Symmetry in 3D Geometry: Extraction and Applications
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Summary
This report surveys and classifies recent developments in symmetry detection, elucidating the key similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general.
- Type
- article
- Published
- 2013-09-01
- Cited by
- 387
- References
- 100
- Access
- Open access
- OpenAlex
- https://openalex.org/W1580065766
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:8738055
Keywords
Computer science, Variety (cybernetics), Computer graphics, Geometry processing, Symmetry (geometry)
References
- A Graph-Based Approach to Symmetry Detection
- Generalized intrinsic symmetry detection
- An Introduction to the Theory of Groups
- A probabilistic framework for partial intrinsic symmetries in geometric data
- Differential geometry of curves and surfaces
- Symmetry Detection Using Line Features
- Differential Geometry of Curves and Surfaces
- Shape Grammars and the Generative Specification of Painting and Sculpture
- Object modeling by registration of multiple range images
- Estimating curvatures and their derivatives on triangle meshes
- Factored Facade Acquisition using Symmetric Line Arrangements
- Finding Surface Correspondences Using Symmetry Axis Curves
- Consistent mesh partitioning and skeletonisation using the shape diameter function
- Partial intrinsic reflectional symmetry of 3D shapes
- Symmetry Hierarchy of Man‐Made Objects
- Non-local scan consolidation for 3D urban scenes
- Joint-aware manipulation of deformable models
- Interactive Facades Analysis and Synthesis of Semi‐Regular Facades
- Salient geometric features for partial shape matching and similarity
- Congruence, similarity, and symmetries of geometric objects
Cited by
- A comparative study of spectral embedding methods for triangle meshes
- State of the Art in Surface Reconstruction from Point Clouds
- Understanding the Structure of Large, Diverse Collections of Shapes
- Evaluating Structural Symmetry of Weighted Brain Networks via Graph Matching
- Quantifying 3D Shape Similarity Using Maps: Recent Trends, Applications and Perspectives
- Real-time continuous self-replicating details for shape deformation
- Applying geometric constraints for perfecting CAD models in reverse engineering
- Management and visualisation of non-linear history of polygonal 3D models
- Towards Automated 3D Reconstruction of Defective Cultural Heritage Objects
- Challenges in Procedural Modeling of Buildings
- Cross-class 3D object synthesis guided by reference examples
- Statistical part-based models for object detection in large 3D scans
- Instance-aware simplification of 3D polygonal meshes
- Computational Shape Understanding for 3D Reconstruction and Modeling
- Of assembling small sculptures and disassembling large geometry
- Constrained camera motion estimation and 3D reconstruction
- Efficient 3D reflection symmetry detection: A view-based approach
- SimSelect: Similarity‐based selection for 3D surfaces
- Efficient r-symmetry detection for triangle meshes
- 3D Timeline: Reverse engineering of a part‐based provenance from consecutive 3D models
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