoph von A1 - Polthier, Konrad T1 - Lossless Compression of Adaptive Multiresolution Meshes T2 - XXII Brazilian Symposium on Computer Graphics and Image Processing N2 - 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. Y1 - 2009 U6 - https://doi.org/10.1109/SIBGRAPI.2009.53 SP - 80 EP - 87 ER -