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298
Progressive Meshes
"... Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new s ..."
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Cited by 1112 (11 self)
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Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuousresolution representation addresses several practical problems in graphics: smooth geomorphing of levelofdetail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.
Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
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Cited by 649 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from twodimensional slices, and interactive surface sketching.
Decimation of triangle meshes
 Computer Graphics (SIGGRAPH '92 Proceedings
, 1992
"... The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software. ..."
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Cited by 568 (2 self)
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The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.
Multiresolution Analysis of Arbitrary Meshes
, 1995
"... In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multire ..."
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Cited by 513 (17 self)
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In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered in practice typically do not meet this requirement. In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form. The method is based on the approximation of an arbitrary initial mesh M by a mesh M that has subdivision connectivity and is guaranteed to be within a specified tolerance. The key
Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 455 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
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).
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.
Using Particles to Sample and Control Implicit Surfaces
, 1994
"... We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement c ..."
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Cited by 223 (3 self)
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We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement control points for direct manipulation by specifying particle motions, then solving for surface motion that maintains the constraint. For sampling and rendering, we run the constraint in the other direction, creating floater particles that roam freely over the surface. Local repulsion is used to make floaters spread evenly across the surface. By varying the radius of repulsion adaptively, and fissioning or killing particles based on the local density, we can achieve good sampling distributions very rapidly, and maintain them even in the face of rapid and extreme deformations and changes in surface topology. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling:...
Fitting Smooth Surfaces to Dense Polygon Meshes
 Proceedings of SIGGRAPH 96
, 1996
"... Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with ..."
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Cited by 208 (5 self)
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Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for animation and a fine but more expensive model suitable for rendering. The first step in our process consists of interactively painting patch boundaries over a rendering of the mesh. In many applications, interactive placement of patch boundaries is considered part of the creative process and is not amenable to automation. The next step is gridded resampling of eachboundedsection of the mesh. Our resampling algorithm lays a grid of springs acrossthe polygonmesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, w...
Survey of Polygonal Surface Simplification Algorithms
, 1997
"... This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons ..."
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Cited by 192 (3 self)
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This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons