Symmetry Hierarchy of Man‐Made Objects

@article{Wang2011SymmetryHO,
  title={Symmetry Hierarchy of Man‐Made Objects},
  author={Yanzhen Wang and Kai Xu and Jun Li and Hao Zhang and Ariel Shamir and Ligang Liu and Z. Cheng and Yueshan Xiong},
  journal={Computer Graphics Forum},
  year={2011},
  volume={30}
}
We introduce symmetry hierarchy of man‐made objects, a high‐level structural representation of a 3D model providing a symmetry‐induced, hierarchical organization of the model's constituent parts. Given an input mesh, we segment it into primitive parts and build an initial graph which encodes inter‐part symmetries and connectivity relations, as well as self‐symmetries in individual parts. The symmetry hierarchy is constructed from the initial graph via recursive graph contraction which either… Expand
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References

SHOWING 1-10 OF 41 REFERENCES
Structuring 3D Geometry based on Symmetry and Instancing Information
TLDR
This thesis proposes an original method to structure the geometry at the object level based on the information of symmetry and presents an approach to represent an unstructured 3D scene as a hierarchy of instances adapted to common tasks such as rendering or geometry editing. Expand
A connection between partial symmetry and inverse procedural modeling
In this paper, we address the problem of inverse procedural modeling: Given a piece of exemplar 3D geometry, we would like to find a set of rules that describe objects that are similar to theExpand
Folding meshes: hierarchical mesh segmentation based on planar symmetry
TLDR
An algorithm for detecting such symmetries and segmenting the mesh into the symmetric and remaining regions and an application of the method: the folding tree data structure, which encodes the non redundant regions of the original mesh as well as the reflection planes. Expand
Partial and approximate symmetry detection for 3D geometry
TLDR
A new algorithm is presented that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries, which captures important high-level information about the structure of a geometric model which enables a large set of further processing operations. Expand
Partial intrinsic reflectional symmetry of 3D shapes
TLDR
An algorithm to extract partial intrinsic reflectional symmetries (PIRS) of a 3D shape and how the extracted IRSA curves can be incorporated into a conventional mesh segmentation scheme so that the implied symmetry cues can be utilized to obtain more meaningful results are introduced. Expand
Partial intrinsic reflectional symmetry of 3D shapes
While many 3D objects exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized. Such partial symmetries are oftenExpand
Discovering structural regularity in 3D geometry
TLDR
An optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements is introduced and yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. Expand
Symmetry-Aware Mesh Processing
TLDR
A framework for mesh processing that includes steps for symmetrization and symmetric remeshing is investigated, used to enhance the symmetries of a mesh, to decompose a mesh into its symmetric parts and asymmetric residuals, and to establish correspondences between symmetric mesh features. Expand
Constructing Regularity Feature Trees for Solid Models
TLDR
This paper describes a systematic approach for finding regularity features based on recovering broken symmetries in the model, and the output is a tree ofRegularity features for subsequent use in regularity detection and selection. Expand
Symmetries of non-rigid shapes
TLDR
This paper poses the problem of finding intrinsic symmetries of non-rigid shapes and proposes an efficient method for their computation. Expand
...
1
2
3
4
5
...