TOM: totally ordered mesh. A multiresolution data structure for time-critical graphics applications

Tridimensional interactive applications are confronted to situations where very large databases have to be animated, transmitted and displayed in very short bounded times. As it is generally impossible to handle the complete graphics description while meeting timing constraint, techniques enabling the extraction and manipulation of a significant part of the geometric database have been the focus of many research works in the field of computer graphics. Multiresolution representations of 3D models provide access to 3D objects at arbitrary resolutions while minimizing appearance degradation. Several kinds of data structures have been recently proposed for dealing with polygonal or parametric representations, but where not generally optimized for time-critical applications. We describe the TOM (Totally Ordered Mesh), a multiresolution triangle mesh structure tailored to the support of time-critical adaptive rendering. The structure grants high speed access to the continuous levels of detail of a mesh and allows very fast traversal of the list of triangles at arbitrary resolution so that bottlenecks in the graphic pipeline are avoided. Moreover, and without specific compression, the memory footprint of the TOM is small (about 108% of the single resolution object in face-vertex form) so that large scenes can be effectively handled. The TOM structure also supports storage of per vertex (or per corner of triangle) attributes such as colors, normals, texture coordinates or dynamic properties. Implementation details are presented along with the results of tests for memory needs, approximation quality, timing and efficacy

Efficient Decimation of Polygonal Models Using Normal Field Deviation

A simple and robust greedy algorithm has been proposed for efficient and quality decimation of polygonal models. The performance of a simplification algorithm depends on how the local geometric deviation caused by a local decimation operation is measured. As normal field of a surface plays key role in its visual appearance, exploiting the local normal field deviation in a novel way, a new measure of geometric fidelity has been introduced. This measure has the potential to identify and preserve the salient features of a surface model automatically. The resulting algorithm is simple to implement, produces approximations of better quality and is efficient in running time. Subjective and objective comparisons validate the assertion. It is suitable for applications where the focus is better speed-quality trade-off, and simplification is used as a processing step in other algorithms

Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $\sigma$ (where $\sigma=1$ corresponds to no rotational symmetry), we prove that $k=\sigma+1$ searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with $k=2$ searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations, and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.Comment: 37 pages, 9 figure

Analytic simplification of animated characters

Traditionally, levels of detail (LOD) for animated characters are computed from a single pose. Later techniques refined this approach by considering a set of sample poses and evaluating a more representative error metric. A recent approach to the character animation problem, animation space, provides a framework for measuring error analytically. The work presented here uses the animation-space framework to derive two new techniques to improve the quality of LOD approximations. Firstly, we use an animation-space distance metric within a progressive mesh-based LOD scheme, giving results that are reasonable across a range of poses, without requiring that the pose space be sampled. Secondly, we simplify individual vertices by reducing the number of bones that influence them, using a constrained least-squares optimisation. This influence simplification is combined with the progressive mesh to form a single stream of simplifications. Influence simplification reduces the geometric error by up to an order of magnitude, and allows models to be simplified further than is possible with only a progressive mesh. Quantitative (geometric error metrics) and qualititative (user perceptual) experiements confirm that these new extensions provide significant improvements in quality over traditional, naïve simplification; and while there is naturally some impact on the speed of the off-line simplification process, it is not prohibitive

A Comparative Study on Polygonal Mesh Simplification Algorithms

Polygonal meshes are a common way of representing three dimensional surface models in many different areas of computer graphics and geometry processing. However, with the evolution of the technology, polygonal models are becoming more and more complex. As the complexity of the models increase, the visual approximation to the real world objects get better but there is a trade-off between the cost of processing these models and better visual approximation. In order to reduce this cost, the number of polygons in a model can be reduced by mesh simplification algorithms. These algorithms are widely used such that nearly all of the popular mesh editing libraries include at least one of them. In this work, polygonal simplification algorithms that are embedded in open source libraries: CGAL, VTK and OpenMesh are compared with the Metro geometric error measuring tool. By this way we try to supply a guidance for developers for publicly available mesh libraries in order to implement polygonal mesh simplification

Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for k>=2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of P, we minimize the number of searchers k for which the Meeting problem is solvable. Specifically, if P has a rotational symmetry of order sigma (where sigma=1 corresponds to no rotational symmetry), we prove that k=sigma+1 searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with k=2 searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations (provided that the coordinates of the polygon\u27s vertices are algebraic real numbers in some global coordinate system), and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest

Force shading for shape preception in haptic virtual environments

Also issued as Thesis (M. Eng.)--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 76-77).Supported in part by the Office of Naval Research from the Naval Air Warfare Center Training Systems Division. N161339-94-C-0087by Hugh B. Morgenbesser and Mandayam A. Srinivasan

Vertex classification for non-uniform geometry reduction.

Complex models created from isosurface extraction or CAD and highly accurate 3D models produced from high-resolution scanners are useful, for example, for medical simulation, Virtual Reality and entertainment. Often models in general require some sort of manual editing before they can be incorporated in a walkthrough, simulation, computer game or movie. The visualization challenges of a 3D editing tool may be regarded as similar to that of those of other applications that include an element of visualization such as Virtual Reality. However the rendering interaction requirements of each of these applications varies according to their purpose. For rendering photo-realistic images in movies computer farms can render uninterrupted for weeks, a 3D editing tool requires fast access to a model's fine data. In Virtual Reality rendering acceleration techniques such as level of detail can temporarily render parts of a scene with alternative lower complexity versions in order to meet a frame rate tolerable for the user. These alternative versions can be dynamic increments of complexity or static models that were uniformly simplified across the model by minimizing some cost function. Scanners typically have a fixed sampling rate for the entire model being scanned, and therefore may generate large amounts of data in areas not of much interest or that contribute little to the application at hand. It is therefore desirable to simplify such models non-uniformly. Features such as very high curvature areas or borders can be detected automatically and simplified differently to other areas without any interaction or visualization. However a problem arises when one wishes to manually select features of interest in the original model to preserve and create stand alone, non-uniformly reduced versions of large models, for example for medical simulation. To inspect and view such models the memory requirements of LoD representations can be prohibitive and prevent storage of a model in main memory. Furthermore, although asynchronous rendering of a base simplified model ensures a frame rate tolerable to the user whilst detail is paged, no guarantees can be made that what the user is selecting is at the original resolution of the model or of an appropriate LoD owing to disk lag or the complexity of a particular view selected by the user. This thesis presents an interactive method in the con text of a 3D editing application for feature selection from any model that fits in main memory. We present a new compression/decompression of triangle normals and colour technique which does not require dedicated hardware that allows for 87.4% memory reduction and allows larger models to fit in main memory with at most 1.3/2.5 degrees of error on triangle normals and to be viewed interactively. To address scale and available hardware resources, we reference a hierarchy of volumes of different sizes. The distances of the volumes at each level of the hierarchy to the intersection point of the line of sight with the model are calculated and these distances sorted. At startup an appropriate level of the tree is automatically chosen by separating the time required for rendering from that required for sorting and constraining the latter according to the resources available. A clustered navigation skin and depth buffer strategy allows for the interactive visualisation of models of any size, ensuring that triangles from the closest volumes are rendered over the navigation skin even when the clustered skin may be closer to the viewer than the original model. We show results with scanned models, CAD, textured models and an isosurface. This thesis addresses numerical issues arising from the optimisation of cost functions in LoD algorithms and presents a semi-automatic solution for selection of the threshold on the condition number of the matrix to be inverted for optimal placement of the new vertex created by an edge collapse. We show that the units in which a model is expressed may inadvertently affect the condition of these matrices, hence affecting the evaluation of different LoD methods with different solvers. We use the same solver with an automatically calibrated threshold to evaluate different uniform geometry reduction techniques. We then present a framework for non-uniform reduction of regular scanned models that can be used in conjunction with a variety of LoD algorithms. The benefits of non-uniform reduction are presented in the context of an animation system. (Abstract shortened by UMI.)

Multivariate Topology Simplification

Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph