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Book ChapterDOI

Multi-resolution 3D approximations for rendering complex scenes

Jarek Rossignac1, Paul Borrel1
01 Jan 1993-pp 455-465
TL;DR: This work presents a simple, effective, and efficient technique for approximating arbitrary polyhedra based on triangulation and vertex-clustering, and produces a series of 3D approximations that resemble the original object from all viewpoints, but contain an increasingly smaller number of faces and vertices.
Abstract: We present a simple, effective, and efficient technique for approximating arbitrary polyhedra. It is based on triangulation and vertex-clustering, and produces a series of 3D approximations (also called “levels of detail”) that resemble the original object from all viewpoints, but contain an increasingly smaller number of faces and vertices. The simplification is more efficient than competing techniques because it does not require building and maintaining a topological adjacency graph. Furthermore, it is better suited for mechanical CAD models which often exhibit patterns of small features, because it automatically groups and simplifies features that are geometrically close, but need not be topologically close or even part of a single connected component Using a lower level of detail when displaying small, distant, or background objects improves graphic performance without a significant loss of perceptual information, and thus enables realtime inspection of complex scenes or a convenient environment for animation or walkthrough preview.
Citations
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Proceedings ArticleDOI
03 Aug 1997
TL;DR: This work has developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models, and which also supports non-manifold surface models.
Abstract: 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 non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface and object representations

3,564 citations


Cites background from "Multi-resolution 3D approximations ..."

  • ...The primary benefit which we gain by utilizing general vertex pair contractions is the ability of the algorithm to join previously unconnected regions of the model together....

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Proceedings ArticleDOI
Hugues Hoppe1
01 Aug 1996
TL;DR: The progressive mesh (PM) representation is introduced, a new scheme for storing and transmitting arbitrary triangle meshes that addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement.
Abstract: 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, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail 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

3,206 citations


Cites background or methods from "Multi-resolution 3D approximations ..."

  • ...Some of the above methods [12, 17] permit the construction of geomorphs between successive simplified meshes....

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  • ...Rossignac and Borrel [12] merge vertices of a model using spatial binning....

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Proceedings ArticleDOI
01 Jul 1992
TL;DR: A general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points that is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners.
Abstract: This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces.

3,119 citations


Cites background or methods from "Multi-resolution 3D approximations ..."

  • ...Surface approximations for parts and groups of parts should be allowed to change topologically at various levels (as in the method of Rossignac and Borrel [53])....

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  • ...Rossignac and Borrel [53] describe a simple and efficient simplification method that generalizes to arbitrary simplicial complexes....

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  • ...[60], Turk [71], Rossignac and Borrel [53], and Lounsbery et al....

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Journal ArticleDOI
TL;DR: Metro allows one to compare the difference between a pair of surfaces by adopting a surface sampling approach, and returns both numerical results and visual results, by coloring the input surface according to the approximation error.
Abstract: This paper presents a new tool, Metro, designed to compensate for a deficiency in many simplification methods proposed in literature. Metro allows one to compare the difference between a pair of surfaces (e.g. a triangulated mesh and its simplified representation) by adopting a surface sampling approach. It has been designed as a highly general tool, and it does no assuption on the particular approach used to build the simplified representation. It returns both numerical results (meshes areas and volumes, maximum and mean error, etc.) and visual results, by coloring the input surface according to the approximation error. EMAIL:: r.scopigno@cnuce.cnr.it

1,585 citations

Proceedings ArticleDOI
15 Sep 1995
TL;DR: A method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form, is presented, based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance.
Abstract: 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 MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance. The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain. We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches. CR

1,411 citations


Cites background from "Multi-resolution 3D approximations ..."

  • ...(We should note, however, that Turk, and Rossignac/Borrel, and Varsney present methods for interpolating between models.)...

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  • ...The problems of compression/simplification and level-of-detail control have been addressed by Turk [20], Schroeder et al. [19], Hoppe et al. [8], Rossignac and Borrel [16], and Varsney [22]....

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  • ...[7], Rossignac and Borrel [15], and Varsney [20]....

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References
More filters
Proceedings ArticleDOI
01 Jul 1992
TL;DR: A general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points that is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners.
Abstract: This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces.

3,119 citations

Proceedings ArticleDOI
01 Jul 1992
TL;DR: An application independent algorithm that uses local operations on geometry and topology to reduce the number of triangles in a triangle mesh and results from two different geometric modeling applications illustrate the strengths of the algorithm.
Abstract: 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. However, because the polygon is linear, often thousands or millions of primitives are required to capture the details of complex geometry. Models of this size are generally not practical since rendering speeds and memory requirements are proportional to the number of polygons. Consequently applications that generate large polygonal meshes often use domain-specific knowledge to reduce model size. There remain algorithms, however, where domainspecific reduction techniques are not generally available or appropriate. One algorithm that generates many polygons is marching cubes. Marching cubes is a brute force surface construction algorithm that extracts isodensity surfaces from volume data, producing from one to five triangles within voxels that contain the surface. Although originally developed for medical applications, marching cubes has found more frequent use in scientific visualization where the size of the volume data sets are much smaller than those found in medical applications. A large computational fluid dynamics volume could have a finite difference grid size of order 100 by 100 by 100, while a typical medical computed tomography or magnetic resonance scanner produces over 100 slices at a resolution of 256 by 256 or 512 by 512 pixels each. Industrial computed tomography, used for inspection and analysis, has even greater resolution, varying from 512 by 512 to 1024 by 1024 pixels. For these sampled data sets, isosurface extraction using marching cubes can produce from 500k to 2,000k triangles. Even today’s graphics workstations have trouble storing and rendering models of this size. Other sampling devices can produce large polygonal models: range cameras, digital elevation data, and satellite data. The sampling resolution of these devices is also improving, resulting in model sizes that rival those obtained from medical scanners. This paper describes an application independent algorithm that uses local operations on geometry and topology to reduce the number of triangles in a triangle mesh. Although our implementation is for the triangle mesh, it can be directly applied to the more general polygon mesh. After describing other work related to model creation from sampled data, we describe the triangle decimation process and its implementation. Results from two different geometric modeling applications illustrate the strengths of the algorithm.

1,790 citations

Proceedings ArticleDOI
01 Jul 1983
TL;DR: This paper advances a “pyramidal parametric” prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images.
Abstract: The mapping of images onto surfaces may substantially increase the realism and information content of computer-generated imagery. The projection of a flat source image onto a curved surface may involve sampling difficulties, however, which are compounded as the view of the surface changes. As the projected scale of the surface increases, interpolation between the original samples of the source image is necessary; as the scale is reduced, approximation of multiple samples in the source is required. Thus a constantly changing sampling window of view-dependent shape must traverse the source image.To reduce the computation implied by these requirements, a set of prefiltered source images may be created. This approach can be applied to particular advantage in animation, where a large number of frames using the same source image must be generated. This paper advances a “pyramidal parametric” prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images.Although the mapping of texture onto surfaces is an excellent example of the process and provided the original motivation for its development, pyramidal parametric data structures admit of wider application. The aliasing of not only surface texture, but also highlights and even the surface representations themselves, may be minimized by pyramidal parametric means.

1,000 citations

Proceedings ArticleDOI
01 Jul 1992
TL;DR: This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a re-tiling of a surface that is faithful to both the geometry and the topology of the original surface.
Abstract: This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speeding-up the off-line rendering of complex scenes. Unfortunately, generating these levels of detail is a time-consuming task usually left to a human modeler. This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a re-tiling of a surface that is faithful to both the geometry and the topology of the original surface. The main contributions of this paper are: 1) a robust method of connecting together new vertices over a surface, 2) a way of using an estimate of surface curvature to distribute more new vertices at regions of higher curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the re-tiling procedure is the creation of an intermediate model called the mutual tessellation of a surface that contains both the vertices from the original model and the new points that are to become vertices in the re-tiled surface. The new model is then created by removing each original vertex and locally re-triangulating the surface in a way that matches the local connectedness of the initial surface. This technique for surface retessellation has been successfully applied to iso-surface models derived from volume data, Connolly surface molecular models and a tessellation of a minimal surface of interest to mathematicians.

923 citations

Journal ArticleDOI
TL;DR: The geometric structure suggests a recursive descent, visible surface algorithm in which the computation time potentially grows linearly with the visible complexity of the scene, and the range of complexity of an environment is greatly increased.
Abstract: The geometric structure inherent in the definition of the shapes of three-dimensional objects and environments is used not just to define their relative motion and placement, but also to assist in solving many other problems of systems for producing pictures by computer. By using an extension of traditional structure information, or a geometric hierarchy, five significant improvements to current techniques are possible. First, the range of complexity of an environment is greatly increased while the visible complexity of any given scene is kept within a fixed upper limit. Second, a meaningful way is provided to vary the amount of detail presented in a scene. Third, “clipping” becomes a very fast logarithmic search for the resolvable parts of the environment within the field of view. Fourth, frame to frame coherence and clipping define a graphical “working set,” or fraction of the total structure that should be present in primary store for immediate access by the visible surface algorithm. Finally, the geometric structure suggests a recursive descent, visible surface algorithm in which the computation time potentially grows linearly with the visible complexity of the scene.

817 citations