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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 Online Adaptive PCA for Inverse Kinematics Hand Tracking(The Eurographics Association, 2014) Schröder, Matthias; Botsch, Mario; Jan Bender and Arjan Kuijper and Tatiana von Landesberger and Holger Theisel and Philipp UrbanRecent approaches to real-time bare hand tracking estimate the hand's pose and posture by fitting a virtual hand model to RGBD sensor data using inverse kinematics. It has been shown that exploiting natural hand synergies can improve the efficiency and quality of the tracking, by performing the optimization in a reduced parameter space consisting of realistic hand postures [SMRB14]. The downside, however, is that only postures within this subspace can be tracked reliably, thereby trading off flexibility and accuracy for performance and robustness. In this paper we extend the previous method by introducing an adaptive synergistic model that is automatically adjusted to observed hand articulations that are not covered by the initial subspace. Our adaptive model combines the robustness of tracking in a reduced parameter space with the flexibility of optimizing for the full articulation of the hand, which we demonstrate in several synthetic and real-world experiments.Item Evaluation of Surround-View and Self-Rotation in the OCTAVIS VR-System(The Eurographics Association, 2013) Dyck, Eugen; Pfeiffer, Thies; Botsch, Mario; Betty Mohler and Bruno Raffin and Hideo Saito and Oliver StaadtIn this paper we evaluate spatial presence and orientation in the OCTAVIS system, a novel virtual reality platform aimed at training and rehabilitation of visual-spatial cognitive abilities. It consists of eight touch-screen displays surrounding the user, thereby providing a 360! horizontal panorama view. A rotating office chair and a joystick in the armrest serve as input devices to easily navigate through the virtual environment. We conducted a two-step experiment to investigate spatial orientation capabilities with our device. First, we examined whether the extension of the horizontal field of view from 135! (three displays) to 360! (eight displays) has an effect on spatial presence and on the accuracy in a pointing task. Second, driving the full eight screens, we explored the effect of embodied self-rotation using the same measures. In particular we compare navigation by rotating the world while the user is sitting stable to a stable world and a self-rotating user.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 The Diamond Laplace for Polygonal and Polyhedral Meshes(The Eurographics Association and John Wiley & Sons Ltd., 2021) Bunge, Astrid; Botsch, Mario; Alexa, Marc; Digne, Julie and Crane, KeenanWe introduce a construction for discrete gradient operators that can be directly applied to arbitrary polygonal surface as well as polyhedral volume meshes. The main idea is to associate the gradient of functions defined at vertices of the mesh with diamonds: the region spanned by a dual edge together with its corresponding primal element - an edge for surface meshes and a face for volumetric meshes. We call the operator resulting from taking the divergence of the gradient Diamond Laplacian. Additional vertices used for the construction are represented as affine combinations of the original vertices, so that the Laplacian operator maps from values at vertices to values at vertices, as is common in geometry processing applications. The construction is local, exactly the same for all types of meshes, and results in a symmetric negative definite operator with linear precision. We show that the accuracy of the Diamond Laplacian is similar or better compared to other discretizations. The greater versatility and generally good behavior come at the expense of an increase in the number of non-zero coefficients that depends on the degree of the mesh elements.Item Pose Correction by Space-Time Integration(The Eurographics Association, 2011) Esturo, Janick Martinez; Rössl, Christian; Fröhlich, Stefan; Botsch, Mario; Theisel, Holger; Peter Eisert and Joachim Hornegger and Konrad PolthierThe deformation of a given model into different poses is an important problem in computer graphics and computer animation. In a typical workflow, a carefully designed reference surface is deformed into a couple of poses, which can then act as a basis for interpolating arbitrarily intermediate poses. To this end the input poses should be free of geometric artifacts like self-intersections, since these degeneracies will be reproduced or even amplified by the interpolation. Not only are the resulting artifacts visually disturbing, they typically cause severe numerical problems for further downstream applications. In this paper we present an automatic approach for removing these geometric artifacts from a given set of mesh poses, while maintaining the original mesh connectivity. The deformation from the rest pose to a target pose is faithfully reproduced by integration of a smooth space-time vector field, which by construction guarantees the absence of self-intersections in the repaired target pose. Our approach is computationally efficient, and its effectiveness is demonstrated on a range of typical animation examples.