Providing a two-dimensional parameterization of threedimensional tesselated surfaces is beneficial to many applications in computer graphics, finite-element surface meshing, surface reconstruction and other areas. The applicability of the parameterization depends on how well it preserves the surface metric structures (angles, distances, areas). For a general surface there is no mapping which fully preserves these structures. The distortion usually increases with the rise in surface complexity. For highly complicated surfaces the distortion can become so strong as to make the parameterization unusable for application purposes. One possible solution is to subdivide the surface or introduce seams in a way which will reduce the distortion.

Polygonal simplification is a very active research topic, demonstrated by the recent explosion of papers in the field. The goal of this paper is to give a foundation and overview of this rapidly growing research area. The paper provides a foundation by explaining what polygonal simplification is, describing why it is useful, and defining some terminology of the field. The bulk of the paper classifies and overviews various simplification algorithms. Finally, since polygonal simplification is by no means a solved problem, the paper discusses possible future work.

Introduction Scientific data is often sampled or computed over a dense mesh in order to capture high frequency components or achieve a desired error bound. Interactive display and navigation of such large meshes is impeded by the sheer number of triangles required to sufficiently model highly complex data. A number of simplification techniques have been developed which reduce the number of triangles to a particular desired triangle count or until a particular error Preprint submitted to Elsevier Preprint 3 December 1997 threshold is met. Given an initial triangulation M of a domain D and a function F(x) defined over the triangulation, the simplified mesh can be called M 0 and the resulting function F 0 (x). The measure of error in a simplified mesh M i is usually represented as: ffl(M 0<F1

Current coding techniques for 3-D graphic models mainly focus on coding efficiency, which makes them extremely sensitive to channel errors due to the irregular mesh structure. In this paper, we introduce a new approach for error-resilient coding of arbitrary 3-D graphic models by extending the error-free constructive traversal compression scheme proposed by Li and Kuo. A 3-D mesh of an arbitrary structure is partitioned into pieces of a smaller uniform size with joint boundaries. The size of a piece is determined adaptively based on the channel error rate. The topology and geometry information of each joint boundary and each piece of a connected component is coded independently. The coded topology and first several important bit-planes of the joint-boundary data are protected against channel errors by using the Bose--Chaudhuri--Hocquenghem error-correcting code. At the decoder, each piece is decoded and checked for channel errors. The decoded joint-boundary information is used to perform data recovery and error concealment on the corrupted piece data. All decoded pieces are combined together according to their configuration to reconstruct all connected components of the complete 3-D model. Our experiments demonstrate that the proposed approach has excellent error resiliency at a reasonable bit-rate overhead. The techniques is also capable of incrementally rendering one connected component of the 3-D model at a time.

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.

In this work a new method for CAD model simplification is presented. The method is especially suited for simplifications performed in preparation for meshing the models. It uses a local analysis approach based on a clustering procedure. The method provides a generic approach for model simplification. It is efficient and robust. It works on non-manifold models, free-form and linear faces, and models with large curved regions. It provides symmetric partitioning of details like blends and fillets, resulting in more symmetric simplified models. Keywords: simplification, mesh, CAD models 1 Introduction Real-life CAD models are often highly detailed with a large number of faces representing each feature. Such detailed descriptions are unnecessary for many engineering applications, including mesh generation and analysis. The complexity of the CAD description severely complicates the meshing procedure, often hindering the use of many available meshing techniques. It also requires a si...

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

In recent years several automatic 3D meshing algorithms have emerged. However direct analysis of CAD models is still elusive. Among the major obstacles preventing automation is the necessity to edit the CAD models to be suitable both for the analysis objectives and the available meshing algorithms. Such editing includes topology correction and validation, detail suppression and decomposition. Editing the geometry directly (e.g. surface redefinitions) is cumbersome, tedious, and expensive. Introducing virtual topology allows such operations as modifications to the topology only. In this work the concept and operators of virtual topology are described, along with their use in performing the required editing of the model. A set of automatic and semi-automatic tools for the various editing operations are introduced.

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...