Christian Rössl

Laplacian surface editing

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

Geometric modeling based on polygonal meshes Video files associated with this course are available from the citation page

In the last years triangle meshes have become increasingly popular and are nowadays intensively used in many different areas of computer graphics and geometry processing. In classical CAGD irregular triangle meshes developed into a valuable alternative to traditional spline surfaces, since their conceptual simplicity allows for more flexible and highly efficient processing.

Dense correspondence finding for parametrization-free animation reconstruction from video

We present a dense 3D correspondence finding method that enables spatio-temporally coherent reconstruction of surface animations from multi-view video data. Given as input a sequence of shape-from-silhouette volumes of a moving subject that were reconstructed for each time frame individually, our method establishes dense surface correspondences between subsequent shapes independently of surface discretization. This is achieved in two steps: first, we obtain sparse correspondences from robust optical features between adjacent frames. Second, we generate dense correspondences which serve as map between respective surfaces. By applying this procedure subsequently to all pairs of time steps we can trivially align one shape with all others. Thus, the original input can be reconstructed as a sequence of meshes with constant connectivity and small tangential distortion. We exemplify the performance and accuracy of our method using several synthetic and captured real-world sequences.

Geometric modeling based on triangle meshes

Course Summary This course is designed to cover the entire geometry processing pipeline based on triangle meshes. We will present the latest concepts for mesh generation and mesh repair, for geometry and topology optimizations like mesh smoothing, decimation, and remeshing, for parametrization, segmentation, and shape editing. In addition to describing and discussing the related algorithms, we will also give valuable implementation hints and provide source code for most of the covered topics. The course assumes only very basic knowledge on geometric concepts in general, but does not require specific knowledge on polygonal meshes and how to discretize the respective problems for those. It is intended for computer graphics researchers, software developers and engineers from CAGD, computer games, or the movie industry, who are interested in geometry processing algorithms based on triangle meshes. Stephan Bischoff graduated in 1999 with a masters in computer science from the University of Karlsruhe, Germany. He then worked at the graphics group of the Max-Planck-Institute for Computer Science in Saarbrücken, Germany. In 2001 he joined the Computer Graphics Group at the Aachen University of Technology, Germany, where he is working as a research associate with Prof. Dr. Leif Kobbelt and is currently pursuing his PhD. He is an experienced speaker and presented courses at Eurographics and Shape Modeling International. His research interests focus on freeform shape representations for efficient geometry processing, topology control techniques for level-set surfaces, reconstruction of medical data sets and the restoration and healing of CAD models. of which he is paper co-chair this year. He is an experienced speaker and presented courses at Eurographics and Shape Modeling International. His research interests include geometry processing in general, and mesh generation, mesh optimization, and multiresolution shape editing in particular. His research interests include all areas of Computer Graphics and Geometry Processing with a focus on multiresolution and freeform modeling, 3D model optimization, as well as the efficient handling of polygonal mesh data. during the last years resulted in numerous publications in top scientific journals and international conferences. He is invited regularly to give keynote presentations and tutorial lectures. For his contributions he received several scientific awards. He has ongoing collaborations with colleagues in Europe, North America, and Asia, and frequently serves on international program committees. He organized and co-chaired several workshops and conferences. he was a postdoctoral scholar at Stanford University , where he also held a position as visiting assistant professor during the …

Feature Sensitive Remeshing

Remeshing artifacts are a fundamental problem when converting a given geometry into a triangle mesh. We propose a new remeshing technique that is sensitive to features. First, the resolution of the mesh is iteratively adapted by a global restructuring process which additionally optimizes the connectivity. Then a particle system approach evenly distributes the vertices across the original geometry. To exactly find the features we extend this relaxation procedure by an effective mechanism to attract the vertices to feature edges. The attracting force is imposed by means of a hierarchical curvature field and does not require any thresholding parameters to classify the features.

Line-art rendering of 3D-models

We present an interactive system for computer aided generation of line art drawings to illustrate 3D models that are given as triangulated surfaces. In a preprocessing step, an enhanced 2D view of the scene is computed by sampling for every pixel the shading, the normal vectors and the principal directions obtained from discrete curvature analysis. Then streamlines are traced in the 2D direction fields and are used to define line strokes. In order to reduce noise artifacts, the user may interactively select sparse reference lines and the system will automatically fill in additional strokes. By exploiting the special structure of the streamlines, an intuitive and simple tone mapping algorithm can be derived to generate the final rendering.

Dynamic remeshing and applications

Triangle meshes are a flexible and generally accepted boundary representation for complex geometric shapes. In addition to their geometric qualities or topological simplicity, intrinsic qualities such as the shape of the triangles, their distribution on the surface and the connectivity are essential for many algorithms working on them. In this paper we present a flexible and efficient remeshing framework that improves these intrinsic properties while keeping the mesh geometrically close to the original surface. We use a particle system approach and combine it with an incremental connectivity optimization process to trim the mesh towards the requirements imposed by the user. The particle system uniformly distributes the vertices on the mesh, whereas the connectivity optimization is done by means of Dynamic Connectivity Meshes, a combination of local topological operators that lead to a fairly regular connectivity. A dynamic skeleton ensures that our approach is able to preserve surface features, which are particularly important for the visual quality of the mesh. None of the algorithms requires a global parameterization or patch layouting in a preprocessing step but uses local parameterizations only. In particular we will sketch several application scenarios of our general framework and we will show how the users can adapt the involved algorithms in a way that the resulting remesh meets their personal requirements.

Reconstruction of volume data with quadratic super splines

We propose a new approach to reconstruct nondiscrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition. We discuss the smoothness and approximation properties of our model and compare to alternative piecewise polynomial constructions. We observe, as a nonstandard phenomenon, that the derivatives of our splines yield optimal approximation order for smooth data, while the theoretical error of the values is nearly optimal due to the averaging rules. Our approach enables efficient reconstruction and visualization of the data. As the piecewise polynomials are of the lowest possible total degree two, we can efficiently determine exact ray intersections with an isosurface for ray-casting. Moreover, the optimal approximation properties of the derivatives allow us to simply sample the necessary gradients directly from the polynomial pieces of the splines. Our results confirm the efficiency of the quasiinterpolating method and demonstrate high visual quality for rendered isosurfaces.

Template deformation for point cloud fitting

The reconstruction of high-quality surface meshes from measured data is a vital stage in digital shape processing. We present a new approach to this problem that deforms a template surface to fit a given point cloud. Our method takes a template mesh and a point cloud as input, the latter typically shows missing parts and measurement noise. The deformation process is initially guided by user specified correspondences between template and data, then during iterative fitting new correspondences are established. This approach is based on a Laplacian setting for the template without need of any additional meshing of the data or cross-parameterization. The reconstructed surface fits to the point cloud while it inherits shape properties and topology of the template. We demonstrate the effectiveness of the approach for several point data sets from different sources.

Setting the boundary free: a composite approach to surface parameterization

In the last decade, surface mesh parameterization has emerged as a standard technique in computer graphics. The ever increasing need for processing large and highly detailed data sets fosters the development of efficient parameterization techniques that can capture the geometry of the input meshes and produce low distortion planar maps. We present a set of novel techniques allowing for low distortion parameterization. In particular, we address one of the major shortcomings of linear methods by allowing the parametric representation to evolve freely on the plane without any fixed boundary vertices. Our method consists of several simple steps, each solving a linear problem. Our results exhibit a fair balance between high-quality and computational efficiency.