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Item Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces(The Eurographics Association, 2004) Andersson, Mattias; Giesen, Joachim; Pauly, Mark; Speckmann, Bettina; Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon RusinkiewiczGiven a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view.Item Uncertainty and Variability in Point Cloud Surface Data(The Eurographics Association, 2004) Pauly, Mark; Mitra, Niloy J.; Guibas, Leonidas J.; Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon RusinkiewiczWe present a framework for analyzing shape uncertainty and variability in point-sampled geometry. Our representation is mainly targeted towards discrete surface data stemming from 3D acquisition devices, where a finite number of possibly noisy samples provides only incomplete information about the underlying surface. We capture this uncertainty by introducing a statistical representation that quantifies for each point in space the likelihood that a surface fitting the data passes through that point. This likelihood map is constructed by aggregating local linear extrapolators computed from weighted least squares fits. The quality of fit of these extrapolators is combined into a corresponding confidence map that measures the quality of local tangent estimates. We present an analysis of the effect of noise on these maps, show how to efficiently compute them, and extend the basic definition to a scale-space formulation. Various applications of our framework are discussed, including an adaptive re-sampling method, an algorithm for reconstructing surfaces in the presence of noise, and a technique for robustly merging a set of scans into a single point-based representation.Item Point Based Animation of Elastic, Plastic and Melting Objects(The Eurographics Association, 2004) Müller, Matthias; Keiser, Richard; Nealen, Andrew; Pauly, Mark; Gross, Markus; Alexa, Marc; R. Boulic and D. K. PaiWe present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young s Modulus and Poisson s Ratio. In each step, we compute the spatial derivatives of the discrete displacement field using a Moving Least Squares (MLS) procedure. From these derivatives we obtain strains, stresses and elastic forces at each simulated point. We demonstrate how to solve the equations of motion based on these forces, with both explicit and implicit integration schemes. In addition, we propose techniques for modeling and animating a point-sampled surface that dynamically adapts to deformations of the underlying volumetric model.Item Interactive 3D Painting on Point-Sampled Objects(The Eurographics Association, 2004) Adams, Bart; Wicke, Martin; Dutré, Philip; Gross, Markus; Pauly, Mark; Teschner, Matthias; Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon RusinkiewiczWe present a novel painting system for 3D objects. In order to overcome parameterization problems of existing applications, we propose a unified sample-based approach to represent geometry and appearance of the 3D object as well as the brush surface. The generalization of 2D pixel-based paint models to point samples allows us to elegantly simulate paint transfer for 3D objects. In contrast to mesh-based painting systems, an efficient dynamic resampling scheme permits arbitrary levels of painted detail. Our system provides intuitive user interaction with a six degree-of-freedom (DOF) input device. As opposed to other 3D painting systems, real brushes are simulated including their dynamics and collision handling.Item Quasi-Rigid Objects in Contact(The Eurographics Association, 2004) Pauly, Mark; Pai, Dinesh K.; Guibas, Leonidas J.; R. Boulic and D. K. PaiWe investigate techniques for modeling contact between quasi-rigid objects ? solids that undergo modest deformation in the vicinity of a contact, while the overall object still preserves its basic shape. The quasi-rigid model combines the benefits of rigid body models for dynamic simulation and the benefits of deformable models for resolving contacts and producing visible deformations. We argue that point cloud surface representations are advantageous for modeling rapidly varying, wide area contacts. Using multi-level computations based on point primitives, we obtain a scalable system that efficiently handles complex contact configurations, even for high-resolution models obtained from laser range scans. Our method computes consistent and realistic contact surfacesand traction distributions, which are useful in many applications.