## A Comparison of Mesh Simplification Algorithms (1997)

Venue: | Computers & Graphics |

Citations: | 144 - 8 self |

### BibTeX

@ARTICLE{Cignoni97acomparison,

author = {P. Cignoni and C. Montani and R. Scopigno},

title = {A Comparison of Mesh Simplification Algorithms},

journal = {Computers & Graphics},

year = {1997},

volume = {22},

pages = {37--54}

}

### Years of Citing Articles

### OpenURL

### Abstract

In many applications the need for an accurate simplification of surface meshes is becoming more and more urgent. This need is not only due to rendering speed reasons, but also to allow fast transmission of 3D models in network-based applications. Many different approaches and algorithms for mesh simplification have been proposed in the last few years. We present a survey and a characterization of the fundamental methods. Moreover, the results of an empirical comparison of the simplification codes available in the public domain are discussed. Five implementations, chosen to give a wide spectrum of different topology-preserving methods, were run on a set of sample surfaces. We compared empirical computational complexities and the approximation accuracy of the resulting output meshes. 1 Introduction Triangles are the most popular drawing primitive. They are managed by all graphics libraries and hardware subsystems, and triangular meshes are thus very common in computer graphics. Very c...

### Citations

1113 | Progressive meshes
- Hoppe
- 1996
(Show Context)
Citation Context ...increase in the energy function is deleted. An enhanced version, progressive meshes, provides multiresolution management, mesh compression, selective refinements and enhanced computational efficiency =-=[25, 32]-=-, and is based only on edge collapsing actions; ffl vertex clustering: based on geometric proximity, this approach groups vertices into clusters, and for each cluster it computes a new representative ... |

948 | Surface simplification using quadric error metrics
- Garland, Heckbert
- 1997
(Show Context)
Citation Context ...osed to cope with the perceptual effects of degradation [34]; couples of edges internal to each cluster are merged if a test based on curvature and size is positively verified. A very recent approach =-=[13]-=- applies an efficient error evaluation, based on quadric error matrices, to a clustering approach which performs only vertex pair contractions (a vertex pair is eligible for contraction if either a co... |

568 | Decimation of triangle meshes
- Schroeder, Zarge, et al.
- 1992
(Show Context)
Citation Context ...triangles), chosen upon local geometric optimality criteria. All decimation methods are restricted to manifold surfaces, and generally preserve mesh topology. -- the original mesh decimation approach =-=[40]-=- applies multiple passes over the triangle mesh and progressively removes those vertices that pass a distance or angle criterion (based on local geometry and topology checks). The resulting holes are ... |

516 | Multiresolution analysis of arbitrary meshes
- Eck, DeRose, et al.
- 1995
(Show Context)
Citation Context ...is required to support wavelet decomposition, and computational efficiency is not at the best. Wavelet approaches have been proposed to manage regularly gridded meshes [14, 21] or more generic meshes =-=[10, 4]-=-. In particular, the multiresolutionanalysis approach is based on a three-phase process (re--meshing, re-sampling and wavelet parametrization) to builda multiresolutionrepresentation of the surface, f... |

404 | Re-tiling polygonal surfaces
- Turk
- 1992
(Show Context)
Citation Context ...aluation for a more precise definition. placed over maximal curvature locations; the original vertices are then iteratively removed and a re--tiled mesh, built on the new vertices, is given in output =-=[44]; ffl ener-=-gy function optimization: the mesh optimization approach, originally proposed in [26], defines an energy function which measures the "quality" of each reduced mesh. Mesh reduction is iterati... |

397 | Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments
- Funkhouser, Sequin
- 1999
(Show Context)
Citation Context ...ultiresolution representations of surfaces have been reviewed by Heckbert and Garland [22]. Among other uses, simplification is the basis for the construction of level of detail (LOD) representations =-=[12]-=-; the LOD approach is now widely used due to the support given in de-facto standard graphics libraries [46, 45]. Research on surface simplification has been intense in the last few years. Many papers ... |

355 | Mesh optimization
- Hoppe, Derose, et al.
- 1993
(Show Context)
Citation Context ...unc.edu/��cohenj); 3. Multiresolution Decimation [5]; code Jade rel. 2.0 4 , implemented by the Visual ComputerGroup of CNUCE/IEIC. N.R. (http://miles.cnuce.cnr.it/cg/jade.html); 4. Mesh Optimizat=-=ion [26]-=-; code developed by Hugues Hoppe et al., Univ. of Washington (http://research.microsoft.com/research/graphics/hoppe/); 5. Progressive Meshes [25]; code developed by Hugues Hoppe, Microsoft inc. (http:... |

318 | Geometry compression - Deering - 1998 |

305 |
Multi-Resolution 3D Approximations for Rendering Complex Scenes
- ROSSIGNAC, BORREL
- 1993
(Show Context)
Citation Context ...s based only on edge collapsing actions; ffl vertex clustering: based on geometric proximity, this approach groups vertices into clusters, and for each cluster it computes a new representative vertex =-=[38]-=-. The method is efficient, but neither topology nor small-scale shape details are preserved. The visual and geometric quality of the meshes simplified with a clustering approach have been improved in ... |

270 | Measuring Error on Simplified Surfaces
- CIGNONI, ROCCHINI, et al.
- 1996
(Show Context)
Citation Context ...of approximation precision is needed to compare the results of different simplification methods. For this reason we developed an ad-hoc tool, called Metro. The first release of Metro was described in =-=[7]-=-. The current version of the tool, rel. 2.0, has been completely re-designed in order to increase precision in the evaluation of mesh accuracy, improve efficiency (it is now nearly ten times faster), ... |

260 | View-Dependent Simplification of Arbitrary Polygonal Environments
- LUEBKE, ERIKSON
(Show Context)
Citation Context ...l--clean composition between components. New solutions are required for these applications to provide increased generality and robustness. First attempts in this direction have been recently proposed =-=[31, 13]-=-. 6 Acknowledgements We acknowledge the kind and timely cooperation of Hugues Hoppe and Micheal Garland, who ran their codes on the benchmark datasets. We would also like to thank our collaborators An... |

249 | Geometric Compression through Topological Surgery
- Taubin, Rossignac
- 1998
(Show Context)
Citation Context ...et by adopting an adaptive fitting approach. Moreover, alternative approaches which reduce storing or rendering complexity by adopting compressed representations [9] or triangle strip representations =-=[43] are also -=-out of the scope of this paper. In order to give the reader not only a theoretical evaluation, but also an "objective" comparison of some of the methods reviewed, we adopted an empirical app... |

171 | Simplification envelopes
- Cohen
- 1996
(Show Context)
Citation Context ...o vertices [15, 36, 1], or by collapsing faces [17]; -- extensions to the decimation method which support global error 1 control have been proposed. In particular, the simplification envelopes method =-=[8]-=- supports bounded error control by forcing the simplified mesh to lie between two offset surfaces (but it works only on orientable manifold surfaces). Some other methods adopt heuristics for the evalu... |

158 | Progressive simplicial complexes
- POPOVIĆ, HOPPE
(Show Context)
Citation Context ...increase in the energy function is deleted. An enhanced version, progressive meshes, provides multiresolution management, mesh compression, selective refinements and enhanced computational efficiency =-=[25, 32]-=-, and is based only on edge collapsing actions; ffl vertex clustering: based on geometric proximity, this approach groups vertices into clusters, and for each cluster it computes a new representative ... |

155 |
The Inventor Mentor: Programming ObjectOriented 3D Graphics with Open InventorTM, Release 2
- Wernecke
- 1994
(Show Context)
Citation Context ...s, simplification is the basis for the construction of level of detail (LOD) representations [12]; the LOD approach is now widely used due to the support given in de-facto standard graphics libraries =-=[46, 45]-=-. Research on surface simplification has been intense in the last few years. Many papers and different approaches have appeared, and potential users are being overwelmed by diffuse, unstable or even c... |

133 |
Full-Range Approximation of Triangulated Polyhedra
- RONFARD, ROSSIGNAC
- 1996
(Show Context)
Citation Context ...n process. The candidate vertex selection criterion is based on a local error evaluation; -- a decimation approach can also be adopted to simplify a mesh by iteratively collapsing edges into vertices =-=[15, 36, 1]-=-, or by collapsing faces [17]; -- extensions to the decimation method which support global error 1 control have been proposed. In particular, the simplification envelopes method [8] supports bounded e... |

103 | Multiresolution modeling for fast rendering
- Heckbert, Garland
- 1994
(Show Context)
Citation Context ...t techniques for the controlled simplification of surface meshes. Reasons for the use of both simplification and multiresolution representations of surfaces have been reviewed by Heckbert and Garland =-=[22]-=-. Among other uses, simplification is the basis for the construction of level of detail (LOD) representations [12]; the LOD approach is now widely used due to the support given in de-facto standard gr... |

95 |
Geometric optimization
- Hinker, Hansen
- 1993
(Show Context)
Citation Context ...ds: ffl coplanar facets merging: coplanar or nearly coplanar facets are searched for in the mesh, merged into larger polygons, and then retriangulated into fewer facets than those originally required =-=[16, 28, 24]-=-; face merging is driven by a co-planarity test. The superfaces method [27] extends this approach by providing bounded approximations and more robust re-triangulations of the merged faces; ffl control... |

95 | Mesh reduction with error control
- Klein, Liebich, et al.
- 1996
(Show Context)
Citation Context ...rfaces). Some other methods adopt heuristics for the evaluation of the global error introduced by each vertex removal and re-triangulation step, and work under an incremental simplification framework =-=[42, 5, 3, 29, 36, 15]-=-; -- controlled local modifications of re-triangulated patches, based on edge flipping, have been proposed to improve approximation accuracy in mesh decimation [3, 5]; -- the decimation approach has a... |

88 | Multiresolution Decimation Based on Global Error
- CIAMPALINI, CIGNONI, et al.
- 1997
(Show Context)
Citation Context ...rfaces). Some other methods adopt heuristics for the evaluation of the global error introduced by each vertex removal and re-triangulation step, and work under an incremental simplification framework =-=[42, 5, 3, 29, 36, 15]-=-; -- controlled local modifications of re-triangulated patches, based on edge flipping, have been proposed to improve approximation accuracy in mesh decimation [3, 5]; -- the decimation approach has a... |

83 |
A Data Reduction Scheme for Triangulated Surfaces
- HAMANN
- 1994
(Show Context)
Citation Context ...ction criterion is based on a local error evaluation; -- a decimation approach can also be adopted to simplify a mesh by iteratively collapsing edges into vertices [15, 36, 1], or by collapsing faces =-=[17]-=-; -- extensions to the decimation method which support global error 1 control have been proposed. In particular, the simplification envelopes method [8] supports bounded error control by forcing the s... |

79 | Interactive multiresolution surface viewing
- Certain, Popovic, et al.
- 1996
(Show Context)
Citation Context ... [34]. But taking into account the shape is not enough: pictorial information (color or texture) is an important factor in perception, and therefore color discontinuities have to be managed carefully =-=[34, 25, 4, 41]-=-. 3.1 The Metro tool Due to the many approaches adopted to evaluate simplified mesh accuracy, a uniform and general tool for the evaluation of approximation precision is needed to compare the results ... |

73 | Controlled Topology Simplification
- He, Hong, et al.
(Show Context)
Citation Context ...ate voxel-based hierarchical representation (builtusing signal-processing techniques for the controlled elimination of high-frequency details), together with adaptive surface fitting, was proposed in =-=[19, 20]-=-. 2.1 A characterization A classification of the simplification approaches can be based on the characterization of the input/output data domain, on the simplification goal, on the strategy adopted to ... |

55 | Error-bounded reduction of triangle meshes with multivariate data
- Bajaj, Schikore
- 1996
(Show Context)
Citation Context ...rfaces). Some other methods adopt heuristics for the evaluation of the global error introduced by each vertex removal and re-triangulation step, and work under an incremental simplification framework =-=[42, 5, 3, 29, 36, 15]-=-; -- controlled local modifications of re-triangulated patches, based on edge flipping, have been proposed to improve approximation accuracy in mesh decimation [3, 5]; -- the decimation approach has a... |

52 | A texture-mapping approach for the compression of colored 3d triangulations - Soucy, Godin, et al. - 1996 |

51 | Efficient triangular surface approximation using wavelets and quadtree data structures - Gross, Staadt, et al. - 1996 |

46 | Multiresolution surface modeling based on hierarchical triangulation, Computer Vision and Image Understanding. 17 13: Reconstructed surface. Texture reference
- Soucy, Laurendeau
(Show Context)
Citation Context |

44 | Multiresolution Representation and Visualization of Volume Data - Cignoni, Montani, et al. - 1997 |

43 | Simplification of objects rendered by polygonal approximations
- DeHaemer, Zyda
- 1991
(Show Context)
Citation Context ...ds: ffl coplanar facets merging: coplanar or nearly coplanar facets are searched for in the mesh, merged into larger polygons, and then retriangulated into fewer facets than those originally required =-=[16, 28, 24]-=-; face merging is driven by a co-planarity test. The superfaces method [27] extends this approach by providing bounded approximations and more robust re-triangulations of the merged faces; ffl control... |

39 |
Surface Simplification Inside a Tolerance Volume
- GUÉZIEC
- 1995
(Show Context)
Citation Context ...n process. The candidate vertex selection criterion is based on a local error evaluation; -- a decimation approach can also be adopted to simplify a mesh by iteratively collapsing edges into vertices =-=[15, 36, 1]-=-, or by collapsing faces [17]; -- extensions to the decimation method which support global error 1 control have been proposed. In particular, the simplification envelopes method [8] supports bounded e... |

26 |
Constructing topologically connected surfaces for the comprehensive analysis of 3D medical structures
- Kalvin, Cutting, et al.
- 1991
(Show Context)
Citation Context ...ds: ffl coplanar facets merging: coplanar or nearly coplanar facets are searched for in the mesh, merged into larger polygons, and then retriangulated into fewer facets than those originally required =-=[16, 28, 24]-=-; face merging is driven by a co-planarity test. The superfaces method [27] extends this approach by providing bounded approximations and more robust re-triangulations of the merged faces; ffl control... |

26 | Generalized Unstructured Decimation - Renze, Oliver - 1996 |

25 | Polygonal simplification: An overview
- Erikson
- 1996
(Show Context)
Citation Context ...ny papers and different approaches have appeared, and potential users are being overwelmed by diffuse, unstable or even contradictory knowledge. Survey papers on surface simplification are still rare =-=[11, 37, 23, 33]-=-. This paper presents a brief introduction to surface mesh simplification methods, and proposes a new taxonomy. Its main objective is to analyze and compare the different approaches adopted to measure... |

24 | SCROOGE: Perceptually-Driven Polygon Reduction, Computer Graphics forum
- Reddy
- 1996
(Show Context)
Citation Context ...ic quality of the meshes simplified with a clustering approach have been improved in [30]. Another extension to the clustering approach was proposed to cope with the perceptual effects of degradation =-=[34]-=-; couples of edges internal to each cluster are merged if a test based on curvature and size is positively verified. A very recent approach [13] applies an efficient error evaluation, based on quadric... |

23 |
Mesh simplification
- Algorri, Schmitt
- 1996
(Show Context)
Citation Context ...n process. The candidate vertex selection criterion is based on a local error evaluation; -- a decimation approach can also be adopted to simplify a mesh by iteratively collapsing edges into vertices =-=[15, 36, 1]-=-, or by collapsing faces [17]; -- extensions to the decimation method which support global error 1 control have been proposed. In particular, the simplification envelopes method [8] supports bounded e... |

23 | Simplification using vertex clustering - Low, Tan - 1997 |

21 |
Voxel-based object simplification
- He, Hong, et al.
- 1995
(Show Context)
Citation Context ...ate voxel-based hierarchical representation (builtusing signal-processing techniques for the controlled elimination of high-frequency details), together with adaptive surface fitting, was proposed in =-=[19, 20]-=-. 2.1 A characterization A classification of the simplification approaches can be based on the characterization of the input/output data domain, on the simplification goal, on the strategy adopted to ... |

16 |
Data point selection for piecewise trilinear approximation
- Hamann, Chen
- 1994
(Show Context)
Citation Context ...een proposed to improve approximation accuracy in mesh decimation [3, 5]; -- the decimation approach has also been generalized to the simplification of 3D simplicial decompositions (tetrahedral sets) =-=[35, 6, 18]-=-; ffl re--tiling: new vertices are inserted at random on the original surface mesh, and then moved on the surface to be dis1 Global error is defined here in opposition to local error, i.e. whether the... |

14 |
Survey of surface simplification algorithms
- Heckbert, Garland
- 1997
(Show Context)
Citation Context ...ny papers and different approaches have appeared, and potential users are being overwelmed by diffuse, unstable or even contradictory knowledge. Survey papers on surface simplification are still rare =-=[11, 37, 23, 33]-=-. This paper presents a brief introduction to surface mesh simplification methods, and proposes a new taxonomy. Its main objective is to analyze and compare the different approaches adopted to measure... |

13 |
Image encoding with triangulation wavelets
- Hebert, Kim
- 1995
(Show Context)
Citation Context ...lar, hierarchical decomposition is required to support wavelet decomposition, and computational efficiency is not at the best. Wavelet approaches have been proposed to manage regularly gridded meshes =-=[14, 21]-=- or more generic meshes [10, 4]. In particular, the multiresolutionanalysis approach is based on a three-phase process (re--meshing, re-sampling and wavelet parametrization) to builda multiresolutionr... |

7 |
Polygon Reduction Techniques
- Schroeder
- 1995
(Show Context)
Citation Context ...ex clustering may produce dangling faces, edges, or points). Moreover, taking into account the output produced, simplification methods may be characterized by highlighting two main orthogonal classes =-=[39]-=-: ffl approaches which preserve mesh topology (e.g. mesh decimation, mesh optimization), and those which don't (e.g. vertex clustering, intermediate hierarchical representation); ffl approaches based ... |

6 |
Superfaces: Poligonal mesh simplification with bounded error
- Kalvin, Taylor
- 1996
(Show Context)
Citation Context ...r in the mesh, merged into larger polygons, and then retriangulated into fewer facets than those originally required [16, 28, 24]; face merging is driven by a co-planarity test. The superfaces method =-=[27]-=- extends this approach by providing bounded approximations and more robust re-triangulations of the merged faces; ffl controlled vertex/edge/face decimation: these methods work by the iterative elimin... |

5 |
Multiresolution - Principles and Applications
- Simplification
- 1997
(Show Context)
Citation Context ...ny papers and different approaches have appeared, and potential users are being overwelmed by diffuse, unstable or even contradictory knowledge. Survey papers on surface simplification are still rare =-=[11, 37, 23, 33]-=-. This paper presents a brief introduction to surface mesh simplification methods, and proposes a new taxonomy. Its main objective is to analyze and compare the different approaches adopted to measure... |

1 |
Automatic generation of multiresolutionboundary representations
- Andujar, Ayala, et al.
- 1996
(Show Context)
Citation Context ... An extension to this approach manages the approximation of both geometry and surface color [4]; ffl simplification via intermediate hierarchical representation: an intermediate octree representation =-=[2]-=- may be adopted to automatically produce simplified representations, because the octree may be purged at various levels and then converted into a (simplified) boundary representation; alternatively, a... |