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Item Real-Time Shape Editing using Radial Basis Functions(The Eurographics Association and Blackwell Publishing, Inc, 2005) Botsch, Mario; Kobbelt, LeifItem Efficient High Quality Rendering of Point Sampled Geometry(The Eurographics Association, 2002) Botsch, Mario; Wiratanaya, Andreas; Kobbelt, Leif; P. Debevec and S. GibsonWe propose a highly efficient hierarchical representation for point sampled geometry that automatically balances sampling density and point coordinate quantization. The representation is very compact with a memory consumption of far less than 2 bits per point position which does not depend on the quantization precision. We present an efficient rendering algorithm that exploits the hierarchical structure of the representation to perform fast 3D transformations and shading. The algorithm is extended to surface splatting which yields high quality anti-aliased and water tight surface renderings. Our pure software implementation renders up to 14 million Phong shaded and textured samples per second and about 4 million anti-aliased surface splats on a commodity PC. This is more than a factor 10 times faster than previous algorithms.Item PriMo: Coupled Prisms for Intuitive Surface Modeling(The Eurographics Association, 2006) Botsch, Mario; Pauly, Mark; Gross, Markus; Kobbelt, Leif; Alla Sheffer and Konrad PolthierWe present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh is embedded in a layer of volumetric prisms, which are coupled through non-linear, elastic forces. To deform the mesh, prisms are rigidly transformed to satisfy user constraints while minimizing the elastic energy. The rigidity of the prisms prevents degenerations even under extreme deformations, making the method numerically stable. For the underlying geometric optimization we employ both local and global shape matching techniques. Our modeling framework allows for the specification of various geometrically intuitive parameters that provide control over the physical surface behavior. While computationally more involved than previous methods, our approach significantly improves robustness and simplifies user interaction for large, complex deformations.Item Geometric Modeling Based on Polygonal Meshesv(Eurographics Association, 2000) Kobbelt, Leif P.; Bischoff, Stephan; Botsch, Mario; Kähler, Kolja; Rössl, Christian; Schneider, Robert; Vorsatz, JensWhile traditional computer aided design (CAD) is mainly based on piecewise polynomial surface representations, the recent advances in the efficient handling of polygonal meshes have made available a set of powerful techniques which enable sophisticated modeling operations on freeform shapes. In this tutorial we are going to give a detailed introduction into the various techniques that have been proposed over the last years. Those techniques address important issues such as surface generation from discrete samples (e.g. laser scans) or from control meshes (ab initio design); complexity control by adjusting the level of detail of a given 3D-model to the current application or to the available hardware resources; advanced mesh optimization techniques that are based on the numerical simulation of physical material (e.g. membranes or thin plates) and finally the generation and modification of hierarchical representations which enable sophisticated multiresolution modeling functionality.Item Young Researcher Award 2007(The Eurographics Association and Blackwell Publishing Ltd, 2007) Botsch, MarioItem Geometric Modeling Based on Triangle Meshes(The Eurographics Association, 2006) Botsch, Mario; Pauly, Mark; Rössl, Christian; Bischoff, Stephan; Kobbelt, Leif; Nadia Magnenat-Thalmann and Katja BühlerIn 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. Moreover, the consequent use of triangle meshes as surface representation avoids error-prone conversions, e.g., from CAD surfaces to meshbased input data of numerical simulations. Besides classical geometric modeling, other major areas frequently employing triangle meshes are computer games and movie production. In this context geometric models are often acquired by 3D scanning techniques and have to undergo postprocessing and shape optimization techniques before being actually used in production.This course discusses the whole geometry processing pipeline based on triangle meshes. We will first introduce general concepts of surface representations and point out the advantageous properties of triangle meshes in Section 2, and present efficient data structures for their implementation in Section 3. The different sources of input data and types of geometric and topological degeneracies and inconsistencies are described in Section 4, as well as techniques for their removal, resulting in clean two-manifold meshes suitable for further processing. Mesh quality criteria measuring geometric smoothness and element shape together with the corresponding analysis techniques are presented in Section 6. Mesh smoothing reduces noise in scanned surfaces by generalizing signal processing techniques to irregular triangle meshes (Section 7). Similarly, the underlying concepts from differential geometry are useful for surface parametrization as well (Section 8). Due to the enormous complexity of meshes acquired by 3D scanning, mesh decimation techniques are required for error-controlled simplification (Section 9). The shape of triangles, which is important for the robustness of numerical simulations, can be optimized by general remeshing methods (Section 10). After optimizing meshes with respect to the different quality criteria, we finally present techniques for intuitive and interactive shape deformation (Section 11). Since solving linear systems is a commonly required component for many of the presented mesh processing algorithms, we will discuss their efficient solution and compare several existing libraries in Section 12.Item An Interactive Approach to Point Cloud Triangulation(Blackwell Publishers Ltd and the Eurographics Association, 2000) Kobbelt, Leif P.; Botsch, MarioWe present an interactive system for the generation of high quality triangle meshes that allows us to handle hybrid geometry (point clouds, polygons,. . .) as input data. In order to be able to robustly process huge data sets, we exploit graphics hardware features like the raster manager and the z-buffer for specific sub-tasks in the overall procedure. By this we significantly accelerate the stitching of mesh patches and obtain an algorithm for sub-sampling the data points in linear time. The target resolution and the triangle alignment in sub-regions of the resulting mesh can be controlled by adjusting the screen resolution and viewing transformation. An intuitive user interface provides a flexible tool for application dependent optimization of the mesh.Item Flexible Simulation of Deformable Models Using Discontinuous Galerkin FEM(The Eurographics Association, 2008) Kaufmann, Peter; Martin, Sebastian; Botsch, Mario; Gross, Markus; Markus Gross and Doug JamesWe propose a simulation technique for elastically deformable objects based on the discontinuous Galerkin finite element method (DG FEM). In contrast to traditional FEM, it overcomes the restrictions of conforming basis functions by allowing for discontinuous elements with weakly enforced continuity constraints. This added flexibility enables the simulation of arbitrarily shaped, convex and non-convex polyhedral elements, while still using simple polynomial basis functions. For the accurate strain integration over these elements we propose an analytic technique based on the divergence theorem. Being able to handle arbitrary elements eventually allows us to derive simple and efficient techniques for volumetric mesh generation, adaptive mesh refinement, and robust cuttingItem Resampling Feature and Blend Regions in Polygonal Meshes for Surface Anti-Aliasing(Blackwell Publishers Ltd and the Eurographics Association, 2001) Botsch, Mario; Kobbelt, LeifEfficient surface reconstruction and reverse engineering techniques are usually based on a polygonal mesh representation of the geometry: the resulting models emerge from piecewise linear interpolation of a set of sample points. The quality of the reconstruction not only depends on the number and density of the sample points but also on their alignment to sharp and rounded features of the original geometry. Bad alignment can lead to severe alias artifacts. In this paper we present a sampling pattern for feature and blend regions which minimizes these alias errors. We show how to improve the quality of a given polygonal mesh model by resampling its feature and blend regions within an interactive framework. We further demonstrate sophisticated modeling operations that can be implemented based on this resampling technique.Item GPU-Based Ray-Casting of Quadratic Surfaces(The Eurographics Association, 2006) Sigg, Christian; Weyrich, Tim; Botsch, Mario; Gross, Markus; Mario Botsch and Baoquan Chen and Mark Pauly and Matthias ZwickerQuadratic surfaces are frequently used primitives in geometric modeling and scientific visualization, such as rendering of tensor fields, particles, and molecular structures. While high visual quality can be achieved using sophisticated ray tracing techniques, interactive applications typically use either coarsely tessellated polygonal approximations or pre-rendered depth sprites, thereby trading off visual quality and perspective correctness for higher rendering performance. In contrast, we propose an efficient rendering technique for quadric primitives based on GPU-accelerated splatting. While providing similar performance as point-sprites, our methods provides perspective correctness and superior visual quality using per-pixel ray-casting.