In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.

This paper addresses the problem of simultaneous localisation and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from multigrid methods used for solving partial differential equations. The approach improves on the performance of previous relaxation methods for robot mapping because it optimizes the map at multiple levels of resolution. The resulting algorithm has an update time that is linear in the number of estimated features for typical indoor environments, even when closing very large loops, and offers advantages in handling non-linearities compared to other SLAM algorithms. Experimental comparisons with alternative algorithms using two well-known data sets and mapping results on a real robot are also presented.

Modeling and animation of cloth has experienced important developments in recent years. As a consequence, complex textile models can be used to realistically drape objects or human characters in a fairly efficient way. However, real-time realistic simulation remains a major challenge, even if applications are numerous, from rapid prototyping to e-commerce. In this paper, we present a stable, real-time algorithm for animating cloth-like materials. Using a hybrid explicit/implicit algorithm, we perform fast and stable time integration of a physically-based model with rapid collision detection and response, as well as wind or liquid drag effects to enhance realism. We demonstrate our approach through a series of examples in VR environments, proving that real-time animation of cloth, even on low-end computers, is now achievable.

This paper addresses the problem of simultaneous localisation and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from socalled multigrid methods used for solving partial differential equations. The approach overcomes the relatively slow convergence of previous relaxation methods because it optimizes the map at multiple levels of resolution. The resulting algorithm has an update time that is linear in the number of mapped features, even when closing very large loops, and offers advantages in handling non-linearities compared to previous approaches. Experimental comparisons with alternative algorithms using two well-known data sets are also presented.

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This paper presents a new adaptive sampling method for implicit surfaces that can been used in both interactive modeling and animation. The algorithm samples implicit objects generated by skeletons and e#ciently maintains this sampling, even when their topology changes over time such as during fractures and fusions. It provides two complementary modes of immediate visualization: displaying "scales" lying on the surface, or a piecewise polygonization. The sampling method is particularly well suited to e#ciently avoid "unwanted blending" between di#erent parts of an object.

Given two spatial datasets P (e.g., facilities) and Q (queries), an aggregate nearest neighbor (ANN) query retrieves the point(s) of P with the smallest aggregate distance(s) to points in Q. Assuming, for example, n users at locations q1,... qn,anANN query outputs the facility p ∈ P that minimizes the sum of distances |pqi | for 1 ≤ i ≤ n that the users have to travel in order to meet there. Similarly, another ANN query may report the point p ∈ P that minimizes the maximum distance that any user has to travel, or the minimum distance from some user to his/her closest facility. If Q fits in memory and P is indexed by an R-tree, we develop algorithms for aggregate nearest neighbors that capture several versions of the problem, including weighted queries and incremental reporting of results. Then, we analyze their performance and propose cost models for query optimization. Finally, we extend our techniques for disk-resident queries and approximate ANN retrieval. The efficiency of the algorithms and the accuracy of the cost models are evaluated through extensive experiments with real and synthetic datasets.

Abstract — For the Simultaneous Localization and Mapping problem several efficient algorithms have been proposed that make use of a sparse information matrix representation (e.g. SEIF, TJTF, treemap). Since the exact SLAM information matrix is dense, these algorithm have to approximate it (sparsification). It has been empirically observed that this approximation is adequate because entries in the matrix corresponding to distant landmarks are extremely small. This paper provides a theoretical proof for this observation, specifically showing that the off-diagonal entries corresponding to two landmarks decay exponentially with the distance traveled between observation of first and second landmark. PSfrag replacements

This paper describes an new and optimized direct ray tracing algorithm over complex implicit surfaces generated by skeletons. Its main originality is its ability to avoid unwanted blending between parts of the same object, thanks to the partitioning of the surface into several pieces, so called Implicit Patches. Moreover, these patches enable to exploit the properties of local field functions, and to speed-up considerably the rendering. Extensive statistics of the various optimizations proposed are given and discussed. The implementation into the public domain software RayShade is sketched.

This report presents an approach for efficiently yet precisely simulating highly deformable substances ranging from solids to liquids. The key idea is to use a state equation for specifying the dynamics of the substance. During a simulation, the material is sampled by particles that derive their interaction forces from this state equation. Since this ensures the same qualitative behavior whatever the discretization rate, an adaptivescheme can be used during simulations: the particle system adapts over space and time according to a given compromise between precision and computational efficiency. The system re#nes (i.e., particles are subdivided) in areas undergoing large or fast deformations, while it simplifies (i.e., neighboring particles are merged) in stable regions. Meanwhile, the values of the individual integration time steps used for each particle are automatically adapted to avoid instabilities. An active implicit surface is used to visualize the substance. It smoothly coats the particles and filters over time internal changes of granularity.