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637
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 1321 (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 Simplification Using Quadric Error Metrics
"... Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplifi ..."
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Cited by 1178 (14 self)
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Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports nonmanifold surface models.
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 668 (15 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
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 605 (16 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
ViewDependent Refinement of Progressive Meshes
"... Levelofdetail (LOD) representations are an important tool for realtime rendering of complex geometric environments. The previously introduced progressive mesh representation defines for an arbitrary triangle mesh a sequence of approximating meshes optimized for viewindependent LOD. In this paper, ..."
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Cited by 456 (5 self)
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Levelofdetail (LOD) representations are an important tool for realtime rendering of complex geometric environments. The previously introduced progressive mesh representation defines for an arbitrary triangle mesh a sequence of approximating meshes optimized for viewindependent LOD. In this paper, we introduce a framework for selectively refining an arbitrary progressive mesh according to changing view parameters. We define efficient refinement criteria based on the view frustum, surface orientation, and screenspace geometric error, and develop a realtime algorithm for incrementally refining and coarsening the mesh according to these criteria. The algorithm exploits view coherence, supports frame rate regulation, and is found to require less than 15 % of total frame time on a graphics workstation. Moreover, for continuous motions this work can be amortized over consecutive frames. In addition, smooth visual transitions (geomorphs) can be constructed between any two selectively refined meshes. A number of previous schemes create viewdependent LOD meshes for height fields (e.g. terrains) and parametric surfaces (e.g. NURBS). Our framework also performs well for these special cases. Notably, the absence of a rigid subdivision structure allows more accurate approximations than with existing schemes. We include results for these cases as well as for general meshes.
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 wH, produce a mesh w, of the same topological type as wH, 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 397 (8 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 wH, produce a mesh w, of the same topological type as wH, 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).
RealTime, Continuous Level of Detail Rendering of Height Fields
, 1996
"... We present an algorithm for realtime level of detail reduction and display of highcomplexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screenspace threshold to bound the maximum error of the projected image. A coarse lev ..."
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Cited by 291 (15 self)
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We present an algorithm for realtime level of detail reduction and display of highcomplexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screenspace threshold to bound the maximum error of the projected image. A coarse level of simplification is performed to select discrete levels of detail for blocks of the surface mesh, followed by further simplification through repolygonalization in which individual mesh vertices are considered for removal. These steps compute and generate the appropriate level of detail dynamically in realtime, minimizing the number of rendered polygons and allowing for smooth changes in resolution across areas of the surface. The algorithm has been implemented for approximating and rendering digital terrain models and other height fields, and consistently performs at interactive frame rates with high image quality.
ROAMing Terrain: Realtime Optimally Adapting Meshes
, 1997
"... Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and groundbased aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, viewdepend ..."
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Cited by 286 (10 self)
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Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and groundbased aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, viewdependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible viewdependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly, and uses frametoframe coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Realtime Optimally Adapting Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from preprocessed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and prioritycomputation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.
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 280 (28 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
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 228 (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