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Progressive Tetrahedralizations
, 1998
"... This paper describes some fundamental issues for robust implementations of progressively refined tetrahedralizations generated through sequences of edge collapses. We address the definition of appropriate cost functions and explain on various tests which are necessary to preserve the consistency of ..."
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Cited by 63 (3 self)
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This paper describes some fundamental issues for robust implementations of progressively refined tetrahedralizations generated through sequences of edge collapses. We address the definition of appropriate cost functions and explain on various tests which are necessary to preserve the consistency of the mesh when collapsing edges. Although being considered a special case of progressive simplicial complexes [10], the results of our method are of high practical importance and can be used in many different applications, such as finite element meshing, scattered data interpolation, or rendering of unstructured volume data. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  surfaces and object representations. Keywords: mesh simplification, multiresolution, levelofdetail, unstructured meshes, mesh generation. 1 INTRODUCTION Progressive meshes [7] and its generalizations to higher dimensions [10] proofed to be an extremely powerful notion for the effic...
Topology Preserving and Controlled Topology Simplifying Multiresolution Isosurface Extraction
, 2000
"... Multiresolution methods are becoming increasingly important tools for the interactive visualization of very large data sets. Multiresolution isosurface visualization allows the user to explore volume data using simplified and coarse representations of the isosurface for overview images, and finer re ..."
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Cited by 56 (2 self)
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Multiresolution methods are becoming increasingly important tools for the interactive visualization of very large data sets. Multiresolution isosurface visualization allows the user to explore volume data using simplified and coarse representations of the isosurface for overview images, and finer resolution in areas of high interest or when zooming into the data. Ideally, a coarse isosurface should have the same topological structure as the original. The topological genus of the isosurface is one important property which is often neglected in multiresolution algorithms. This results in uncontrolled topological changes which can occur whenever the levelofdetail is changed. The scope of this paper is to propose an efficient technique which allows preservation of topology as well as controlled topology simplification in multiresolution isosurface extraction. CR Categories: G.1.2 [Numerical Analysis]: Approximation Approximation of Surfaces and Contours I.3.5 [Computer Graphics ]: Co...
Multiresolution Representation and Visualization of Volume Data
, 1997
"... A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built offline through data simplification techni ..."
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Cited by 44 (3 self)
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A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built offline through data simplification techniques, and stored in a compact data structure that supports fast online access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task, and to the performance of a specific hardware platform. Representations at different resolutions can be used together to enhance further interaction and performance through progressive and multiresolution rendering. Index Terms  Volume data visualization, multiresolution representation, tetrahedral meshes. I. Introduction Volume datasets used in current applic...
Multiresolutional Parallel Isosurface Extraction based on Tetrahedral Bisection
 In Proc. Symp. Volume Visualization
, 1999
"... Nowadays, multiresolution visualization methods become an indispensable ingredient of real time interactive post processing. We will here present an efficient approach for tetrahedral grids recursively generated by bisection, which is based on a more general method for arbitrary nested grids. It esp ..."
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Cited by 28 (6 self)
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Nowadays, multiresolution visualization methods become an indispensable ingredient of real time interactive post processing. We will here present an efficient approach for tetrahedral grids recursively generated by bisection, which is based on a more general method for arbitrary nested grids. It especially applies to regular grids, the hexahedra of which are procedurally subdivided into tetrahedra. Besides different types of error indicators, we especially focus on improving the algorithm's performance and reducing the memory requirements. Furthermore, parallelization combined with an appropriate load balancing on multiprocessor workstations is discussed. 1 Introduction A variety of multiresolution visualization methods has been designed to serve as tools for interactive visualization of large data sets. The local resolution of the generated visual objects, such as isosurfaces, is thereby steered by error indicators which measure the error due to a locally coarser approximation of the...
Hierarchical Representation of Timevarying Volume Data with 4√2 Subdivision and Quadrilinear Bspline Wavelets
, 2002
"... ... levels of detail are widely used for largescale two and threedimensional data sets. We present a fourdimensional multiresolution approach for timevarying volume data. This approach supports a hierarchy with spatial and temporal scalability. The ..."
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Cited by 25 (1 self)
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... levels of detail are widely used for largescale two and threedimensional data sets. We present a fourdimensional multiresolution approach for timevarying volume data. This approach supports a hierarchy with spatial and temporal scalability. The
Multiresolution Mesh Representation: Models and Data Structures
 Tutorials on Multiresolution in Geometric Modelling
, 2002
"... Multiresolution meshes are a common basis for building representations of a geometric shape at dierent levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to t ..."
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Cited by 24 (17 self)
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Multiresolution meshes are a common basis for building representations of a geometric shape at dierent levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to the density (size and number) of its cells. A multiresolution mesh provides several alternative meshbased approximations of a spatial object (e.g., a surface describing the boundary of a solid object, or the graph of a scalar eld).
Topological Volume Skeletonization Using Adaptive Tetrahedralization
 in Proc. Geometric Modeling and Processing
, 2004
"... Topological volume skeletons represent levelset graphs of 3D scalar fields, and have recently become crucial to visualizing the global isosurface transitions in the volume. However, it is still a timeconsuming task to extract them especially when input volumes are largescale data and/or prone to ..."
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Cited by 22 (4 self)
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Topological volume skeletons represent levelset graphs of 3D scalar fields, and have recently become crucial to visualizing the global isosurface transitions in the volume. However, it is still a timeconsuming task to extract them especially when input volumes are largescale data and/or prone to smallamplitude noise. This paper presents an efficient method for accelerating the computation of such skeletons using adaptive tetrahedralization. The present tetrahedralization is a topdown approach to linear interpolation of the scalar fields in that it selects tetrahedra to be subdivided adaptively using several criteria. As the criteria, the method employs a topological criterion as well as a geometric one in order to pursue all the topological isosurface transitions that may contribute to the global skeleton of the volume. The tetrahedralization also allows us to avoid unnecessary tracking of minor degenerate features that hide the global skeleton. Experimental results are included to demonstrate that the present method smoothes out the original scalar fields effectively without missing any significant topological features. 1
Reconstruction of volume data with quadratic super splines
 Transactions on Visualization and Computer Graphics (to appear
"... ). The approximation error to the 2 original function in the uniform norm is color coded (from red ≥ 0.075 to blue=0) for the standard trilinear model (left) and our new quadratic super splines (right). The center image shows a visually perfect reconstruction using our model for (4 × 41) 3 samples. ..."
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Cited by 22 (5 self)
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). The approximation error to the 2 original function in the uniform norm is color coded (from red ≥ 0.075 to blue=0) for the standard trilinear model (left) and our new quadratic super splines (right). The center image shows a visually perfect reconstruction using our model for (4 × 41) 3 samples. The maximum error is 0.0065 (center) compared to 0.088 (right) which illustrates that the quasiinterpolating spline yields nearly optimal approximation order. We develop a new approach to reconstruct nondiscrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition ∆. The approximating splines are determined in a natural and completely symmetric way by averaging local data samples, such that appropriate smoothness conditions are automatically satisfied. On each tetrahedron of ∆, the quasiinterpolating spline is a polynomial of total degree two which provides several advantages including efficient computation, evaluation and visualization of the model. We apply BernsteinBézier techniques wellknown in CAGD to compute and evaluate the trivariate spline and its gradient. With this approach the volume data can be visualized efficiently e.g. with isosurface raycasting. Along an arbitrary ray the splines are univariate, piecewise quadratics and thus the exact intersection for a prescribed isovalue can be easily determined in an analytic and exact way. Our results confirm the efficiency of the quasiinterpolating method and demonstrate high visual quality for rendered isosurfaces.
Adaptive physics based tetrahedral mesh generation using level sets
 Eng. Comput. (Lond
, 2005
"... We present a tetrahedral mesh generation algorithm designed for the Lagrangian simulation of deformable bodies. The algorithm’s input is a level set (i.e., a signed distance function on a Cartesian grid or octree). First a bounding box of the object is covered with a uniform lattice of subdivisioni ..."
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Cited by 19 (3 self)
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We present a tetrahedral mesh generation algorithm designed for the Lagrangian simulation of deformable bodies. The algorithm’s input is a level set (i.e., a signed distance function on a Cartesian grid or octree). First a bounding box of the object is covered with a uniform lattice of subdivisioninvariant tetrahedra. The level set is then used to guide a red green adaptive subdivision procedure that is based on both the local curvature and the proximity to the object boundary. The final topology is carefully chosen so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, this candidate mesh is compressed to match the object boundary. To maintain element quality during this compression phase we relax the positions of the nodes using finite elements, masses and springs, or an optimization procedure. The resulting mesh is well suited for simulation since it is highly structured, has topology chosen specifically for large deformations, and is readily refined if required during subsequent simulation. We then use this algorithm to generate meshes for the simulation of skeletal muscle from level set representations of the anatomy. The geometric complexity of biological materials makes it very difficult to generate these models procedurally and as a result we obtain most if not all data from an actual human subject. Our current method involves using voxelized data from the Visible Male [1] to create level set representations of muscle and bone geometries. Given this representation, we use simple level set operations to rebuild and repair errors in the segmented data as well as to smooth aliasing inherent in the voxelized data.
ConstantTime Neighbor Finding in Hierarchical Tetrahedral Meshes
 IN PROCEEDINGS INTERNATIONAL CONFERENCE ON SHAPE MODELING
, 2001
"... Techniques are presented for moving between adjacent tetrahedra in a tetrahedral mesh. The tetrahedra result from a recursive decomposition of a cube into six initial congruent tetrahedra. A new technique is presented for labelingthe triangular faces. The labeling enables the implementation of a bin ..."
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Cited by 16 (12 self)
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Techniques are presented for moving between adjacent tetrahedra in a tetrahedral mesh. The tetrahedra result from a recursive decomposition of a cube into six initial congruent tetrahedra. A new technique is presented for labelingthe triangular faces. The labeling enables the implementation of a binarylike decomposition of each tetrahedron which is represented using a pointerless representation. Outlines of algorithms are given for traversing adjacent triangular faces of equal size in constant time.