My thesis presents a physics-based simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulator within frictional regime with only a few small additions to account for inter-grain and boundary friction, yet with visually acceptable result. We also propose an alternative method for simulating fluids. Our core representation is a cloud of particles, which allows for accurate and flexible surface tracking and advection, but we use an auxiliary grid to efficiently enforce boundary conditions and incompressibility. We further address the issue of reconstructing a surface from particle data to render each frame. ii Contents ii

Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete surface scans, using a database of 3D shapes to provide geometric priors for regions of missing data. Our method retrieves suitable context models from the database, warps the retrieved models to conform with the input data, and consistently blends the warped models to obtain the final consolidated 3D shape. We define a shape matching penalty function and corresponding optimization scheme for computing the non-rigid alignment of the context models with the input data. This allows a quantitative evaluation and comparison of the quality of the shape extrapolation provided by each model. Our algorithms are explicitly designed to accommodate uncertain data and can thus be applied directly to raw scanner output. We show on a variety of real data sets how consistent models can be obtained from highly incomplete input. The information gained during the shape completion process can be utilized for future scans, thus continuously simplifying the creation of complex 3D models.

This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with regular hexahedral cells in a single mesh. This hybrid mesh offers both accuracy near obstacles and efficiency in open regions.

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Figure 1: Illustration of the central features of our algebraic MLS framework. From left to right: efficient handling of very complex point sets, fast mean curvature evaluation and shading, significantly increased stability in regions of high curvature, sharp features with controlled sharpness. Sample positions are partly highlighted. In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.

In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key idea of this paper is to define both measurements and reconstructions as point clouds and describe all statistical assumptions in terms of this finite dimensional representation. This yields a discretization of the problem that can be solved using numerical optimization techniques. The resulting algorithm reconstructs both topology and geometry in form of a well-sampled point cloud with noise removed. In a final step, this representation is then converted into a triangle mesh. The proposed approach is conceptually simple and easy to extend. We apply the approach to reconstruct piecewise-smooth surfaces with sharp features and examine the performance of the algorithm on different synthetic and real-world data sets. Categories and Subject Descriptors (according to ACM CCS): I.5.1 [Models]: Statistical; I.3.5 [Computer Graphics]: Curve, surface, solid and object representations

Point Set Surfaces define a (typically) manifold surface from a set of scattered points. The definition involves weighted centroids and a gradient field. The data points are interpolated if singular weight functions are used to define the centroids. While this way of deriving an interpolatory scheme appears natural we show that it has two deficiencies: convexity of the input is not preserved and the extension to Hermite data is numerically unstable. We present a generalization of the standard scheme that we call Hermite Point Set Surface. It allows interpolating given normal constraints in a stable way. In addition, it yields an intuitive parameter for shape control and preserves convexity in most situations.

We discuss the problem of fitting an implicit shape model to a set of points sampled from a co-dimension one manifold of arbitrary topology. The method solves a non-convex optimisation problem in the embedding function that defines the implicit by way of its zero level set. By assuming that the solution is a mixture of radial basis functions of varying widths we attain the globally optimal solution by way of an equivalent eigenvalue problem, without using or constructing as an intermediate step the normal vectors of the manifold at each data point. We demonstrate the system on two and three dimensional data, with examples of missing data interpolation and set operations on the resultant shapes. 1.

We propose a novel approach to generate coarse tetrahedral meshes which can be used in interactive simulation frameworks. The proposed algorithm processes unconstrained, i. e. unorientable and nonmanifold triangle soups. Since the volume bounded by an unconstrained surface is not defined, we tetrahedralize the pseudo volume of the surface, namely the space that is intuitively occupied by the surface. Therefore, a new signed distance field approach is employed and a tetrahedral lattice is laid onto the distance field. Elements outside the pseudo volume are discarded and a smoothing filter is applied to the mesh boundary as a postprocessing step. Using our approach, we can generate coarse tetrahedral meshes from damaged surfaces and even triangle soups without any connectivity. Various examples underline the robustness of our approach. The usability of the resulting meshes is illustrated in the context of interactive deformable modeling. surface is a non-trivial task. Most mesh generators assume that the boundary surface is a closed and orientable manifold. However, many surfaces do not obey these criteria and the enclosed volume is not defined. Surfaces that are obtained by laser scans often contain holes and cracks (see Fig. 1), making it non-manifold. Models that have been constructed using CAD software are composed of interpenetrating subparts (see Fig. 2). In theses cases, traditional volumization approaches have difficulties to determine the object volume which has to be tetrahedralized. Moreover, there exist object representations that are modeled from unconnected triangles (see Fig. 3). While a human observer can intuitively recognize the space occupied by this structure, a volumization approach fails to compute a plausible volumetric representation which hinders the generation of a tetrahedral mesh. 1

Abstract—Real-time evaluation of distributed contact forces between rigid or deformable 3D objects is a key ingredient of 6-DoF force-feedback rendering. Unfortunately, at very high temporal rates, there is often insufficient time to resolve contact between geometrically complex objects. We propose a spatially and temporally adaptive approach to approximate distributed contact forces under hard real-time constraints. Our method is CPU-based and supports contact between rigid or reduced deformable models with complex geometry. We propose a contact model that uses a point-based representation for one object and a signed-distance field for the other. This model is related to the Voxmap-PointShell (VPS) method, but gives continuous contact forces and torques, enabling stable rendering of stiff penalty-based distributed contacts. We demonstrate that stable haptic interactions can be achieved by point-sampling offset surfaces to input “polygon soup ” geometry using particle repulsion. We introduce a multiresolution nested pointshell construction that permits level-of-detail contact forces and enables graceful degradation of contact in close-proximity scenarios. Parametrically deformed distance fields are proposed for contact between reduced deformable objects. We present several examples of 6-DoF haptic rendering of geometrically complex rigid and deformable objects in distributed contact at real-time kilohertz rates.