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489
Vivaldi: A Decentralized Network Coordinate System
 In SIGCOMM
, 2004
"... Largescale Internet applications can benefit from an ability to predict roundtrip times to other hosts without having to contact them first. Explicit measurements are often unattractive because the cost of measurement can outweigh the benefits of exploiting proximity information. Vivaldi is a simp ..."
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Cited by 470 (5 self)
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Largescale Internet applications can benefit from an ability to predict roundtrip times to other hosts without having to contact them first. Explicit measurements are often unattractive because the cost of measurement can outweigh the benefits of exploiting proximity information. Vivaldi is a simple, lightweight algorithm that assigns synthetic coordinates to hosts such that the distance between the coordinates of two hosts accurately predicts the communication latency between the hosts.
A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 355 (8 self)
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We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
Mesh optimization
, 1993
"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
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Cited by 352 (9 self)
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 341 (11 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on "local feature size", the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a surface from scattered sample points arises in many applications such as computer graphics, medical imaging, and cartography. In this paper we consider the specific reconstruction problem in which the input is a set of sample points S drawn from a smooth twodimensional manifold F embedded in three dimensions, and the desired output is a triangular mesh with vertex set equal to S that faithfully represen...
Piecewise smooth surface reconstruction
, 1994
"... We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of t ..."
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Cited by 270 (13 self)
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We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.
Parametrization and smooth approximation of surface triangulations
 Computer Aided Geometric Design
, 1997
"... Abstract. A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular pa ..."
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Cited by 254 (15 self)
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Abstract. A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular parametrization, called shapepreserving, is found to lead to visually smooth surface approximations. A standard approach to fitting a smooth parametric curve c(t) through a given sequence of points xi = (xi,yi,zi) ∈ IR 3, i = 1,...,N is to first make a parametrization, a corresponding increasing sequence of parameter values ti. By finding smooth functions x,y,z: [t1,tN] → IR for which x(ti) = xi, y(ti) = yi, z(ti) = zi, an interpolatory curve
Geometric Compression through Topological Surgery
 ACM TRANSACTIONS ON GRAPHICS
, 1998
"... ... this article introduces a new compressed representation for complex triangulated models and simple, yet efficient, compression and decompression algorithms. In this scheme, vertex positions are quantized within the desired accuracy, a vertex spanning tree is used to predict the position of each ..."
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Cited by 250 (26 self)
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... this article introduces a new compressed representation for complex triangulated models and simple, yet efficient, compression and decompression algorithms. In this scheme, vertex positions are quantized within the desired accuracy, a vertex spanning tree is used to predict the position of each vertex from 2, 3, or 4 of its ancestors in the tree, and the correction vectors are entropy encoded. Properties, such as normals, colors, and texture coordinates, are compressed in a similar manner. The connectivity is encoded with no loss of information to an average of less than two bits per triangle. The vertex spanning tree and a small set of jump edges are used to split the model into a simple polygon. A triangle spanning tree and a sequence of marching bits are used to encode the triangulation of the polygon. Our approach improves on Michael Deering's pioneering results by exploiting the geometric coherence of several ancestors in the vertex spanning tree, preserving the connectivity with no loss of information, avoiding vertex repetitions, and using about three times fewer bits for the connectivity. However, since decompression requires random access to all vertices, this method must be modified for hardware rendering with limited onboard memory. Finally, we demonstrate implementation results for a variety of VRML models with up to two orders of magnitude compression
Point Set Surfaces
, 2001
"... We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We pre ..."
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Cited by 241 (34 self)
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We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.
A Simple Algorithm for Homeomorphic Surface Reconstruction
 International Journal of Computational Geometry and Applications
, 2000
"... The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm [1] using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from ..."
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Cited by 208 (28 self)
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The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm [1] using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming the sample was `suciently dense'. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the rst such topological guarantee for this problem. 1 Introduction A number of applications in CAD, computer graphics, computer vision and mathematical modeling involve the computation of a piecewise lin Dept. of Computer Science, U. of Texas, Austin TX 78712. email: amenta@cs.utexas.edu, supported by NSF grant CCR9731977 y Dept. of Computer Science, U. of Texas, Austin, TX 78712. email: sunghe...
The Power Crust
, 2001
"... The power crust is a construction which takes a sample of points from the surface of a threedimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce ..."
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Cited by 201 (6 self)
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The power crust is a construction which takes a sample of points from the surface of a threedimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation from the MAT.