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28
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 search engine for 3d models
 ACM Transactions on Graphics
, 2003
"... As the number of 3D models available on the Web grows, there is an increasing need for a search engine to help people find them. Unfortunately, traditional textbased search techniques are not always effective for 3D data. In this paper, we investigate new shapebased search methods. The key challen ..."
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Cited by 228 (21 self)
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As the number of 3D models available on the Web grows, there is an increasing need for a search engine to help people find them. Unfortunately, traditional textbased search techniques are not always effective for 3D data. In this paper, we investigate new shapebased search methods. The key challenges are to develop query methods simple enough for novice users and matching algorithms robust enough to work for arbitrary polygonal models. We present a webbased search engine system that supports queries based on 3D sketches, 2D sketches, 3D
Shape Distributions
 ACM Transactions on Graphics
, 2002
"... this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The pr ..."
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Cited by 192 (0 self)
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this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting
Matching 3D Models with Shape Distributions
"... Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, whi ..."
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Cited by 172 (7 self)
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Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is a simpler problem than the comparison of 3D surfaces by traditional shape matching methods that require pose registration, feature correspondence, or model fitting. We find that the dissimilarities be...
Computing and Rendering Point Set Surfaces
, 2002
"... 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). The co ..."
Abstract

Cited by 167 (20 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). The computation of points on the surface is local, which results in an outofcore technique that can handle any point set.
Multiresolution Modeling: Survey & Future Opportunities
, 1999
"... For twenty years, it has been clear that many datasets are excessively complex for applications such as realtime display, and that techniques for controlling the level of detail of models are crucial. More recently, there has been considerable interest in techniques for the automatic simplificati ..."
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Cited by 118 (7 self)
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For twenty years, it has been clear that many datasets are excessively complex for applications such as realtime display, and that techniques for controlling the level of detail of models are crucial. More recently, there has been considerable interest in techniques for the automatic simplification of highly detailed polygonal models into faithful approximations using fewer polygons. Several effective techniques for the automatic simplification of polygonal models have been developed in recent years. This report begins with a survey of the most notable available algorithms. Iterative edge contraction algorithms are of particular interest because they induce a certain hierarchical structure on the surface. An overview of this hierarchical structure is presented,including a formulation relating it to minimum spanning tree construction algorithms. Finally, we will consider the most significant directions in which existing simplification methods can be improved, and a summary of o...
G.: Simplification and repair of polygonal models using volumetric techniques
 IEEE Transactions on Visualization and Computer Graphics
, 2003
"... Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxelbased methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double wall ..."
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Cited by 88 (3 self)
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Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxelbased methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double walls, and intersecting parts. This allows us to perform polygon model repair simply by converting a model to and from the volumetric domain. We also describe a new topologyaltering simplification method that is based on 3D morphological operators. Visually unimportant features such as tubes and holes may be eliminated from a model by the open and close morphological operators. Our simplification approach accepts polygonal models as input, scan converts these to create a volumetric description, performs topology modification, and then converts the results back to polygons. We then apply a topologypreserving polygon simplification technique to produce a final model. Our simplification method produces results that are everywhere manifold. Index Terms—Mesh simplification, mesh repair, volumetric models, morphological operators. æ 1
Wrap&Zip decompression of the connectivity of triangle meshes compressed with Edgebreaker
 Journal of Computational Geometry, Theory and Applications
, 1999
"... The Edgebreaker compression (Rossignac, 1999; King and Rossignac, 1999) is guaranteed to encode any unlabeled triangulated planar graph of t triangles with at most 1.84t bits. It stores the graph as a CLERS string a sequence of t symbols from the set {C, L,E,R,S}, each represented by a 1, 2 or ..."
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Cited by 41 (13 self)
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The Edgebreaker compression (Rossignac, 1999; King and Rossignac, 1999) is guaranteed to encode any unlabeled triangulated planar graph of t triangles with at most 1.84t bits. It stores the graph as a CLERS string a sequence of t symbols from the set {C, L,E,R,S}, each represented by a 1, 2 or 3 bit code. We show here that, in practice, the string can be further compressed to between 0.91t and 1.26t bits using an entropy code. These results improve over the 2.3t bits code proposed by Keeler and Westbrook (1995) and over the various 3D triangle mesh compression techniques published recently (Gumhold and Strasser, 1998; Itai and Rodeh, 1982; Naor, 1990; Touma and Gotsman, 1988; Turan, 1984), which exhibit either larger constants or cannot guarantee a linear worst case storage complexity. The decompression proposed by Rossignac (1999) is complicated and exhibits a nonlinear time complexity. The main contribution reported here is a simpler and efficient decompression algorithm, calle...
Efficient Compression of NonManifold Polygonal Meshes
, 1999
"... We present a method for compressing nonmanifold polygonal meshes, i.e., polygonal meshes with singularities, which occur very frequently in the realworld. Most efficient polygonal compression methods currently available are restricted to a manifold mesh: they require converting a nonmanifold mesh ..."
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Cited by 36 (0 self)
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We present a method for compressing nonmanifold polygonal meshes, i.e., polygonal meshes with singularities, which occur very frequently in the realworld. Most efficient polygonal compression methods currently available are restricted to a manifold mesh: they require converting a nonmanifold mesh to a manifold mesh, and fail to retrieve the original model connectivity after decompression. The present method works by converting the original model to a manifold model, encoding the manifold model using an existing mesh compression technique, and clustering, or stitching together during the decompression process vertices that were duplicated earlier to faithfully recover the original connectivity. This paper focuses on efficiently encoding and decoding the stitching information. Using a naive method, the stitching information would incur a prohibitive cost, while our methods guarantee a worst case cost of O(logm) bits per vertex replication, where m is the number of nonmanifold vertices. Furthermore, when exploiting the adjacency between vertex replications, many replications can be encoded with an insignificant cost. By interleaving the connectivity, stitching information, geometry and properties, we can avoid encoding repeated vertices (and properties bound to vertices) multiple times; thus a reduction of the size of the bitstream of about 10% is obtained compared with encoding the model as a manifold.
Matchmaker: Manifold BReps for nonmanifold rsets
 Proceedings of the ACM Symposium on Solid Modeling
, 1999
"... Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be ..."
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Cited by 36 (17 self)
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Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some nonmanifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a nonmanifold solid may be encoded using simpler and more compact datastructures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a nonmanifold repre...