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576
ViewDependent displacement mapping
 In: Proc. of the SIGGRAPH 2003
, 2003
"... ment mapping, and (d) viewdependent displacement mapping with selfshadowing. Significant visual effects arise from surface mesostructure, such as finescale shadowing, occlusion and silhouettes. To efficiently render its detailed appearance, we introduce a technique called viewdependent displace ..."
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Cited by 87 (3 self)
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ment mapping, and (d) viewdependent displacement mapping with selfshadowing. Significant visual effects arise from surface mesostructure, such as finescale shadowing, occlusion and silhouettes. To efficiently render its detailed appearance, we introduce a technique called viewdependent displacement mapping (VDM) that models surface displacements along the viewing direction. Unlike traditional displacement mapping, VDM allows for efficient rendering of selfshadows, occlusions and silhouettes without increasing the complexity of the underlying surface mesh. VDM is based on perpixel processing, and with hardware acceleration it can render mesostructure with rich visual appearance in real time.
A Simple Mesh Generator in MATLAB
 SIAM Review
, 2004
"... Abstract. Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple MATLAB code, described in more detai ..."
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Cited by 86 (4 self)
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Abstract. Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple MATLAB code, described in more detail than usual, so the reader can experiment (and add to the code) knowing the underlying principles. We find the node locations by solving for equilibrium in a truss structure (using piecewise linear forcedisplacement relations) and we reset the topology by the Delaunay algorithm. The geometry is described implicitly by its distance function. In addition to being much shorter and simpler than other meshing techniques, our algorithm typically produces meshes of very high quality. We discuss ways to improve the robustness and the performance, but our aim here is simplicity. Readers can download (and edit) the codes from
On Combining Laplacian And OptimizationBased Mesh Smoothing Techniques
 TRENDS IN UNSTRUCTURED MESH GENERATION
, 1997
"... Local mesh smoothing algorithms have been shown to be effective in repairing distorted elements in automatically generated meshes. The simplest such algorithm is Laplacian smoothing, which moves grid points to the geometric center of incident vertices. Unfortunately, this method operates heuristical ..."
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Cited by 77 (9 self)
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Local mesh smoothing algorithms have been shown to be effective in repairing distorted elements in automatically generated meshes. The simplest such algorithm is Laplacian smoothing, which moves grid points to the geometric center of incident vertices. Unfortunately, this method operates heuristically and can create invalid meshes or elements of worse quality than those contained in the original mesh. In contrast, optimizationbased methods are designed to maximize some measure of mesh quality and are very effective at eliminating extremal angles in the mesh. These improvements come at a higher computational cost, however. In this article we propose four smoothing techniques that combine a smart variant of Laplacian smoothing with an optimizationbased approach. Several numerical experiments are performed that compare the mesh quality and computational cost for each of the methods in two and three dimensions. We find that the combined approaches are very cost effective and yield highquality meshes.
A Flowguided Streamline Seeding Strategy
 In Proceedings IEEE Visualization 2000
"... This paper presents a seed placement strategy for streamlines based on ow features in the data set. The primary goal of our seeding strategy is to capture ow patterns in the vicinity of critical points in the ow eld, even as the density of streamlines is reduced. Secondary goals are to place stre ..."
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Cited by 70 (0 self)
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This paper presents a seed placement strategy for streamlines based on ow features in the data set. The primary goal of our seeding strategy is to capture ow patterns in the vicinity of critical points in the ow eld, even as the density of streamlines is reduced. Secondary goals are to place streamlines such that there is sucient coverage in noncritical regions, and to vary the streamline placements and lengths so that the overall presentation is aesthetically pleasing (avoid clustering of streamlines, avoid sharp discontinuities across several streamlines, etc.). The procedure is straight forward and noniterative. First, critical points are identied. Next, the ow eld is segmented into regions, each containing a single critical point. The critical point in each region is then seeded with a template depending on the type of critical point. Finally, additional seed points are randomly distributed around the eld using a Poisson disk distribution to minimize closely spaced seed points. The main advantage of this approach is that it does not miss the features around critical points. Since the strategy is not imageguided, and hence not view dependent, signicant savings are possible when examining ow elds from dierent viewpoints, especially for 3D ow elds. Key Words and Phrases: seed placement, streamline, critical point, Voronoi diagram, Poisson disk distribution. 1
Topological fisheye views for visualizing large graphs
 IEEE Transactions on Visualization and Computer Graphics
"... Graph drawing is a basic visualization tool. For graphs of up to hundreds of nodes and edges, there are many effective techniques available. At greater scale, data density and occlusion problems often negate its effectiveness. Conventional panandzoom, and multiscale and geometric fisheye views are ..."
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Cited by 65 (2 self)
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Graph drawing is a basic visualization tool. For graphs of up to hundreds of nodes and edges, there are many effective techniques available. At greater scale, data density and occlusion problems often negate its effectiveness. Conventional panandzoom, and multiscale and geometric fisheye views are not fully satisfactory solutions to this problem. As an alternative, we describe a topological zooming method. It is based on the precomputation of a hierarchy of coarsened graphs, which are combined onthefly into renderings with the level of detail dependent on the distance from one or more foci. We also discuss a related distortion method that allows our technique to achieve constant information density displays.
Local OptimizationBased Simplicial Mesh Untangling And Improvement
 International Journal of Numerical Methods in Engineering
"... . We present an optimizationbased approach for mesh untangling that maximizes the minimum area or volume of simplicial elements in a local submesh. These functions are linear with respect to the free vertex position; thus the problem can be formulated as a linear program that is solved by using the ..."
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Cited by 63 (7 self)
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. We present an optimizationbased approach for mesh untangling that maximizes the minimum area or volume of simplicial elements in a local submesh. These functions are linear with respect to the free vertex position; thus the problem can be formulated as a linear program that is solved by using the computationally inexpensive simplex method. We prove that the function level sets are convex regardless of the position of the free vertex, and hence the local subproblem is guaranteed to converge. Maximizing the minimum area or volume of mesh elements, although wellsuited for mesh untangling, is not ideal for mesh improvement, and its use often results in poor quality meshes. We therefore combine the mesh untangling technique with optimizationbased mesh improvement techniques and expand previous results to show that a commonly used twodimensional mesh quality criterion can be guaranteed to converge when starting with a valid mesh. Typical results showing the effectiveness of the combine...
Fast randomized point location without preprocessing in two and threedimensional Delaunay triangulations
 Computational Geometry—Theory and Applications
, 1999
"... This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through ” the triangulation, after selecting a “good starting point ” by random sampling. The analysis generalizes an ..."
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Cited by 63 (4 self)
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This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through ” the triangulation, after selecting a “good starting point ” by random sampling. The analysis generalizes and extends a recent result for d D 2 dimensions by proving this procedure takes expected time close to O.n1=.dC1/ / for point location in Delaunay triangulations of n random points in d D 3 dimensions. Empirical results in both two and three dimensions show
The Natural Element Method In Solid Mechanics
, 1998
"... The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal descripti ..."
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Cited by 61 (14 self)
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The application of the Natural Element Method (NEM) (Traversoni, 1994; Braun and Sambridge, 1995) to boundary value problems in twodimensional small displacement elastostatics is presented. The discrete model of the domain \Omega consists of a set of distinct nodes N , and a polygonal description of the boundary @ In the Natural Element Method, the trial and test functions are constructed using natural neighbor interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N . The interpolants are smooth (C NEM is identical to linear finite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and nonconvex bodies (cracks) using NEM is also described.
Bayesian graph edit distance
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2000
"... AbstractÐThis paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of editdistance originally introduced for graphmatching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution ..."
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Cited by 60 (5 self)
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AbstractÐThis paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of editdistance originally introduced for graphmatching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution for structural errors in the graphmatching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graphmatching algorithm with that recently reported by Wilson and Hancock. The use of editdistance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worstcase complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match.
Robust Adaptive FloatingPoint Geometric Predicates
 in Proc. 12th Annu. ACM Sympos. Comput. Geom
, 1996
"... Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floatingpoint numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary precision ..."
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Cited by 57 (2 self)
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Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floatingpoint numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary precision arithmetic that have a strong advantage over other software techniques in computations that manipulate values of extended but small precision. Second, they are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floatingpoint arithmetic uses radix two and exact rounding, including machines that comply with the IEEE 754 floatingpoint standard. Timings of the predicates, in isolation and embedded in 2D and 3D Delaunay triangulation programs, verify their effectiveness. 1 Introduction Algorithms that make decisions based on geometric tests, such as determining which side of a line a point falls on, ...