This paper introduces an algorithm for rapid progressive simplification of tetrahedral meshes: TetFusion. We describe how a simple geometry decimation operation steers a rapid and controlled progressive simplification of tetrahedral meshes, while also taking care of complex mesh-inconsistency problems. The algorithm features a high decimation ratio per step, and inherently discourages any cases of self-intersection of boundary, elementboundary intersection at concave boundary-regions, and negative volume tetrahedra (flipping). We achieved rigorous reduction ratios of up to 98% for meshes consisting of 827,904 elements in less than 2 minutes, progressing through a series of level-ofdetails (LoDs) of the mesh in a controlled manner. We describe how the approach supports a balanced re-distribution of space between tetrahedral elements, and explain some useful control parameters that make it faster and more intuitive than `edge collapse'-based decimation methods for volumetric meshes [3, 18, 20, 21]. Finally, we discuss how this approach can be employed for rapid LoD prototyping of large time-varying datasets as an aid to interactive visualization.

Aiming at robust surface structure recovery, we extend the powerful optimization technique of variational shape approximation by allowing for several different primitives to represent the geometric proxy of a surface region. While the original paper only considered planes, we also include spheres, cylinders, and more complex rollingball blend patches. The motivation for this choice is the fact that most technical CAD objects consist of patches from these four categories. The robust segmentation and global optimization properties which have been observed for the variational shape approximation carry over to our hybrid extension. Hence, we can use our algorithm to segment a given mesh model into characteristic patches and provide a corresponding geometric proxy for each patch. The expected result that we recover surface structures more robustly and thus obtain better approximations with a smaller number of primitives, is validated and demonstrated on a number of examples. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid and object representations

We introduce the permission grid, a spatial occupancy grid used to guide almost any standard polygonal surface simplification algorithm into generating an approximation with a guaranteed geometric error bound. In particular, the distance between any point on the approximation and the original surface is bounded by a user-specified tolerance. Such bounds are notably absent from most current simplification methods, and are becoming increasingly important for applications such as collision detection and scientific computing. Conceptually simple, the permission grid defines a volume in which the approximation must lie, and does not permit the underlying simplification algorithm to generate approximations outside of this volume. The permission grid makes three important, practical improvements over current error-bounded simplification methods. First, it works on arbitrary triangular models, handling all manners of mesh degeneracies gracefully. Further, the error tolerance may be expanded as simplification proceeds, allowing the construction

Many real-world graphs have been shown to be scale-free--- vertex degrees follow power law distributions, vertices tend to cluster, and the average length of all shortest paths is small. We present a new model for understanding scale-free networks based on multilevel geodesic approximation, using a new data structure called a multilevel mesh. Using this

The paper presents a simple and efficient algorithm for the removal of small topological inconsistencies and high frequency details from surface models. The method, called Marching Intersections (MI), adopts a volumetric approach and acts as a resampling filter: all the intersection points between the input model and the lines of a user selected 3D reference grid are located and then, beginning from these intersections, an output surface is reconstructed. MI, which presents good characteristics in terms of efficiency, compactness, and quality of the output models, can be also used: for the conversion between different representation schemes; to perform logical operations on geometric models; for the topological simplification of surfaces; and for the simplification of huge meshes, i.e. meshes too large to be allocated in main memory during the simplification process. All these aspects are discussed in the paper and timing and graphic results are presented.

We consider the problem of transmitting huge triangle meshes in the context of a Web-like client-server architecture. Approximations of the original mesh are transmitted by applying selective refinement. A multiresolution geometric model is maintained by the server. A client may query the server for a mesh at an arbitrary, continuously variable, level of detail. The client makes repeated queries over time with different query parameters. The server answers to queries by traversing the multiresolution model and transmitting updates to the client, which uses them to progressively modify a current mesh. We study this problem in the context of a vertex-based multiresolution model, which is a special instance of the Multi-Triangulation [Pup96, DFPM97], based on vertex insertion and removal. We define a compact data structure for such a model which exploits the specific update rule. We propose a dynamic algorithm for selective refinement and we discuss in detail its implementation as a...

We address the problem of representing and processing 3D objects, described through simplicial meshes, which consist of parts of mixed dimensions, and with a non-manifold topology, at di#erent levels of detail. First, we describe a multi-resolution model, that we call a Non-manifold Multi-Tessellation (NMT), and we consider the selective refinement query, which is at the heart of several analysis operations on multi-resolution meshes. Next, we focus on a specific instance of a NMT, generated by simplifying simplicial meshes based on vertex-pair contraction, and we describe a compact data structure for encoding such a model. We also propose a new data structure for twodimensional simplicial meshes, capable of representing both connectivity and adjacency information with a small memory overhead, which is used to describe the mesh extracted from an NMT through selective refinement. Finally, we present algorithms to e#ciently perform updates on such a data structure.

We present semisimp, a tool for semiautomatic simplification of three dimensional polygonal models. Existing automatic simplification technology is quite mature, but is not sensitive to the heightened importance of distinct semantic model regions such as faces and limbs, nor to simplification constraints imposed by model usage such as animation. semisimp allows users to preserve such regions by intervening in the simplification process. Users can manipulate the order in which basic simplifications are applied to redistribute model detail, improve the simplified models themselves by repositioning vertices with propagation to neighboring levels of detail, and adjust the hierarchical partitioning of the model surface to segment simplification and improve control of reordering and position propagation. ACM Category and Subject Descriptor: I.3.5 [Computer Graphics] Computational Geometry and Object Modeling - hierarchy and geometric transformations Additional Keywords: model simplificatio...

We present a new mesh decimation framework which is based on the probabilistic optimization technique of Multiple-Choice algorithms. While producing the same expected quality of the output meshes, the Multiple-Choice approach leads to a significant speed-up compared to the wellestablished standard framework for mesh decimation as a greedy optimization scheme. Moreover, Multiple-Choice decimation does not require a global priority queue data structure which reduces the memory overhead and simplifies the algorithmic structure. We explain why and how the MultipleChoice optimization works well for the mesh decimation problem and give a detailed CPU profile analysis to explain where the speed-up comes from.

Abstract Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multi-resolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accuracy.