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38
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
Simplification Envelopes
"... We propose the idea of simplification envelopes for generating a hierarchy of levelofdetail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a userspecifiable distance # from the original model and that all points of the original m ..."
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Cited by 205 (17 self)
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We propose the idea of simplification envelopes for generating a hierarchy of levelofdetail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a userspecifiable distance # from the original model and that all points of the original model are within a distance # from the approximation. Simplificationenvelopes provide a general framework within which a large collection of existing simplification algorithms can run. We demonstrate this technique in conjunction with two algorithms, one local, the other global. The local algorithm provides a fast method for generating approximations to large input meshes (at least hundreds of thousands of triangles). The global algorithm provides the opportunity to avoid local "minima" and possibly achieve better simplifications as a result. Each approximation attempts to minimize the total number of polygons required to satisfy the above # constraint. The key advantages of our approach are...
Appearancepreserving simplification
 IN PROC. SIGGRAPH’98
, 1998
"... We present a new algorithm for appearancepreserving simplification. Not only does it generate a lowpolygoncount approximation of a model, but it also preserves the appearance. This is accomplished for a particular display resolution in the sense that we properly sample the surface position, curva ..."
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Cited by 153 (9 self)
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We present a new algorithm for appearancepreserving simplification. Not only does it generate a lowpolygoncount approximation of a model, but it also preserves the appearance. This is accomplished for a particular display resolution in the sense that we properly sample the surface position, curvature, and color attributes of the input surface. We convert the input surface to a representation that decouples the sampling of these three attributes, storing the colors and normals in texture and normal maps, respectively. Our simplification algorithm employs a new texture deviation metric, which guarantees that these maps shift by no more than a userspecified number of pixels on the screen. The simplification process filters the surface position, while the runtime system filters the colors and normals on a perpixel basis. We have applied our simplification technique to several large models achieving significant amounts of simplification with little or no loss in rendering quality.
Adaptive RealTime Levelofdetailbased Rendering for Polygonal Models
, 1997
"... We present an algorithm for performing adaptive realtime levelofdetailbased rendering for triangulated polygonal models. The simplifications are dependent on viewing direction, lighting, and visibility and are performed by taking advantage of imagespace, objectspace, and frametoframe coheren ..."
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Cited by 97 (11 self)
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We present an algorithm for performing adaptive realtime levelofdetailbased rendering for triangulated polygonal models. The simplifications are dependent on viewing direction, lighting, and visibility and are performed by taking advantage of imagespace, objectspace, and frametoframe coherences. In contrast to the traditional approaches of precomputing a fixed number of levelofdetail representations for a given object our approach involves statically generating a continuous levelofdetail representation for the object. This representation is then used at runtime to guide the selection of appropriate triangles for display. The list of displayed triangles is updated incrementally from one frame to the next. Our approach is more effective than the current levelofdetailbased rendering approaches for most scientific visualization applications where there are a limited number of highly complex objects that stay relatively close to the viewer. Our approach is applicable for scalar (such as distance from the viewer) as well as vector (such as normal direction) attributes.
Interactive Multiresolution Surface Viewing
, 1996
"... Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and levelofdetail control of complex meshes in a unified and theoretically sound way. ..."
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Cited by 91 (5 self)
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Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and levelofdetail control of complex meshes in a unified and theoretically sound way.
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 73 (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...
Generalized ViewDependent Simplification
 EUROGRAPHICS '99 / P. BRUNET AND R. SCOPIGNO
, 1999
"... We propose a technique for performing viewdependent geometry and topology simplifications for levelofdetailbased renderings of large models. The algorithm proceeds by preprocessing the input dataset into a binary tree, the viewdependence tree of general vertexpair collapses. A subset of the ..."
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Cited by 71 (8 self)
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We propose a technique for performing viewdependent geometry and topology simplifications for levelofdetailbased renderings of large models. The algorithm proceeds by preprocessing the input dataset into a binary tree, the viewdependence tree of general vertexpair collapses. A subset of the Delaunay edges is used to limit the number of vertex pairs considered for topology simplification. Dependencies to avoid mesh foldovers in manifold regions of the input object are stored in the viewdependence tree in an implicit fashion. We have observed that this not only reduces the space requirements by a factor of two, it also highly localizes the memory accesses at run time. The viewdependence tree is used at run time to generate the triangles for display. We also propose a cubicsplinebased distance metric that can be used to unify the geometry and topology simplifications by considering the vertex positions and normals in an integrated manner.
Navigating Static Environments Using ImageSpace Simplification and Morphing
, 1997
"... We present a zbuffered imagespacebased rendering technique that allows navigation in complex static environments. The rendering speed is relatively insensitive to the complexity of the scene as the rendering is performed apriori, and the scene is converted into a bounded complexity representation ..."
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Cited by 56 (4 self)
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We present a zbuffered imagespacebased rendering technique that allows navigation in complex static environments. The rendering speed is relatively insensitive to the complexity of the scene as the rendering is performed apriori, and the scene is converted into a bounded complexity representation in the image space. Realtime performance is attained by using hardware texture mapping to implement the imagespace warping and hardware affine transformations to compute the viewpointdependent warping function. Our proposed method correctly simulates the kinetic depth effect (parallax), occlusion, and can resolve the missing visibility information by combining zbuffered environment maps from multiple viewpoints. CRCategories and Subject Descriptors: I.3.3 [Computer Graphics ]: Picture/Image Generation  Display Algorithms, Viewing Algorithms; I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism  Animation, Texture; I.4.8 [Image Processing]: Scene Analysis  Range data. A...
Simplifying Polygonal Models Using Successive Mappings
, 1997
"... We present the use of mapping functions to automatically generate levels of detail with known error bounds for polygonal models. We develop a piecewise linear mapping function for each simplification operation and use this function to measure deviation of the new surface from both the previous leve ..."
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Cited by 53 (9 self)
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We present the use of mapping functions to automatically generate levels of detail with known error bounds for polygonal models. We develop a piecewise linear mapping function for each simplification operation and use this function to measure deviation of the new surface from both the previous level of detail and from the original surface. In addition, we use the mapping function to compute appropriate texture coordinates if the original map has texture coordinates at its vertices. Our overall algorithm uses edge collapse operations. We present rigorous procedures for the generation of local planar projections as well as for the selection of a new vertex position for the edge collapse operation. As compared to earlier methods, our algorithm is able to compute tight error bounds on surface deviation and produce an entire continuum of levels of detail with mappings between them. We demonstrate the effectiveness of our algorithm on several models: a Ford Bronco consisting of over 300 ...
Controlled Simplification of Genus for Polygonal Models
, 1997
"... Genusreducing simplifications are important in constructing multiresolution hierarchies for levelofdetailbased rendering, especially for datasets that have several relatively small holes, tunnels, and cavities. We present a genusreducing simplification approach that is complementary to the exis ..."
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Cited by 50 (1 self)
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Genusreducing simplifications are important in constructing multiresolution hierarchies for levelofdetailbased rendering, especially for datasets that have several relatively small holes, tunnels, and cavities. We present a genusreducing simplification approach that is complementary to the existing work on genuspreserving simplifications. We propose a simplification framework in which genusreducing and genuspreserving simplifications alternate to yield much better multiresolution hierarchies than would have been possible by using either one of them. In our approach we first identify the holes and the concavities by extending the concept of # hulls to polygonal meshes under the L1 distance metric and then generate valid triangulations to fill them. 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 represent...