## Efficient edgebreaker for surfaces of arbitrary topology (2004)

Venue: | in Proceedings of 17th Brazilian Symposium on Computer Graphics and Image Processing |

Citations: | 7 - 2 self |

### BibTeX

@INPROCEEDINGS{Lewiner04efficientedgebreaker,

author = {Thomas Lewiner and Hélio Lopes and Jarek Rossignac and T. Lewiner H. Lopes},

title = {Efficient edgebreaker for surfaces of arbitrary topology},

booktitle = {in Proceedings of 17th Brazilian Symposium on Computer Graphics and Image Processing},

year = {2004},

pages = {218--225},

publisher = {IEEE}

}

### OpenURL

### Abstract

Abstract. The typical surfaces models handled by contemporary Computer Graphics applications have millions of triangles and numerous connected component, handles and boundaries. Edgebreaker and Spirale Reversi are examples of efficient schemes to compress and decompress their connectivity. A surprisingly simple linear–time implementation has been proposed for triangulated surfaces homeomorphic to a sphere and was subsequently extended to surfaces with handles. Here, we further extend its scope to surfaces with multiple components, handles, and multiple boundaries. The result is a simple and efficient compression/decompression solution for the broad class of orientable manifold surfaces.

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Citation Context ...er encodes the connectivity of the mesh by producing the clers string of symbols taken from the set C,L,E,R,S. A different approach encodes the connectivity of the mesh by the valence of its vertices =-=[17, 1]-=-. Valence–based compression approaches are very efficient, especially for regular meshes and it can also be extended to general polygonal meshes. Another approach [10] computes a uniquely defined trav... |

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Citation Context ...l. The corresponding work was published in the proceedings of the Sibgrapi 2004, pp. 218–225 IEEE Press, 2004.sT. Lewiner, H. Lopes, J. Rossignac and A. Vieira 2 1 Introduction The Edgebreaker scheme =-=[12]-=- encodes the connectivity of any manifold triangle mesh homeomorphic to a sphere with a guaranteed worst case code of 1.83 bits per triangle [6]. The Spirale Reversi algorithm [5] enhanced the Edgebre... |

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Citation Context ...ts simplicity, Edgebreaker is viewed as the emerging standard for 3D compression [15] and may provide an alternative for the current MPEG–4 standard which is based on the Topological Surgery approach =-=[16]-=-. Prior Works. There are many different compression schemes for triangular meshes. In order to encode efficiently their geometry, the best known methods traverse the cells of the mesh, and differ in t... |

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Citation Context ...nnectivity of the mesh. This simple algorithm has been extended to deal with surfaces with handles in [8]. Because of its simplicity, Edgebreaker is viewed as the emerging standard for 3D compression =-=[15]-=- and may provide an alternative for the current MPEG–4 standard which is based on the Topological Surgery approach [16]. Prior Works. There are many different compression schemes for triangular meshes... |

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Citation Context ...er encodes the connectivity of the mesh by producing the clers string of symbols taken from the set C,L,E,R,S. A different approach encodes the connectivity of the mesh by the valence of its vertices =-=[17, 1]-=-. Valence–based compression approaches are very efficient, especially for regular meshes and it can also be extended to general polygonal meshes. Another approach [10] computes a uniquely defined trav... |

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Citation Context ... set of adjacent edges of the boundary. Each boundary curve is closed. From now on, we denote by T (S), E(S) and V(S) the set of triangles, edges and vertices of S. Theorem 2 (Surface classification) =-=[2]-=- Any compact oriented connected surface S is homeomorphic to a sphere (g(S) = 0) or a connected sum of g(S) tori (g(S) > 0), in both cases with possibly some finite number b(S) ≥ 0 of open disks remov... |

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Citation Context ... and A. Vieira 2 1 Introduction The Edgebreaker scheme [12] encodes the connectivity of any manifold triangle mesh homeomorphic to a sphere with a guaranteed worst case code of 1.83 bits per triangle =-=[6]-=-. The Spirale Reversi algorithm [5] enhanced the Edgebreaker decompression worst–case complexity from O(n 2 ) to O(n). But the true value of Edgebreaker and Spirale Reversi lies in the efficiency and ... |

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Citation Context ... Edgebreaker scheme [12] encodes the connectivity of any manifold triangle mesh homeomorphic to a sphere with a guaranteed worst case code of 1.83 bits per triangle [6]. The Spirale Reversi algorithm =-=[5]-=- enhanced the Edgebreaker decompression worst–case complexity from O(n 2 ) to O(n). But the true value of Edgebreaker and Spirale Reversi lies in the efficiency and in the simplicity of their implemen... |

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Citation Context ...d the Edgebreaker decompression worst–case complexity from O(n 2 ) to O(n). But the true value of Edgebreaker and Spirale Reversi lies in the efficiency and in the simplicity of their implementations =-=[14]-=-, which is very concise. They can be simply implemented on a reduced topological data structure (the Corner–Table) which only uses two arrays of integers to represent the connectivity of the mesh. Thi... |

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Citation Context ...on doesn’t add a new symbol to the Edgebreaker original clers set. Surfaces with boundary are usually encoded by closing each boundary curve, using a dummy vertex to maintain the triangular structure =-=[4, 12]-=-. This is a very simple but expensive solution: first, it requires encoding each boundary edge with a useless triangle; second, it requires extra code to localize the dummy vertex; and third, it gives... |

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Citation Context ...y the valence of its vertices [17, 1]. Valence–based compression approaches are very efficient, especially for regular meshes and it can also be extended to general polygonal meshes. Another approach =-=[10]-=- computes a uniquely defined traversal for a given mesh, leading to asymptotically optimal results for the worst case. However, it is restricted to meshes without boundary and without handle. The Spir... |

24 |
N.: Range encoding: an algorithm for removing redundancy from a digitised message, in: Video & Data Recording conference
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Citation Context ...e graphs are encoded simultaneously, the way Θ(S) and Γ(S) are interlaced is obvious and the connectivity of S can be reconstructed. 9 Results We encoded the Edgebreaker symbols using a range encoder =-=[9, 11]-=-, which is a one–pass approximation of the entropy coder. This gives very good results for big meshes (on the contrary of the ‘sphere’ model of Table 1, or meshes with high auto–similarity (like the m... |

19 |
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Citation Context ...: Clearly Γ(S) is connected, although the formal proof can involve basic topological techniques as thickening [2] or cell collapse (the fundamental group is unchanged by removing a dual spanning tree =-=[3]-=-). By definition, Θ(S) is a tree with |T (S)| nodes, hence, it has |T (S)| − 1 lines. Also by definition, Γ(S) has |V(S)| nodes, and the number of lines of Θ(S) and Γ(S) together is |E(S)| . Hence, th... |

14 |
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Citation Context ... The Edgebreaker scheme has been enhanced and adapted from the Topological Surgery [16] to yield an efficient but initially restricted algorithm [12], and subsequently extended to more general meshes =-=[5, 7]-=-. Edgebreaker encodes the connectivity of the mesh by producing the clers string of symbols taken from the set C,L,E,R,S. A different approach encodes the connectivity of the mesh by the valence of it... |

3 |
Edgebreaker: a simple implementation for surfaces with handles
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(Show Context)
Citation Context ...gical data structure (the Corner–Table) which only uses two arrays of integers to represent the connectivity of the mesh. This simple algorithm has been extended to deal with surfaces with handles in =-=[8]-=-. Because of its simplicity, Edgebreaker is viewed as the emerging standard for 3D compression [15] and may provide an alternative for the current MPEG–4 standard which is based on the Topological Sur... |