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## Generating Levels of Detail for Large-Scale Polygonal Models (1995)

Citations: | 6 - 0 self |

### Citations

14070 |
Computers and Intractability, A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...approach we get jP j = n instead of jP j = O(n 4 ). We have implemented this latter formulation. 6.2 The Greedy Heuristic The set cover and the set partition problems are both known to be NP-complete =-=[14]-=-, so we cannot hope to have a polynomial-time algorithm for computing an optimal solution to our polygonal approximation problem. However, there exist several heuristics that compute approximate solut... |

1142 |
Curves and surfaces for computer aided geometric design
- Farin
- 2002
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Citation Context ...s1 as: x(u; v) = b 00 (1 \Gamma u)(1 \Gamma v) +b 01 (1 \Gamma u)v +b 10 u(1 \Gamma v) +b 11 uv, where b 00 ; b 01 ; b 10 ; and b 11 are the four corner points of a bilinear patch. For details, refer =-=[12]-=-. e v 1 v 2 - e e + e 1 n 2 n e v 1 v 2 1 n 2 n - e e e + (a) (b) Figure 1: Edge Halfspaces 4.2 The Fundamental Prism Let us refer to the triangles of the given polygonal representation P as the funda... |

640 | Decimation of triangle meshes
- Schroeder, Zarge, et al.
- 1992
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Citation Context ...oring them in their original form as opposed to storing their approximations, amounts to wasting memory for storage as well as CPU cycles during processing, with disproportionately few or no benefits =-=[27, 26, 17, 19, 16]-=-. In this paper we discuss an approach for generating minimal approximations to a given polygonal representation of an object that are guaranteed not to deviate from the original by more than a user-s... |

595 |
T.: Illumination for computer generated pictures
- PHONG
- 1975
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Citation Context ...e latter should have unique normals at each vertex and edge that are equal to the normal of the sphere at those points. With this representation, shading models such as those of Gouraud [15] or Phong =-=[22]-=- give an approximately sphere-like shading to the octahedral approximation. In general, polygonal approximations to curved objects have unique vertex and edge normals to avoid the discontinuities in t... |

502 |
A greedy heuristic for the set-covering problem
- Chvátal
- 1979
(Show Context)
Citation Context ...ind such a triangulation T 0 j , we try the same with the next triangle that covers the maximum number of triangles of M i\Gamma1 . 6.4 Estimating Solution Quality It has been shown in the literature =-=[20, 4]-=- that the greedy heuristic yields a solution to the set cover problem that is guaranteed to be within a factor of (1 + lg d) of the optimal, where d is the maximum number of elements in any set t j . ... |

450 | Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments
- Funkhouser, Séquin
- 1993
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Citation Context ...given polygonal model. Multiresolution representations of an object find several uses in computer graphics: (a) In a level-of-detail based rendering algorithm for providing desired frame update rates =-=[5, 7, 8, 13, 2]-=-. (b) Using low-detail approximations of objects for illumination algorithms, especially radiosity [24]. (c) Simplifying traditionally over-sampled models such as those generated from volume datasets,... |

445 | Re-tiling polygonal surfaces.
- Turk
- 1992
(Show Context)
Citation Context ...oring them in their original form as opposed to storing their approximations, amounts to wasting memory for storage as well as CPU cycles during processing, with disproportionately few or no benefits =-=[27, 26, 17, 19, 16]-=-. In this paper we discuss an approach for generating minimal approximations to a given polygonal representation of an object that are guaranteed not to deviate from the original by more than a user-s... |

392 | Mesh optimization
- Hoppe, DeRose, et al.
- 1993
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Citation Context ...ken by Rossignac and Borrel in [23] where 1 vertices that are close to each other are clustered and a new vertex generated to represent them. The mesh is suitably updated to reflect this. Hoppe et al =-=[18]-=- proceed by iteratively optimizing an energy function over a mesh to minimize both the distance of the approximating mesh from the original, as well as the number of approximating vertices. An interes... |

388 | Multiresolution Analysis For Surfaces Of Arbitrary Topological Type
- Lounsbery, DeRose, et al.
- 1997
(Show Context)
Citation Context ...m the original, as well as the number of approximating vertices. An interesting and elegant solution to the problem of polygonal simplification by using wavelets has been presented by DeRose et al in =-=[11]-=-. In computational geometry, it has been shown that computing the minimal-facet ffl-approximation is NP-hard for both convex polytopes [9] and polyhedral terrains [1]. Thus, algorithms to these proble... |

371 |
Hierarchical geometric models for visible surface algorithms.
- Clark
- 1976
(Show Context)
Citation Context ...given polygonal model. Multiresolution representations of an object find several uses in computer graphics: (a) In a level-of-detail based rendering algorithm for providing desired frame update rates =-=[5, 7, 8, 13, 2]-=-. (b) Using low-detail approximations of objects for illumination algorithms, especially radiosity [24]. (c) Simplifying traditionally over-sampled models such as those generated from volume datasets,... |

341 |
Multi-resolution 3D approximation for rendering complex scenes
- Rossignac, Borrel
- 1993
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Citation Context ...nar adjacent faces, followed by local re-triangulation. These rules are applied iteratively till they are no longer applicable. A somewhat different local approach is taken by Rossignac and Borrel in =-=[23]-=- where 1 vertices that are close to each other are clustered and a new vertex generated to represent them. The mesh is suitably updated to reflect this. Hoppe et al [18] proceed by iteratively optimiz... |

320 |
On the ratio of optimal integral and fractional covers
- Lovasz
- 1975
(Show Context)
Citation Context ...ind such a triangulation T 0 j , we try the same with the next triangle that covers the maximum number of triangles of M i\Gamma1 . 6.4 Estimating Solution Quality It has been shown in the literature =-=[20, 4]-=- that the greedy heuristic yields a solution to the set cover problem that is guaranteed to be within a factor of (1 + lg d) of the optimal, where d is the maximum number of elements in any set t j . ... |

275 | Hierarchical Z-buffer visibility
- Greene, Kass
- 1993
(Show Context)
Citation Context ...oring them in their original form as opposed to storing their approximations, amounts to wasting memory for storage as well as CPU cycles during processing, with disproportionately few or no benefits =-=[27, 26, 17, 19, 16]-=-. In this paper we discuss an approach for generating minimal approximations to a given polygonal representation of an object that are guaranteed not to deviate from the original by more than a user-s... |

191 | Almost optimal set covers in finite VC-dimension
- Brönnimann, Goodrich
- 1995
(Show Context)
Citation Context ... an approximation of size O(k o log k o ) in expected time O(k o n 1+ffi ) for any ffi ? 0 (the constant of proportionality depends on ffi, and tends to +1 as ffi tends to 0). Bronnimann and Goodrich =-=[3]-=- observed that a variant of Clarkson's algorithm yields a polynomial-time deterministic algorithm that computes an approximation of size O(k 0 ). Working with polyhedral terrains, Agarwal and Suri [1]... |

165 |
Continuous Shading of Curved Surfaces,"
- Gouraud
- 1971
(Show Context)
Citation Context ...the former, the latter should have unique normals at each vertex and edge that are equal to the normal of the sphere at those points. With this representation, shading models such as those of Gouraud =-=[15]-=- or Phong [22] give an approximately sphere-like shading to the octahedral approximation. In general, polygonal approximations to curved objects have unique vertex and edge normals to avoid the discon... |

109 |
Lipschitz optimization
- Hansen, Jaumard
- 1995
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100 | Surface approximation and geometric partitions
- Agarwal, Suri
- 1998
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Citation Context ...een presented by DeRose et al in [11]. In computational geometry, it has been shown that computing the minimal-facet ffl-approximation is NP-hard for both convex polytopes [9] and polyhedral terrains =-=[1]-=-. Thus, algorithms to these problems have evolved around finding polynomial-time approximations that are close to the optimal. Let k o be the size of a min-# approximation. An algorithm has been given... |

61 |
Algorithms for polytope covering and approximation
- Clarkson
- 1993
(Show Context)
Citation Context ...o be the size of a min-# approximation. An algorithm has been given in [21] for computing an fflapproximation of size O(k o log n) for convex polytopes. This has recently been improved by Clarkson in =-=[6]-=-; he proposes a randomized algorithm for computing an approximation of size O(k o log k o ) in expected time O(k o n 1+ffi ) for any ffi ? 0 (the constant of proportionality depends on ffi, and tends ... |

43 |
As adaptive subdivision method for surface-fitting from sampled data
- Schmitt, Barsky, et al.
(Show Context)
Citation Context ... number of vertices of the approximation A, the objective is to minimize the error, or the difference, between A and I. In computer graphics, work in the area of min-# approximations has been done by =-=[25]-=- and [10] where they adaptively subdivide a series of bicubic patches and polygons over a surface until they fit the data within the tolerance levels. In the second category, work has been done by Tur... |

38 |
Geometric simplification for indirect illumination calculations
- Rushmeier, Patterson, et al.
- 1993
(Show Context)
Citation Context ...a level-of-detail based rendering algorithm for providing desired frame update rates [5, 7, 8, 13, 2]. (b) Using low-detail approximations of objects for illumination algorithms, especially radiosity =-=[24]-=-. (c) Simplifying traditionally over-sampled models such as those generated from volume datasets, laser scanners, and satellites. Storing them in their original form as opposed to storing their approx... |

31 |
The complexity of minimum convex nested polyhedra
- Das, Joseph
- 1990
(Show Context)
Citation Context ...tion by using wavelets has been presented by DeRose et al in [11]. In computational geometry, it has been shown that computing the minimal-facet ffl-approximation is NP-hard for both convex polytopes =-=[9]-=- and polyhedral terrains [1]. Thus, algorithms to these problems have evolved around finding polynomial-time approximations that are close to the optimal. Let k o be the size of a min-# approximation.... |

29 |
Simplifiaction of objects rendered by polygonal approximations
- Zyda
- 1991
(Show Context)
Citation Context ...f vertices of the approximation A, the objective is to minimize the error, or the difference, between A and I. In computer graphics, work in the area of min-# approximations has been done by [25] and =-=[10]-=- where they adaptively subdivide a series of bicubic patches and polygons over a surface until they fit the data within the tolerance levels. In the second category, work has been done by Turk, Schroe... |

29 |
Separation and approximation of polyhedral surfaces
- Mitchell, Suri
- 1992
(Show Context)
Citation Context ...us, algorithms to these problems have evolved around finding polynomial-time approximations that are close to the optimal. Let k o be the size of a min-# approximation. An algorithm has been given in =-=[21]-=- for computing an fflapproximation of size O(k o log n) for convex polytopes. This has recently been improved by Clarkson in [6]; he proposes a randomized algorithm for computing an approximation of s... |

26 |
SuperFaces: Polyhedral approximation with bounded error
- KALVIN, TAYLOR
- 1994
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24 |
A more flexible image generation environment
- Crow
- 1982
(Show Context)
Citation Context ...given polygonal model. Multiresolution representations of an object find several uses in computer graphics: (a) In a level-of-detail based rendering algorithm for providing desired frame update rates =-=[5, 7, 8, 13, 2]-=-. (b) Using low-detail approximations of objects for illumination algorithms, especially radiosity [24]. (c) Simplifying traditionally over-sampled models such as those generated from volume datasets,... |

16 |
System Strategies to Optimize CIG Image Content
- Cosman, Schumacker
- 1981
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1 |
Polygonalization of implicit references
- Bloomenthal
- 1988
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