Results 1  10
of
27
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 523 (13 self)
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In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fairing, to lowpass filtering. We describe a very simple surface signal lowpass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimizationbased fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/image generation  display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  curve, surface, solid, and object representations;J.6[Com puter Applications]: ComputerAided Engineering  computeraided design General Terms: Algorithms, Graphics. 1
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 ..."
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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.
Surface Approximation and Geometric Partitions
 IN PROC. 5TH ACMSIAM SYMPOS. DISCRETE ALGORITHMS
, 1994
"... Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x ..."
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Cited by 97 (15 self)
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Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x; y) of minimum complexity (that is, a xymonotone polyhedral surface, with a minimum number of vertices, edges, or faces) such that j\Sigma(x p ; y p ) \Gamma z p j "; for all (x p ; y p ; z p ) 2 S: We prove that the decision version of this problem is NPHard . The main result of our paper is a polynomialtime approximation algorithm that computes a piecewise linear surface of size O(K o log K o ), where K o is the complexity of an optimal surface satisfying the constraints of the problem. The technique
A Topology Modifying Progressive Decimation Algorithm
"... Triangle decimation techniques reduce the number of triangles in a mesh, typically to improve interactive rendering performance or reduce data storage and transmission requirements. Most of these algorithms are designed to preserve the original topology of the mesh. Unfortunately, this characteristi ..."
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Cited by 70 (0 self)
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Triangle decimation techniques reduce the number of triangles in a mesh, typically to improve interactive rendering performance or reduce data storage and transmission requirements. Most of these algorithms are designed to preserve the original topology of the mesh. Unfortunately, this characteristic is a strong limiting factor in overall reduction capability, since objects with a large number of holes or other topological constraints cannot be effectively reduced. In this paper we present an algorithm that yields a guaranteed reduction level, modifying topology as necessary to achieve the desired result. In addition, the algorithm is based on a fast local decimation technique, and its operations can be encoded for progressive storage, transmission, and reconstruction. In this paper we describe the new progressive decimation algorithm, introduce mesh splitting operations and show how they can be encoded as a progressive mesh. We also demonstrate the utility of the algorithm on models r...
Explicit Surface Remeshing
, 2003
"... We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an areabased smoothing technique. Areabased smoothing allows the control of bo ..."
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Cited by 60 (7 self)
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We present a new remeshing scheme based on the idea of improving mesh quality by a series of local modifications of the mesh geometry and connectivity. Our contribution to the family of local modification techniques is an areabased smoothing technique. Areabased smoothing allows the control of both triangle quality and vertex sampling over the mesh, as a function of some criteria, e.g. the mesh curvature. To perform local modifications of arbitrary genus meshes we use dynamic patchwise parameterization. The parameterization is constructed and updated onthefly as the algorithm progresses with local updates. As a postprocessing stage, we introduce a new algorithm to improve the regularity of the mesh connectivity. The algorithm is able to create an unstructured mesh with a very small number of irregular vertices. Our remeshing scheme is robust, runs at interactive speeds and can be applied to arbitrary complex meshes.
Outofcore algorithms for scientific visualization and computer graphics
 In Visualization’02 Course Notes
, 2002
"... Recently, several external memory techniques have been developed for a wide variety of graphics and visualization problems, including surface simplification, volume rendering, isosurface generation, ray tracing, surface reconstruction, and so on. This work has had significant impact given that in re ..."
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Cited by 46 (11 self)
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Recently, several external memory techniques have been developed for a wide variety of graphics and visualization problems, including surface simplification, volume rendering, isosurface generation, ray tracing, surface reconstruction, and so on. This work has had significant impact given that in recent years there has been a rapid increase in the raw size of datasets. Several technological trends are contributing to this, such as the development of highresolution 3D scanners, and the need to visualize ASCIsize (Accelerated Strategic Computing Initiative) datasets. Another important push for this kind of technology is the growing speed gap between main memory and caches, which penalizes algorithms that do not optimize for coherence of access. Because of these reasons, much research in computer graphics focuses on developing outofcore (and often cachefriendly) techniques. This paper surveys fundamental issues, current problems, and unresolved questions, and aims to provide graphics researchers and professionals with an effective knowledge of current techniques, as well as the foundation to develop novel techniques on their own. Keywords: Outofcore algorithms, scientific visualization, computer graphics, interactive rendering, volume rendering, surface simplification.
Recent advances in remeshing of surfaces
 Shape Analysis and Structuring, Mathematics and Visualization
, 2008
"... Summary. Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent develop ..."
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Cited by 31 (1 self)
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Summary. Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. We classify the techniques into five categories based on their end goal: structured, compatible, high quality, feature and errordriven remeshing. We limit our description to the main ideas and intuition behind each technique, and a brief comparison between some of the techniques. We also list some open questions and directions for future research. 1
Voxel Based Object Simplification
 Proc. SIGGRAPH Symposium on Interactive 3D Graphics
, 1995
"... We present a simple, robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by sampling and lowpass filtering the object into multiresolution volume buffers and applying the marching cubes algorit ..."
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Cited by 30 (2 self)
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We present a simple, robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by sampling and lowpass filtering the object into multiresolution volume buffers and applying the marching cubes algorithm to generate a multiresolution trianglemesh hierarchy. Our method simplifies the genus of objects and can also help existing object simplification algorithms achieve better results. At each level of detail a multilayered mesh can be used for an optional and efficient antialiased rendering. 1.
Model simplification through refinement
 Proc. of Graphics Interface
, 2000
"... As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because they are either too slow (requiring the simplified model to be ..."
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Cited by 29 (4 self)
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As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because they are either too slow (requiring the simplified model to be precomputed) or produce models that are too poor in quality. These shortcomings become particularly acute when models are extremely large. We present an algorithm suitable for simplification of large models at interactive speeds. The algorithm is fast and can guarantee displayable results within a given time limit. Results also have good quality. Inspired by splitting algorithms from vector quantization literature, we simplify models in reverse, beginning with an extremely coarse approximation and refining it. Approximations of surface curvature guide the simplification process. Previously produced simplifications can be further refined by using them as input to the algorithm. 1
Topology Simplification for Polygonal Virtual Environments
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... We present a topology simplifying approach that can be used for genus reductions, removal of protuberances, and repair of cracks in polygonal models in a unified framework. Our work is complementary to the existing work on geometry simplification of polygonal datasets and we demonstrate that using ..."
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Cited by 25 (1 self)
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We present a topology simplifying approach that can be used for genus reductions, removal of protuberances, and repair of cracks in polygonal models in a unified framework. Our work is complementary to the existing work on geometry simplification of polygonal datasets and we demonstrate that using topology and geometry simplifications together yields superior multiresolution hierarchies than is possible by using either of them alone. Our approach can also address the important issue of repair of cracks in polygonal models as well as for rapid identification and removal of protuberances based on internal accessibility in polygonal models. Our approach is based on identifying holes and cracks by extending the concept of #shapes to polygonal meshes under the L1 distance metric. We then generate valid triangulations to fill them using the intuitive notion of sweeping a L1 cube over the identified regions. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture...